Recent Advances in Compressed Sensing: Discrete Uncertainty Principles and Fast Hyperspectral Imaging

DTIC Science & Technology

2015-03-26

Fourier Analysis and Applications, vol. 14, pp. 838–858, 2008. 11. D. J. Cooke, “A discrete X - ray transform for chromotomographic hyperspectral imaging ... medical imaging , e.g., magnetic resonance imaging (MRI). Since the early 1980s, MRI has granted doctors the ability to distinguish between healthy tissue...i.e., at most K entries of x are nonzero. In many settings, this is a valid signal model; for example, JPEG2000 exploits the fact that natural images

Midwave Infrared Imaging Fourier Transform Spectrometry of Combustion Plumes

DTIC Science & Technology

2009-09-01

nonuniformity by spatially-smoothing the image cube. The algorithm was applied to a LWIR hyperspectral image of simultaneous release of CHF3 (trifluo...99 43. A series of LWIR thermal images of the explosive detonation release of MeS...Abbreviation Page IEDs Improvised Explosive Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 LWIR longwave infrared

Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

NASA Astrophysics Data System (ADS)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

Development of a Spectropolarimetric Remote Sensing Capability

DTIC Science & Technology

2013-03-01

34Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453-5469 (2006). [8] D. B. Chenault, "Infrared...Annen, “Hyperspectral IR polarimetry with application in demining and unexploded ordnance detection,” SPIE Vol. 3534 (1998). [30] Pesses, M... Polarimetry , Fourier Transform Spectrometer, DOLP, Spectropolarimetry, Stokes 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18

Physically motivated correlation formalism in hyperspectral imaging

NASA Astrophysics Data System (ADS)

Roy, Ankita; Rafert, J. Bruce

2004-05-01

Most remote sensing data-sets contain a limiting number of independent spatial and spectral measurements, beyond which no effective increase in information is achieved. This paper presents a Physically Motivated Correlation Formalism (PMCF) ,which places both Spatial and Spectral data on an equivalent mathematical footing in the context of a specific Kernel, such that, optimal combinations of independent data can be selected from the entire Hypercube via the method of "Correlation Moments". We present an experimental and computational analysis of Hyperspectral data sets using the Michigan Tech VFTHSI [Visible Fourier Transform Hyperspectral Imager] based on a Sagnac Interferometer, adjusted to obtain high SNR levels. The captured Signal Interferograms of different targets - aerial snaps of Houghton and lab-based data (white light , He-Ne laser , discharge tube sources) with the provision of customized scan of targets with the same exposures are processed using inverse imaging transformations and filtering techniques to obtain the Spectral profiles and generate Hypercubes to compute Spectral/Spatial/Cross Moments. PMCF answers the question of how optimally the entire hypercube should be sampled and finds how many spatial-spectral pixels are required for a particular target recognition.

Hyper-spectral Atmospheric Sounding. Appendixes 1

NASA Technical Reports Server (NTRS)

Smith, W. L.; Zhou, D. K.; Revercomb, H. E.; Huang, H. L.; Antonelli, P.; Mango, S. A.

2002-01-01

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) is the first hyper-spectral remote sounding system to be orbited aboard a geosynchronous satellite. The GETS is designed to obtain revolutionary observations of the four dimensional atmospheric temperature, moisture, and wind structure as well as the distribution of the atmospheric trace gases, CO and O3. Although GIFTS will not be orbited until 2006-2008, a glimpse at the its measurement capabilities has been obtained by analyzing data from the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Airborne Sounder Test-bed-Interferometer (NAST-I) and Aqua satellite Atmospheric Infrared Sounder (AIRS). In this paper we review the GIFTS experiment and empirically assess measurement expectations based on meteorological profiles retrieved from the NAST aircraft and Aqua satellite AIRS spectral radiances.

Recent applications of hyperspectral imaging in microbiology.

PubMed

Gowen, Aoife A; Feng, Yaoze; Gaston, Edurne; Valdramidis, Vasilis

2015-05-01

Hyperspectral chemical imaging (HSI) is a broad term encompassing spatially resolved spectral data obtained through a variety of modalities (e.g. Raman scattering, Fourier transform infrared microscopy, fluorescence and near-infrared chemical imaging). It goes beyond the capabilities of conventional imaging and spectroscopy by obtaining spatially resolved spectra from objects at spatial resolutions varying from the level of single cells up to macroscopic objects (e.g. foods). In tandem with recent developments in instrumentation and sampling protocols, applications of HSI in microbiology have increased rapidly. This article gives a brief overview of the fundamentals of HSI and a comprehensive review of applications of HSI in microbiology over the past 10 years. Technical challenges and future perspectives for these techniques are also discussed. Copyright © 2015 Elsevier B.V. All rights reserved.

ORBS: A reduction software for SITELLE and SpiOMM data

NASA Astrophysics Data System (ADS)

Martin, Thomas

2014-09-01

ORBS merges, corrects, transforms and calibrates interferometric data cubes and produces a spectral cube of the observed region for analysis. It is a fully automatic data reduction software for use with SITELLE (installed at the Canada-France-Hawaii Telescope) and SpIOMM (a prototype attached to the Observatoire du Mont Mégantic); these imaging Fourier transform spectrometers obtain a hyperspectral data cube which samples a 12 arc-minutes field of view into 4 millions of visible spectra. ORBS is highly parallelized; its core classes (ORB) have been designed to be used in a suite of softwares for data analysis (ORCS and OACS), data simulation (ORUS) and data acquisition (IRIS).

Nonnegative Matrix Factorization for Efficient Hyperspectral Image Projection

NASA Technical Reports Server (NTRS)

Iacchetta, Alexander S.; Fienup, James R.; Leisawitz, David T.; Bolcar, Matthew R.

2015-01-01

Hyperspectral imaging for remote sensing has prompted development of hyperspectral image projectors that can be used to characterize hyperspectral imaging cameras and techniques in the lab. One such emerging astronomical hyperspectral imaging technique is wide-field double-Fourier interferometry. NASA's current, state-of-the-art, Wide-field Imaging Interferometry Testbed (WIIT) uses a Calibrated Hyperspectral Image Projector (CHIP) to generate test scenes and provide a more complete understanding of wide-field double-Fourier interferometry. Given enough time, the CHIP is capable of projecting scenes with astronomically realistic spatial and spectral complexity. However, this would require a very lengthy data collection process. For accurate but time-efficient projection of complicated hyperspectral images with the CHIP, the field must be decomposed both spectrally and spatially in a way that provides a favorable trade-off between accurately projecting the hyperspectral image and the time required for data collection. We apply nonnegative matrix factorization (NMF) to decompose hyperspectral astronomical datacubes into eigenspectra and eigenimages that allow time-efficient projection with the CHIP. Included is a brief analysis of NMF parameters that affect accuracy, including the number of eigenspectra and eigenimages used to approximate the hyperspectral image to be projected. For the chosen field, the normalized mean squared synthesis error is under 0.01 with just 8 eigenspectra. NMF of hyperspectral astronomical fields better utilizes the CHIP's capabilities, providing time-efficient and accurate representations of astronomical scenes to be imaged with the WIIT.

Unmixing the Materials and Mechanics Contributions in Non-resolved Object Signatures

DTIC Science & Technology

2008-09-01

abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier analysis of temporal variation of material abundance provides...factorization technique to extract the temporal variation of material abundances from hyperspectral or multi-spectral time - resolved signatures. A Fourier...approximately one hundred wavelengths in the visible spectrum. The frame rate for the instrument was not large enough to collect time resolved data. However

3D-FFT for Signature Detection in LWIR Images

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

Medvick, Patricia A.; Lind, Michael A.; Mackey, Patrick S.

Improvements in analysis detection exploitation are possible by applying whitened matched filtering within the Fourier domain to hyperspectral data cubes. We describe an implementation of a Three Dimensional Fast Fourier Transform Whitened Matched Filter (3DFFTMF) approach and, using several example sets of Long Wave Infra Red (LWIR) data cubes, compare the results with those from standard Whitened Matched Filter (WMF) techniques. Since the variability in shape of gaseous plumes precludes the use of spatial conformation in the matched filtering, the 3DFFTMF results were similar to those of two other WMF methods. Including a spatial low-pass filter within the Fourier spacemore » can improve signal to noise ratios and therefore improve detection limit by facilitating the mitigation of high frequency clutter. The improvement only occurs if the low-pass filter diameter is smaller than the plume diameter.« less

Demonstration of the Wide-Field Imaging Interferometer Testbed Using a Calibrated Hyperspectral Image Projector

NASA Technical Reports Server (NTRS)

Bolcar, Matthew R.; Leisawitz, David; Maher, Steve; Rinehart, Stephen

2012-01-01

The Wide-field Imaging Interferometer testbed (WIIT) at NASA's Goddard Space Flight Center uses a dual-Michelson interferometric technique. The WIIT combines stellar interferometry with Fourier-transform interferometry to produce high-resolution spatial-spectral data over a large field-of-view. This combined technique could be employed on future NASA missions such as the Space Infrared Interferometric Telescope (SPIRIT) and the Sub-millimeter Probe of the Evolution of Cosmic Structure (SPECS). While both SPIRIT and SPECS would operate at far-infrared wavelengths, the WIIT demonstrates the dual-interferometry technique at visible wavelengths. The WIIT will produce hyperspectral image data, so a true hyperspectral object is necessary. A calibrated hyperspectral image projector (CHIP) has been constructed to provide such an object. The CHIP uses Digital Light Processing (DLP) technology to produce customized, spectrally-diverse scenes. CHIP scenes will have approximately 1.6-micron spatial resolution and the capability of . producing arbitrary spectra in the band between 380 nm and 1.6 microns, with approximately 5-nm spectral resolution. Each pixel in the scene can take on a unique spectrum. Spectral calibration is achieved with an onboard fiber-coupled spectrometer. In this paper we describe the operation of the CHIP. Results from the WIIT observations of CHIP scenes will also be presented.

Design and Performance of the Hyper-Cam, an Infrared Hyperspectral Imaging Sensor

DTIC Science & Technology

2009-10-01

helps to reduce the noise level, since the FIRST is shot noise limited . 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 200 250 300 350 ab s( O...performed using a Fourier-Transform Spectrometer (FTS). It uses a 320x256 LWIR PV- MCT focal plane array detector that can be windowed and formatted...cooled down to 68 K. The offset is very low (~215 K), which indicates that the shot noise coming from the instrument radiance is minimized. This

Filtering high resolution hyperspectral imagery and analyzing it for quantification of water quality parameters and aquatic vegetation

NASA Astrophysics Data System (ADS)

Pande-Chhetri, Roshan

High resolution hyperspectral imagery (airborne or ground-based) is gaining momentum as a useful analytical tool in various fields including agriculture and aquatic systems. These images are often contaminated with stripes and noise resulting in lower signal-to-noise ratio, especially in aquatic regions where signal is naturally low. This research investigates effective methods for filtering high spatial resolution hyperspectral imagery and use of the imagery in water quality parameter estimation and aquatic vegetation classification. The striping pattern of the hyperspectral imagery is non-parametric and difficult to filter. In this research, a de-striping algorithm based on wavelet analysis and adaptive Fourier domain normalization was examined. The result of this algorithm was found superior to other available algorithms and yielded highest Peak Signal to Noise Ratio improvement. The algorithm was implemented on individual image bands and on selected bands of the Maximum Noise Fraction (MNF) transformed images. The results showed that image filtering in the MNF domain was efficient and produced best results. The study investigated methods of analyzing hyperspectral imagery to estimate water quality parameters and to map aquatic vegetation in case-2 waters. Ground-based hyperspectral imagery was analyzed to determine chlorophyll-a (Chl-a) concentrations in aquaculture ponds. Two-band and three-band indices were implemented and the effect of using submerged reflectance targets was evaluated. Laboratory measured values were found to be in strong correlation with two-band and three-band spectral indices computed from the hyperspectral image. Coefficients of determination (R2) values were found to be 0.833 and 0.862 without submerged targets and stronger values of 0.975 and 0.982 were obtained using submerged targets. Airborne hyperspectral images were used to detect and classify aquatic vegetation in a black river estuarine system. Image normalization for water surface reflectance and water depths was conducted and non-parametric classifiers such as ANN, SVM and SAM were tested and compared. Quality assessment indicated better classification and detection when non-parametric classifiers were applied to normalized or depth invariant transform images. Best classification accuracy of 73% was achieved when ANN is applied on normalized image and best detection accuracy of around 92% was obtained when SVM or SAM was applied on depth invariant images.

First results of ground-based LWIR hyperspectral imaging remote gas detection

NASA Astrophysics Data System (ADS)

Zheng, Wei-jian; Lei, Zheng-gang; Yu, Chun-chao; Wang, Hai-yang; Fu, Yan-peng; Liao, Ning-fang; Su, Jun-hong

2014-11-01

The new progress of ground-based long-wave infrared remote sensing is presented. The LWIR hyperspectral imaging by using the windowing spatial and temporal modulation Fourier spectroscopy, and the results of outdoor ether gas detection, verify the features of LWIR hyperspectral imaging remote sensing and technical approach. It provides a new technical means for ground-based gas remote sensing.

All-optical framing photography based on hyperspectral imaging method

NASA Astrophysics Data System (ADS)

Liu, Shouxian; Li, Yu; Li, Zeren; Chen, Guanghua; Peng, Qixian; Lei, Jiangbo; Liu, Jun; Yuan, Shuyun

2017-02-01

We propose and experimentally demonstrate a new all optical-framing photography that uses hyperspectral imaging methods to record a chirped pulse's temporal-spatial information. This proposed method consists of three parts: (1) a chirped laser pulse encodes temporal phenomena onto wavelengths; (2) a lenslet array generates a series of integral pupil images;(3) a dispersive device disperses the integral images at void space of image sensor. Compared with Ultrafast All-Optical Framing Technology(Daniel Frayer,2013,2014) and Sequentially Time All-Optical Mapping Photography( Nakagawa 2014, 2015), our method is convenient to adjust the temporal resolution and to flexibly increase the numbers of frames. Theoretically, the temporal resolution of our scheme is limited by the amount of dispersion that is added to a Fourier transform limited femtosecond laser pulse. Correspondingly, the optimal number of frames is decided by the ratio of the observational time window to the temporal resolution, and the effective pixels of each frame are mostly limited by the dimensions M×N of the lenslet array. For example, if a 40fs Fourier transform limited femtosecond pulse is stretched to 10ps, a CCD camera with 2048×3072 pixels can record 15 framing images with temporal resolution of 650fs and image size of 100×100 pixels. As spectrometer structure, our recording part has another advantage that not only amplitude images but also frequency domain interferograms can be imaged. Therefore, it is comparatively easy to capture fast dynamics in the refractive index change of materials. A further dynamic experiment is being conducted.

Fourier Transform Infrared (FT-IR) and Laser Ablation Inductively Coupled Plasma-Mass Spectrometry (LA-ICP-MS) Imaging of Cerebral Ischemia: Combined Analysis of Rat Brain Thin Cuts Toward Improved Tissue Classification.

PubMed

Balbekova, Anna; Lohninger, Hans; van Tilborg, Geralda A F; Dijkhuizen, Rick M; Bonta, Maximilian; Limbeck, Andreas; Lendl, Bernhard; Al-Saad, Khalid A; Ali, Mohamed; Celikic, Minja; Ofner, Johannes

2018-02-01

Microspectroscopic techniques are widely used to complement histological studies. Due to recent developments in the field of chemical imaging, combined chemical analysis has become attractive. This technique facilitates a deepened analysis compared to single techniques or side-by-side analysis. In this study, rat brains harvested one week after induction of photothrombotic stroke were investigated. Adjacent thin cuts from rats' brains were imaged using Fourier transform infrared (FT-IR) microspectroscopy and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The LA-ICP-MS data were normalized using an internal standard (a thin gold layer). The acquired hyperspectral data cubes were fused and subjected to multivariate analysis. Brain regions affected by stroke as well as unaffected gray and white matter were identified and classified using a model based on either partial least squares discriminant analysis (PLS-DA) or random decision forest (RDF) algorithms. The RDF algorithm demonstrated the best results for classification. Improved classification was observed in the case of fused data in comparison to individual data sets (either FT-IR or LA-ICP-MS). Variable importance analysis demonstrated that both molecular and elemental content contribute to the improved RDF classification. Univariate spectral analysis identified biochemical properties of the assigned tissue types. Classification of multisensor hyperspectral data sets using an RDF algorithm allows access to a novel and in-depth understanding of biochemical processes and solid chemical allocation of different brain regions.

LWIR hyperspectral imaging application and detection of chemical precursors

NASA Astrophysics Data System (ADS)

Lavoie, Hugo; Thériault, Jean-Marc; Bouffard, François; Puckrin, Eldon; Dubé, Denis

2012-10-01

Detection and identification of Toxic industrial chemicals (TICs) represent a major challenge to protect and sustain first responder and public security. In this context, passive Hyperspectral Imaging (HSI) is a promising technology for the standoff detection and identification of chemical vapors emanating from a distant location. To investigate this method, the Department of National Defense and Public Safety Canada have mandated Defense Research and Development Canada (DRDC) - Valcartier to develop and test Very Long Wave Infrared (VLWIR) HSI sensors for standoff detection. The initial effort was focused to address the standoff detection and identification of toxic industrial chemicals (TICs), surrogates and precursors. Sensors such as the Improved Compact ATmospheric Sounding Interferometer (iCATSI) and the Multi-option Differential Detection and Imaging Fourier Spectrometer (MoDDIFS) were developed for this application. This paper presents the sensor developments and preliminary results of standoff detection and identification of TICs and precursors. The iCATSI and MoDDIFS sensors are based on the optical differential Fourier-transform infrared (FTIR) radiometric technology and are able to detect, spectrally resolve and identify small leak at ranges in excess of 1 km. Results from a series of trials in asymmetric threat type scenarios are reported. These results serve to establish the potential of passive standoff HSI detection of TICs, precursors and surrogates.

Detection of chemical pollutants by passive LWIR hyperspectral imaging

NASA Astrophysics Data System (ADS)

Lavoie, Hugo; Thériault, Jean-Marc; Bouffard, François; Puckrin, Eldon; Dubé, Denis

2012-09-01

Toxic industrial chemicals (TICs) represent a major threat to public health and security. Their detection constitutes a real challenge to security and first responder's communities. One promising detection method is based on the passive standoff identification of chemical vapors emanating from the laboratory under surveillance. To investigate this method, the Department of National Defense and Public Safety Canada have mandated Defense Research and Development Canada (DRDC) - Valcartier to develop and test passive Long Wave Infrared (LWIR) hyperspectral imaging (HSI) sensors for standoff detection. The initial effort was focused to address the standoff detection and identification of toxic industrial chemicals (TICs) and precursors. Sensors such as the Multi-option Differential Detection and Imaging Fourier Spectrometer (MoDDIFS) and the Improved Compact ATmospheric Sounding Interferometer (iCATSI) were developed for this application. This paper describes the sensor developments and presents initial results of standoff detection and identification of TICs and precursors. The standoff sensors are based on the differential Fourier-transform infrared (FTIR) radiometric technology and are able to detect, spectrally resolve and identify small leak plumes at ranges in excess of 1 km. Results from a series of trials in asymmetric threat type scenarios will be presented. These results will serve to establish the potential of the method for standoff detection of TICs precursors and surrogates.

Analysis for signal-to-noise ratio of hyper-spectral imaging FTIR interferometer

NASA Astrophysics Data System (ADS)

Li, Xun-niu; Zheng, Wei-jian; Lei, Zheng-gang; Wang, Hai-yang; Fu, Yan-peng

2013-08-01

Signal-to-noise Ratio of hyper-spectral imaging FTIR interferometer system plays a decisive role on the performance of the instrument. It is necessary to analyze them in the development process. Based on the simplified target/background model, the energy transfer model of the LWIR hyper-spectral imaging interferometer has been discussed. The noise equivalent spectral radiance (NESR) and its influencing factors of the interferometer system was analyzed, and the signal-to-noise（SNR） was calculated by using the properties of NESR and incident radiance. In a typical application environment, using standard atmospheric model of USA(1976 COESA) as a background, and set a reasonable target/background temperature difference, and take Michelson spatial modulation Fourier Transform interferometer as an example, the paper had calculated the NESR and the SNR of the interferometer system which using the commercially LWIR cooled FPA and UFPA detector. The system noise sources of the instrument were also analyzed in the paper. The results of those analyses can be used to optimize and pre-estimate the performance of the interferometer system, and analysis the applicable conditions of use different detectors. It has important guiding significance for the LWIR interferometer spectrometer design.

Hyperspectral imager for components identification in the atmosphere

NASA Astrophysics Data System (ADS)

Dewandel, Jean-Luc; Beghuin, Didier; Dubois, Xavier; Antoine, Philippe

2017-11-01

Several applications require the identification of chemical elements during re-entry of material in the atmosphere. The materials can be from human origin or meteorites. The Automated Transfer Vehicle (ATV) re-entry has been filmed with conventional camera from airborne manual operation. In order to permit the identification of the separate elements from their glow, spectral analysis needs to be added to the video data. In a LET-SME contract with ESA, Lambda-X has built a Fourier Transform Imaging Spectrometer to permit, in a future work, to bring the technology to the readiness level required for the application. In this paper, the principles of the Fourier Transform Imaging spectroscopy are recalled, the different interferometers suitable for supporting the technique are reviewed and the selection process is explained. The final selection of the interferometer corresponds to a birefringent prism based common path shear interferometer. The design of the breadboard and its performances are presented in terms of spatial resolution, aperture, and spectral resolution. A discussion is open regarding perspective of the technique for other remote sensing applications compared to more usual push broom configurations.

Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability

NASA Technical Reports Server (NTRS)

Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.

2007-01-01

The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

Ground-Based Measurement Experiment and First Results with Geosynchronous-Imaging Fourier Transform Spectrometer Engineering Demonstration Unit

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Smith, William L.; Bingham, Gail E.; Huppi, Ronald J.; Revercomb, Henry E.; Zollinger, Lori J.; Larar, Allen M.; Liu, Xu; Tansock, Joseph J.; Reisse, Robert A.;

Wavelet compression techniques for hyperspectral data

NASA Technical Reports Server (NTRS)

Evans, Bruce; Ringer, Brian; Yeates, Mathew

1994-01-01

Hyperspectral sensors are electro-optic sensors which typically operate in visible and near infrared bands. Their characteristic property is the ability to resolve a relatively large number (i.e., tens to hundreds) of contiguous spectral bands to produce a detailed profile of the electromagnetic spectrum. In contrast, multispectral sensors measure relatively few non-contiguous spectral bands. Like multispectral sensors, hyperspectral sensors are often also imaging sensors, measuring spectra over an array of spatial resolution cells. The data produced may thus be viewed as a three dimensional array of samples in which two dimensions correspond to spatial position and the third to wavelength. Because they multiply the already large storage/transmission bandwidth requirements of conventional digital images, hyperspectral sensors generate formidable torrents of data. Their fine spectral resolution typically results in high redundancy in the spectral dimension, so that hyperspectral data sets are excellent candidates for compression. Although there have been a number of studies of compression algorithms for multispectral data, we are not aware of any published results for hyperspectral data. Three algorithms for hyperspectral data compression are compared. They were selected as representatives of three major approaches for extending conventional lossy image compression techniques to hyperspectral data. The simplest approach treats the data as an ensemble of images and compresses each image independently, ignoring the correlation between spectral bands. The second approach transforms the data to decorrelate the spectral bands, and then compresses the transformed data as a set of independent images. The third approach directly generalizes two-dimensional transform coding by applying a three-dimensional transform as part of the usual transform-quantize-entropy code procedure. The algorithms studied all use the discrete wavelet transform. In the first two cases, a wavelet transform coder was used for the two-dimensional compression. The third case used a three dimensional extension of this same algorithm.

A methodological approach to study the stability of selected watercolours for painting reintegration, through reflectance spectrophotometry, Fourier transform infrared spectroscopy and hyperspectral imaging

NASA Astrophysics Data System (ADS)

Pelosi, Claudia; Capobianco, Giuseppe; Agresti, Giorgia; Bonifazi, Giuseppe; Morresi, Fabio; Rossi, Sara; Santamaria, Ulderico; Serranti, Silvia

2018-06-01

The aim of this work is to investigate the stability to simulated solar radiation of some paintings samples through a new methodological approach adopting non-invasive spectroscopic techniques. In particular, commercial watercolours and iron oxide based pigments were used, these last ones being prepared for the experimental by gum Arabic in order to propose a possible substitute for traditional reintegration materials. Reflectance spectrophotometry in the visible range and Hyperspectral Imaging in the short wave infrared were chosen as non-invasive techniques for evaluation the stability to irradiation of the chosen pigments. These were studied before and after artificial ageing procedure performed in Solar Box chamber under controlled conditions. Data were treated and elaborated in order to evaluate the sensitivity of the chosen techniques in identifying the variations on paint layers, induced by photo-degradation, before they could be observed by eye. Furthermore a supervised classification method for monitoring the painted surface changes adopting a multivariate approach was successfully applied.

Recent Developments on Airborne Forward Looking Interferometer for the Detection of Wake Vortices

NASA Technical Reports Server (NTRS)

Daniels, Taumi S.; Smith, William L.; Kirev, Stanislav

2012-01-01

A goal of these studies was development of the measurement methods and algorithms necessary to detect wake vortex hazards in real time from either an aircraft or ground-based hyperspectral Fourier Transform Spectrometer (FTS). This paper provides an update on research to model FTS detection of wake vortices. The Terminal Area Simulation System (TASS) was used to generate wake vortex fields of 3-D winds, temperature, and absolute humidity. These fields were input to the Line by Line Radiative Transfer Model (LBLRTM), a hyperspectral radiance model in the infrared, employed for the FTS numerical modeling. An initial set of cases has been analyzed to identify a wake vortex IR signature and signature sensitivities to various state variables. Results from the numerical modeling case studies will be presented. Preliminary results indicated that an imaging IR instrument sensitive to six narrow bands within the 670 to 3150 per centimeter spectral region would be sufficient for wake vortex detection. Noise floor estimates for a recommended instrument are a current research topic.

Isograde mapping and mineral identification on the island of Naxos, Greece, using DAIS 7915 hyperspectral data

NASA Astrophysics Data System (ADS)

Echtler, Helmut; Segl, Karl; Dickerhof, Corinna; Chabrillat, Sabine; Kaufmann, Hermann J.

2003-03-01

The ESF-LSF 1997 flight campaign conducted by the German Aerospace Center (DLR) recorded several transects across the island of Naxos using the airborne hyperspectral scanner DAIS. The geological targets cover all major litho-tectonic units of a metamorphic dome with the transition of metamorphic zonations from the outer meta-sedimentary greenschist envelope to the gneissic amphibolite facies and migmatitic core. Mineral identification of alternating marble-dolomite sequences and interlayered schists bearing muscovite and biotite has been accomplished using the airborne hyperspectral DAIS 7915 sensor. Data have been noise filtered based on maximum noise fraction (MNF) and fast Fourier transform (FFT) and converted from radiance to reflectance. For mineral identification, constrained linear spectral unmixing and spectral angle mapper (SAM) algorithms were tested. Due to their unsatisfying results a new approach was developed which consists of a linear mixture modeling and spectral feature fitting. This approach provides more detailed and accurate information. Results are discussed in comparison with detailed geological mapping and additional information. Calcites are clearly separated from dolomites as well as the mica-schist sequences by a good resolution of the mineral muscovite. Thereon an outstanding result represents the very good resolution of the chlorite/mica (muscovite, biotite)-transition defining a metamorphic isograde.

Comparison of hyperspectral transformation accuracies of multispectral Landsat TM, ETM+, OLI and EO-1 ALI images for detecting minerals in a geothermal prospect area

NASA Astrophysics Data System (ADS)

Hoang, Nguyen Tien; Koike, Katsuaki

2018-03-01

Hyperspectral remote sensing generally provides more detailed spectral information and greater accuracy than multispectral remote sensing for identification of surface materials. However, there have been no hyperspectral imagers that cover the entire Earth surface. This lack points to a need for producing pseudo-hyperspectral imagery by hyperspectral transformation from multispectral images. We have recently developed such a method, a Pseudo-Hyperspectral Image Transformation Algorithm (PHITA), which transforms Landsat 7 ETM+ images into pseudo-EO-1 Hyperion images using multiple linear regression models of ETM+ and Hyperion band reflectance data. This study extends the PHITA to transform TM, OLI, and EO-1 ALI sensor images into pseudo-Hyperion images. By choosing a part of the Fish Lake Valley geothermal prospect area in the western United States for study, the pseudo-Hyperion images produced from the TM, ETM+, OLI, and ALI images by PHITA were confirmed to be applicable to mineral mapping. Using a reference map as the truth, three main minerals (muscovite and chlorite mixture, opal, and calcite) were identified with high overall accuracies from the pseudo-images (> 95% and > 42% for excluding and including unclassified pixels, respectively). The highest accuracy was obtained from the ALI image, followed by ETM+, TM, and OLI images in descending order. The TM, OLI, and ALI images can be alternatives to ETM+ imagery for the hyperspectral transformation that aids the production of pseudo-Hyperion images for areas without high-quality ETM+ images because of scan line corrector failure, and for long-term global monitoring of land surfaces.

Fukunaga-Koontz transform based dimensionality reduction for hyperspectral imagery

NASA Astrophysics Data System (ADS)

Ochilov, S.; Alam, M. S.; Bal, A.

2006-05-01

Fukunaga-Koontz Transform based technique offers some attractive properties for desired class oriented dimensionality reduction in hyperspectral imagery. In FKT, feature selection is performed by transforming into a new space where feature classes have complimentary eigenvectors. Dimensionality reduction technique based on these complimentary eigenvector analysis can be described under two classes, desired class and background clutter, such that each basis function best represent one class while carrying the least amount of information from the second class. By selecting a few eigenvectors which are most relevant to desired class, one can reduce the dimension of hyperspectral cube. Since the FKT based technique reduces data size, it provides significant advantages for near real time detection applications in hyperspectral imagery. Furthermore, the eigenvector selection approach significantly reduces computation burden via the dimensionality reduction processes. The performance of the proposed dimensionality reduction algorithm has been tested using real-world hyperspectral dataset.

A methodological approach to study the stability of selected watercolours for painting reintegration, through reflectance spectrophotometry, Fourier transform infrared spectroscopy and hyperspectral imaging.

PubMed

Pelosi, Claudia; Capobianco, Giuseppe; Agresti, Giorgia; Bonifazi, Giuseppe; Morresi, Fabio; Rossi, Sara; Santamaria, Ulderico; Serranti, Silvia

2018-06-05

The aim of this work is to investigate the stability to simulated solar radiation of some paintings samples through a new methodological approach adopting non-invasive spectroscopic techniques. In particular, commercial watercolours and iron oxide based pigments were used, these last ones being prepared for the experimental by gum Arabic in order to propose a possible substitute for traditional reintegration materials. Reflectance spectrophotometry in the visible range and Hyperspectral Imaging in the short wave infrared were chosen as non-invasive techniques for evaluation the stability to irradiation of the chosen pigments. These were studied before and after artificial ageing procedure performed in Solar Box chamber under controlled conditions. Data were treated and elaborated in order to evaluate the sensitivity of the chosen techniques in identifying the variations on paint layers, induced by photo-degradation, before they could be observed by eye. Furthermore a supervised classification method for monitoring the painted surface changes adopting a multivariate approach was successfully applied. Copyright © 2018 Elsevier B.V. All rights reserved.

Pesticide residue quantification analysis by hyperspectral imaging sensors

NASA Astrophysics Data System (ADS)

Liao, Yuan-Hsun; Lo, Wei-Sheng; Guo, Horng-Yuh; Kao, Ching-Hua; Chou, Tau-Meu; Chen, Junne-Jih; Wen, Chia-Hsien; Lin, Chinsu; Chen, Hsian-Min; Ouyang, Yen-Chieh; Wu, Chao-Cheng; Chen, Shih-Yu; Chang, Chein-I.

2015-05-01

Pesticide residue detection in agriculture crops is a challenging issue and is even more difficult to quantify pesticide residue resident in agriculture produces and fruits. This paper conducts a series of base-line experiments which are particularly designed for three specific pesticides commonly used in Taiwan. The materials used for experiments are single leaves of vegetable produces which are being contaminated by various amount of concentration of pesticides. Two sensors are used to collected data. One is Fourier Transform Infrared (FTIR) spectroscopy. The other is a hyperspectral sensor, called Geophysical and Environmental Research (GER) 2600 spectroradiometer which is a batteryoperated field portable spectroradiometer with full real-time data acquisition from 350 nm to 2500 nm. In order to quantify data with different levels of pesticide residue concentration, several measures for spectral discrimination are developed. Mores specifically, new measures for calculating relative power between two sensors are particularly designed to be able to evaluate effectiveness of each of sensors in quantifying the used pesticide residues. The experimental results show that the GER is a better sensor than FTIR in the sense of pesticide residue quantification.

Rapidly updated hyperspectral sounding and imaging data for severe storm prediction

NASA Astrophysics Data System (ADS)

Bingham, Gail; Jensen, Scott; Elwell, John; Cardon, Joel; Crain, David; Huang, Hung-Lung (Allen); Smith, William L.; Revercomb, Hank E.; Huppi, Ronald J.

2013-09-01

Several studies have shown that a geostationary hyperspectral imager/sounder can provide the most significant value increase in short term, regional numerical prediction weather models over a range of other options. In 1998, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) proposal was selected by NASA as the New Millennium Earth Observation 3 program over several other geostationary instrument development proposals. After the EO3 GIFTS flight demonstration program was changed to an Engineering Development Unit (EDU) due to funding limitations by one of the partners, the EDU was subjected to flight-like thermal vacuum calibration and testing and successfully validated the breakthrough technologies needed to make a successful observatory. After several government stops and starts, only EUMETSAT's Meteosat Third Generation (MTG-S) sounder is in operational development. Recently, a commercial partnership has been formed to fill the significant data gap. AsiaSat has partnered with GeoMetWatch (GMW)1 to fund the development and launch of the Sounding and Tracking Observatory for Regional Meteorology (STORMTM) sensor, a derivative of the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) EDU that was designed, built, and tested by Utah State University (USU). STORMTM combines advanced technologies to observe surface thermal properties, atmospheric weather, and chemistry variables in four dimensions to provide high vertical resolution temperature and moisture sounding information, with the fourth dimension (time) provided by the geosynchronous satellite platform ability to measure a location as often as desired. STORMTM will enhance the polar orbiting imaging and sounding measurements by providing: (1) a direct measure of moisture flux and altitude-resolved water vapor and cloud tracer winds throughout the troposphere, (2) an observation of the time varying atmospheric thermodynamics associated with storm system development, and (3) the transport of tropospheric pollutant gases. The AsiaSat/GMW partnership will host the first STORMTM sensor on their AsiaSat 9 telecommunications satellite at 122 E over the Asia Pacific area. GMW's business plan is to sell the unique STORM data and data products to countries and companies in the satellite coverage area. GMW plans to place 6 STORMTM sensors on geostationary telecommunications satellites to provide global hyperspectral sounding and imaging data. Utah State University's Advanced Weather Systems Laboratory (AWS) will build the sensors for GMW.

Airborne infrared-hyperspectral mapping for detection of gaseous and solid targets

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Farley, V.; Lagueux, P.; Marcotte, F.; Chamberland, M.

2010-04-01

Airborne 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. The Telops Hyper-Cam is a rugged and compact infrared hyperspectral imager based on the Fourier-transform technology. It 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. The technology offers fine spectral resolution (up to 0.25 cm-1) and high accuracy radiometric calibration (better than 1 degree Celsius). Furthermore, the spectral resolution, spatial resolution, swath width, integration time and sensitivity are all flexible parameters that can be selected and optimized to best address the specific objectives of each mission. The system performance and a few measurements have been presented in previous publications. This paper focuses on analyzing additional measurements in which detection of fertilizer and Freon gas has been demonstrated.

Characterization of methane emissions in Los Angeles with airborne hyperspectral imaging

NASA Astrophysics Data System (ADS)

Saad, K.; Tratt, D. M.; Buckland, K. N.; Roehl, C. M.; Wennberg, P. O.; Wunch, D.

2017-12-01

As urban areas develop regulations to limit atmospheric methane (CH4), accurate quantification of anthropogenic emissions will be critical for program development and evaluation. However, relating emissions derived from process-level metadata to those determined from assimilating atmospheric observations of CH4 concentrations into models is particularly difficult. Non-methane hydrocarbons (NMHCs) can help differentiate between thermogenic and biogenic CH4 emissions, as they are primarily co-emitted with the former; however, these trace gases are subject to the same limitations as CH4. Remotely-sensed hyperspectral imaging bridges these approaches by measuring emissions plumes directly with spatial coverage on the order of 10 km2 min-1. We identify the sources of and evaluate emissions plumes measured by airborne infrared hyperspectral imagers flown over the Los Angeles (LA) metropolitan area, which encompasses various CH4 sources, including petroleum and natural gas wells and facilities. We quantify total CH4 and NMHC emissions, as well as their relative column densities, at the point-source level to create fingerprints of source types. We aggregate these analyses to estimate the range of variability in chemical composition across source types. These CH4 and NMHC emissions factors are additionally compared to their tropospheric column abundances measured by the Total Carbon Column Observing Network (TCCON) Pasadena Fourier transform infrared spectrometer, which provides a footprint for the LA basin.

ORBS, ORCS, OACS, a Software Suite for Data Reduction and Analysis of the Hyperspectral Imagers SITELLE and SpIOMM

NASA Astrophysics Data System (ADS)

Martin, T.; Drissen, L.; Joncas, G.

2015-09-01

SITELLE (installed in 2015 at the Canada-France-Hawaii Telescope) and SpIOMM (a prototype attached to the Observatoire du Mont-Mégantic) are the first Imaging Fourier Transform Spectrometers (IFTS) capable of obtaining a hyperspectral data cube which samples a 12 arc minutes field of view into four millions of visible spectra. The result of each observation is made up of two interferometric data cubes which need to be merged, corrected, transformed and calibrated in order to get a spectral cube of the observed region ready to be analysed. ORBS is a fully automatic data reduction software that has been entirely designed for this purpose. The data size (up to 68 Gb for larger science cases) and the computational needs have been challenging and the highly parallelized object-oriented architecture of ORBS reflects the solutions adopted which made possible to process 68 Gb of raw data in less than 11 hours using 8 cores and 22.6 Gb of RAM. It is based on a core framework (ORB) that has been designed to support the whole software suite for data analysis (ORCS and OACS), data simulation (ORUS) and data acquisition (IRIS). They all aim to provide a strong basis for the creation and development of specialized analysis modules that could benefit the scientific community working with SITELLE and SpIOMM.

Imaging Fourier transform spectroscopy of the boundary layer plume from laser irradiated polymers and carbon materials

NASA Astrophysics Data System (ADS)

Acosta, Roberto I.

The high-energy laser (HEL) lethality community needs for enhanced laser weapons systems requires a better understanding of a wide variety of emerging threats. In order to reduce the dimensionality of laser-materials interaction it is necessary to develop novel predictive capabilities of these events. The objective is to better understand the fundamentals of laser lethality testing by developing empirical models from hyperspectral imagery, enabling a robust library of experiments for vulnerability assessments. Emissive plumes from laser irradiated fiberglass reinforced polymers (FRP), poly(methyl methacrylate) (PMMA) and porous graphite targets were investigated primarily using a mid-wave infrared (MWIR) imaging Fourier transform spectrometer (FTS). Polymer and graphite targets were irradiated with a continuous wave (cw) fiber lasers. Data was acquired with a spectral resolution of 2 cm-1 and spatial resolution as high as 0.52 mm2 per pixel. Strong emission from H2O, CO, CO2 and hydrocarbons were observed in the MWIR between 1900-4000 cm-1. A single-layer radiative transfer model was developed to estimate spatial maps of temperature and column densities of CO and CO2 from the hyperspectral imagery of the boundary layer plume. The spectral model was used to compute the absorption cross sections of CO and CO2, using spectral line parameters from the high temperature extension of the HITRAN. Also, spatial maps of gas-phase temperature and methyl methacrylate (MMA) concentration were developed from laser irradiated carbon black-pigmented PMMA at irradiances of 4-22 W/cm2. Global kinetics interplay between heterogeneous and homogeneous combustion kinetics are shown from experimental observations at high spatial resolutions. Overall the boundary layer profile at steady-state is consistent with CO being mainly produced at the surface by heterogeneous reactions followed by a rapid homogeneous combustion in the boundary layer towards buoyancy.

Hyperspectral Imagers for the Study of Massive Star Nebulae

NASA Astrophysics Data System (ADS)

Drissen, L.; Alarie, A.; Martin, T.; Spiomm/Sitelle Team

2012-12-01

We present two wide-field imaging Fourier transform spectrometers built by our team to study the interstellar medium around massive stars in the Milky Way and nearby galaxies. SpIOMM, attached to the Mont Mégantic 1.6-m telescope, is capable of obtaining the visible spectrum of every source of light in a 12 arcminute field of view, with a spectral resolution ranging from R = 1 (wide-band image) to R = 25 000, resulting in about a million spectra with a spatial resolution of one arcsecond. SITELLE will be a similar instrument attached to the Canada-France-Hawaii telescope, and will be in operation in early 2013. We illustrate SpIOMM's capabilities to study the interactions between massive stars and their environment.

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.

Middle infrared (wavelength range: 8 μm-14 μm) 2-dimensional spectroscopy (total weight with electrical controller: 1.7 kg, total cost: less than 10,000 USD) so-called hyperspectral camera for unmanned air vehicles like drones

NASA Astrophysics Data System (ADS)

Yamamoto, Naoyuki; Saito, Tsubasa; Ogawa, Satoru; Ishimaru, Ichiro

2016-05-01

We developed the palm size (optical unit: 73[mm]×102[mm]×66[mm]) and light weight (total weight with electrical controller: 1.7[kg]) middle infrared (wavelength range: 8[μm]-14[μm]) 2-dimensional spectroscopy for UAV (Unmanned Air Vehicle) like drone. And we successfully demonstrated the flights with the developed hyperspectral camera mounted on the multi-copter so-called drone in 15/Sep./2015 at Kagawa prefecture in Japan. We had proposed 2 dimensional imaging type Fourier spectroscopy that was the near-common path temporal phase-shift interferometer. We install the variable phase shifter onto optical Fourier transform plane of infinity corrected imaging optical systems. The variable phase shifter was configured with a movable mirror and a fixed mirror. The movable mirror was actuated by the impact drive piezo-electric device (stroke: 4.5[mm], resolution: 0.01[μm], maker: Technohands Co.,Ltd., type:XDT50-45, price: around 1,000USD). We realized the wavefront division type and near common path interferometry that has strong robustness against mechanical vibrations. Without anti-mechanical vibration systems, the palm-size Fourier spectroscopy was realized. And we were able to utilize the small and low-cost middle infrared camera that was the micro borometer array (un-cooled VOxMicroborometer, pixel array: 336×256, pixel pitch: 17[μm], frame rate 60[Hz], maker: FLIR, type: Quark 336, price: around 5,000USD). And this apparatus was able to be operated by single board computer (Raspberry Pi.). Thus, total cost was less than 10,000 USD. We joined with KAMOME-PJ (Kanagawa Advanced MOdule for Material Evaluation Project) with DRONE FACTORY Corp., KUUSATSU Corp., Fuji Imvac Inc. And we successfully obtained the middle infrared spectroscopic imaging with multi-copter drone.

Spectral-Spatial Scale Invariant Feature Transform for Hyperspectral Images.

PubMed

Al-Khafaji, Suhad Lateef; Jun Zhou; Zia, Ali; Liew, Alan Wee-Chung

2018-02-01

Spectral-spatial feature extraction is an important task in hyperspectral image processing. In this paper we propose a novel method to extract distinctive invariant features from hyperspectral images for registration of hyperspectral images with different spectral conditions. Spectral condition means images are captured with different incident lights, viewing angles, or using different hyperspectral cameras. In addition, spectral condition includes images of objects with the same shape but different materials. This method, which is named spectral-spatial scale invariant feature transform (SS-SIFT), explores both spectral and spatial dimensions simultaneously to extract spectral and geometric transformation invariant features. Similar to the classic SIFT algorithm, SS-SIFT consists of keypoint detection and descriptor construction steps. Keypoints are extracted from spectral-spatial scale space and are detected from extrema after 3D difference of Gaussian is applied to the data cube. Two descriptors are proposed for each keypoint by exploring the distribution of spectral-spatial gradient magnitude in its local 3D neighborhood. The effectiveness of the SS-SIFT approach is validated on images collected in different light conditions, different geometric projections, and using two hyperspectral cameras with different spectral wavelength ranges and resolutions. The experimental results show that our method generates robust invariant features for spectral-spatial image matching.

Hazardous gas detection for FTIR-based hyperspectral imaging system using DNN and CNN

NASA Astrophysics Data System (ADS)

Kim, Yong Chan; Yu, Hyeong-Geun; Lee, Jae-Hoon; Park, Dong-Jo; Nam, Hyun-Woo

2017-10-01

Recently, a hyperspectral imaging system (HIS) with a Fourier Transform InfraRed (FTIR) spectrometer has been widely used due to its strengths in detecting gaseous fumes. Even though numerous algorithms for detecting gaseous fumes have already been studied, it is still difficult to detect target gases properly because of atmospheric interference substances and unclear characteristics of low concentration gases. In this paper, we propose detection algorithms for classifying hazardous gases using a deep neural network (DNN) and a convolutional neural network (CNN). In both the DNN and CNN, spectral signal preprocessing, e.g., offset, noise, and baseline removal, are carried out. In the DNN algorithm, the preprocessed spectral signals are used as feature maps of the DNN with five layers, and it is trained by a stochastic gradient descent (SGD) algorithm (50 batch size) and dropout regularization (0.7 ratio). In the CNN algorithm, preprocessed spectral signals are trained with 1 × 3 convolution layers and 1 × 2 max-pooling layers. As a result, the proposed algorithms improve the classification accuracy rate by 1.5% over the existing support vector machine (SVM) algorithm for detecting and classifying hazardous gases.

SITELLE's Data Release 1

NASA Astrophysics Data System (ADS)

Martin, T. B.; Drissen, L.

2016-12-01

Installed at the Canada-France-Hawaii Telescope (CFHT) since August 2015, SITELLE is an Imaging Fourier Transform Spectrometer (IFTS) with an 11×11 field of view. After its prototype SpIOMM, installed at Mont Mégantic (Québec, Canada), it is the second IFTS in the world operating in the visible band (350-1000 nm). It delivers hyperspectral data cubes of 4 million spectra at R˜1500-5000 with a spatial sampling of 0.32" and a filling factor of 100 %. A suite of softwares has been designed to reduce (ORBS) and analyze (ORCS) the data. Based on commissioning data obtained in August 2015, a first stable version has been released in March 2016 which is capable of reducing all the data. In this paper the quality of the calibration is discussed.

Airborne mapping of chemical plumes in the aftermath of Hurricanes Katrina and Rita

NASA Astrophysics Data System (ADS)

Lewis, Paul E.; Thomas, Mark J.; Kroutil, Robert T.; Combs, Roger; Cummings, Alan S.; Miller, Dave; Curry, Tim; Shen, Sylvia S.

2006-05-01

Infrared airborne spectral measurements were collected over the Gulf Coast area during the aftermath of Hurricanes Katrina and Rita. These measurements allowed surveillance for potentially hazardous chemical vapor releases from industrial facilities caused by storm damage. Data was collected with a mid-longwave infrared multispectral imager and a hyperspectral Fourier transform infrared spectrometer operating in a low altitude aircraft. Signal processing allowed detection and identification of targeted spectral signatures in the presence of interferents, atmospheric contributions, and thermal clutter. Results confirmed the presence of a number of chemical vapors. All detection results were immediately passed along to emergency first responders on the ground. The chemical identification, location, and vapor species concentration information were used by the emergency response ground teams for identification of critical plume releases and subsequent mitigation.

High-Throughput Metabolic Fingerprinting of Legume Silage Fermentations via Fourier Transform Infrared Spectroscopy and Chemometrics

PubMed Central

Johnson, Helen E.; Broadhurst, David; Kell, Douglas B.; Theodorou, Michael K.; Merry, Roger J.; Griffith, Gareth W.

2004-01-01

Silage quality is typically assessed by the measurement of several individual parameters, including pH, lactic acid, acetic acid, bacterial numbers, and protein content. The objective of this study was to use a holistic metabolic fingerprinting approach, combining a high-throughput microtiter plate-based fermentation system with Fourier transform infrared (FT-IR) spectroscopy, to obtain a snapshot of the sample metabolome (typically low-molecular-weight compounds) at a given time. The aim was to study the dynamics of red clover or grass silage fermentations in response to various inoculants incorporating lactic acid bacteria (LAB). The hyperspectral multivariate datasets generated by FT-IR spectroscopy are difficult to interpret visually, so chemometrics methods were used to deconvolute the data. Two-phase principal component-discriminant function analysis allowed discrimination between herbage types and different LAB inoculants and modeling of fermentation dynamics over time. Further analysis of FT-IR spectra by the use of genetic algorithms to identify the underlying biochemical differences between treatments revealed that the amide I and amide II regions (wavenumbers of 1,550 to 1,750 cm−1) of the spectra were most frequently selected (reflecting changes in proteins and free amino acids) in comparisons between control and inoculant-treated fermentations. This corresponds to the known importance of rapid fermentation for the efficient conservation of forage proteins. PMID:15006782

Research on ground-based LWIR hyperspectral imaging remote gas detection

NASA Astrophysics Data System (ADS)

Yang, Zhixiong; Yu, Chunchao; Zheng, Weijian; Lei, Zhenggang; Yan, Min; Yuan, Xiaochun; Zhang, Peizhong

2015-10-01

The new progress of ground-based long-wave infrared remote sensing is presented, which describes the windowing spatial and temporal modulation Fourier spectroscopy imaging in details. The prototype forms the interference fringes based on the corner-cube of spatial modulation of Michelson interferometer, using cooled long-wave infrared photovoltaic staring FPA (focal plane array) detector. The LWIR hyperspectral imaging is achieved by the process of collection, reorganization, correction, apodization, FFT etc. from data cube. Noise equivalent sensor response (NESR), which is the sensitivity index of CHIPED-1 LWIR hyperspectral imaging prototype, can reach 5.6×10-8W/(cm-1.sr.cm2) at single sampling. Hyperspectral imaging is used in the field of organic gas VOC infrared detection. Relative to wide band infrared imaging, it has some advantages. Such as, it has high sensitivity, the strong anti-interference ability, identify the variety, and so on.

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

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

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…

A hyperspectral view of Cassiopeia A

NASA Astrophysics Data System (ADS)

Alarie, Alexandre; Bilodeau, Antoine; Drissen, Laurent

2014-07-01

We used the imaging Fourier transform spectrometer Spectromètre Imageur de l'Observatoire du Mont-Mégantic (SpIOMM) to obtain hyperspectral cubes of the young supernova remnant Cassiopeia A (Cas A). The cubes contain over 5000 spatially resolved spectra covering the spectral range 6480-7050 Å. We first investigate the slow-moving N-rich quasi-stationary flocculi by measuring their radial velocity as well as the [N II] λ6583/Hα ratio. No correlation between their radial velocity and [N II] λ6583/Hα ratio with their location has been found. We used multi-epoch observations from the Hubble Space Telescope to create a proper motion map, showing the displacement of several filaments over the most part of Cas A. Combining data from SpIOMM and Hubble, we re-evaluate the distance to Cas A and obtained 3.33 ± 0.10 kpc, which is in good agreement with previous estimates. Finally, we obtain a three-dimensional spatial view of the [S II] λλ6716, 6731 emissions showing their location, expansion velocity and the [S II] doublet line ratio for multiple locations in the remnant. The velocity asymmetry reported by previous analyses is clearly visible. Also, the [S II] doublet ratio (with a mean value of 0.5 ± 0.2) indicates a very high and variable electronic density throughout the remnant.

AIRS Retrieval Validation During the EAQUATE

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Smith, William L.; Cuomo, Vincenzo; Taylor, Jonathan P.; Barnet, Christopher D.; DiGirolamo, Paolo; Pappalardo, Gelsomina; Larar, Allen M.; Liu, Xu; Newman, Stuart M.

2006-01-01

Atmospheric and surface thermodynamic parameters retrieved with advanced hyperspectral remote sensors of Earth observing satellites are critical for weather prediction and scientific research. The retrieval algorithms and retrieved parameters from satellite sounders must be validated to demonstrate the capability and accuracy of both observation and data processing systems. The European AQUA Thermodynamic Experiment (EAQUATE) was conducted mainly for validation of the Atmospheric InfraRed Sounder (AIRS) on the AQUA satellite, but also for assessment of validation systems of both ground-based and aircraft-based instruments which will be used for other satellite systems such as the Infrared Atmospheric Sounding Interferometer (IASI) on the European MetOp satellite, the Cross-track Infrared Sounder (CrIS) from the NPOESS Preparatory Project and the following NPOESS series of satellites. Detailed inter-comparisons were conducted and presented using different retrieval methodologies: measurements from airborne ultraspectral Fourier transform spectrometers, aircraft in-situ instruments, dedicated dropsondes and radiosondes, and ground based Raman Lidar, as well as from the European Center for Medium range Weather Forecasting (ECMWF) modeled thermal structures. The results of this study not only illustrate the quality of the measurements and retrieval products but also demonstrate the capability of these validation systems which are put in place to validate current and future hyperspectral sounding instruments and their scientific products.

Performance and applications of a hypertemporal hyperspectral Fourier-transform infrared spectroradiometer

NASA Astrophysics Data System (ADS)

King, Bruce H.; Ellis, Thomas; Old, Tom E.

2009-05-01

A fast-scanning, high-resolution FTIR spectroradiometer has been designed and built for use in remote sensing, stand-off detection, and spectral-temporal characterization of fast, energetic infrared events. The instrument design uses a Michelson-type interferometer with a rotary modulator which is capable of continuous measurement of infrared spectra at a rate of 1000 scans per second with 4 cm-1 resolution in the 2 - 25 micron spectral range. Sensitivity, spectral accuracy, and radiometric precision are discussed along with specific design parameters. This instrument can be used for passive sensing as a stand-alone sensor, or for active sensing as a receiver when used in conjunction with a highenergy excitation source such as a laser. Applications include muzzle flash signature measurement, ordnance detonation characterization, missile plume identification, and rocket motor combustion diagnostics.

Outlier and target detection in aerial hyperspectral imagery: a comparison of traditional and percentage occupancy hit or miss transform techniques

NASA Astrophysics Data System (ADS)

Young, Andrew; Marshall, Stephen; Gray, Alison

2016-05-01

The use of aerial hyperspectral imagery for the purpose of remote sensing is a rapidly growing research area. Currently, targets are generally detected by looking for distinct spectral features of the objects under surveillance. For example, a camouflaged vehicle, deliberately designed to blend into background trees and grass in the visible spectrum, can be revealed using spectral features in the near-infrared spectrum. This work aims to develop improved target detection methods, using a two-stage approach, firstly by development of a physics-based atmospheric correction algorithm to convert radiance into re ectance hyperspectral image data and secondly by use of improved outlier detection techniques. In this paper the use of the Percentage Occupancy Hit or Miss Transform is explored to provide an automated method for target detection in aerial hyperspectral imagery.

Geometrical calibration of an AOTF hyper-spectral imaging system

NASA Astrophysics Data System (ADS)

Špiclin, Žiga; Katrašnik, Jaka; Bürmen, Miran; Pernuš, Franjo; Likar, Boštjan

2010-02-01

Optical aberrations present an important problem in optical measurements. Geometrical calibration of an imaging system is therefore of the utmost importance for achieving accurate optical measurements. In hyper-spectral imaging systems, the problem of optical aberrations is even more pronounced because optical aberrations are wavelength dependent. Geometrical calibration must therefore be performed over the entire spectral range of the hyper-spectral imaging system, which is usually far greater than that of the visible light spectrum. This problem is especially adverse in AOTF (Acousto- Optic Tunable Filter) hyper-spectral imaging systems, as the diffraction of light in AOTF filters is dependent on both wavelength and angle of incidence. Geometrical calibration of hyper-spectral imaging system was performed by stable caliber of known dimensions, which was imaged at different wavelengths over the entire spectral range. The acquired images were then automatically registered to the caliber model by both parametric and nonparametric transformation based on B-splines and by minimizing normalized correlation coefficient. The calibration method was tested on an AOTF hyper-spectral imaging system in the near infrared spectral range. The results indicated substantial wavelength dependent optical aberration that is especially pronounced in the spectral range closer to the infrared part of the spectrum. The calibration method was able to accurately characterize the aberrations and produce transformations for efficient sub-pixel geometrical calibration over the entire spectral range, finally yielding better spatial resolution of hyperspectral imaging system.

Wavelet packets for multi- and hyper-spectral imagery

NASA Astrophysics Data System (ADS)

Benedetto, J. J.; Czaja, W.; Ehler, M.; Flake, C.; Hirn, M.

2010-01-01

State of the art dimension reduction and classification schemes in multi- and hyper-spectral imaging rely primarily on the information contained in the spectral component. To better capture the joint spatial and spectral data distribution we combine the Wavelet Packet Transform with the linear dimension reduction method of Principal Component Analysis. Each spectral band is decomposed by means of the Wavelet Packet Transform and we consider a joint entropy across all the spectral bands as a tool to exploit the spatial information. Dimension reduction is then applied to the Wavelet Packets coefficients. We present examples of this technique for hyper-spectral satellite imaging. We also investigate the role of various shrinkage techniques to model non-linearity in our approach.

Hyperspectral image classification based on local binary patterns and PCANet

NASA Astrophysics Data System (ADS)

Yang, Huizhen; Gao, Feng; Dong, Junyu; Yang, Yang

2018-04-01

Hyperspectral image classification has been well acknowledged as one of the challenging tasks of hyperspectral data processing. In this paper, we propose a novel hyperspectral image classification framework based on local binary pattern (LBP) features and PCANet. In the proposed method, linear prediction error (LPE) is first employed to select a subset of informative bands, and LBP is utilized to extract texture features. Then, spectral and texture features are stacked into a high dimensional vectors. Next, the extracted features of a specified position are transformed to a 2-D image. The obtained images of all pixels are fed into PCANet for classification. Experimental results on real hyperspectral dataset demonstrate the effectiveness of the proposed method.

Design and operation of SUCHI: the space ultra-compact hyperspectral imager for a small satellite

NASA Astrophysics Data System (ADS)

Crites, S. T.; Lucey, P. G.; Wright, R.; Chan, J.; Garbeil, H.; Horton, K. A.; Imai, A.; Pilger, E. J.; Wood, M.; Yoneshige, Lance

2014-06-01

The primary payload on the University of Hawaii-built `HiakaSat' micro-satellite will be the Space Ultra Compact Hyperspectral Imager (SUCHI). SUCHI is a low-mass (<9kg), low-volume (10x10x36 cm3) long wave infrared hyperspectral imager designed and built at the University of Hawaii. SUCHI is based on a variable-gap Fabry-Perot interferometer employed as a Fourier transform spectrometer with images collected by a commercial 320x256 microbolometer array. The microbolometer camera and vacuum-sensitive electronics are contained within a sealed vessel at 1 atm. SUCHI will collect spectral radiance data from 8 to 14 microns and demonstrate the potential of this instrument for geological studies from orbit (e.g. mapping of major rock-forming minerals) and volcanic hazard observation and assessment (e.g. quantification of volcanic sulfur dioxide pollution and lava flow cooling rates). The sensor has been integrated with the satellite which will launch on the Office of Responsive Space ORS-4 mission scheduled for 2014. The primary mission will last 6 months, with extended operations anticipated for approximately 2 years. A follow-on mission has been proposed to perform imaging of Earth's surface in the 3-5 micron range with a field of view of 5 km with 5.25 m sampling (from a 350 km orbit). The 19-kg proposed instrument will be a prototype sensor for a constellation of small satellites for Earth imaging. The integrated satellite properties will be incorporated into the Hawaii Space Flight Laboratory's constellation maintenance software environment COSMOS (Comprehensive Openarchitecture Space Mission Operations System) to ease future implementation of the instrument as part of a constellation.

Reflectance Hyperspectral Imaging for Investigation of Works of Art: Old Master Paintings and Illuminated Manuscripts.

PubMed

Cucci, Costanza; Delaney, John K; Picollo, Marcello

2016-10-18

Diffuse reflectance hyperspectral imaging, or reflectance imaging spectroscopy, is a sophisticated technique that enables the capture of hundreds of images in contiguous narrow spectral bands (bandwidth < 10 nm), typically in the visible (Vis, 400-750 nm) and the near-infrared (NIR, 750-2500 nm) regions. This sequence of images provides a data set that is called an image-cube or file-cube. Two dimensions of the image-cube are the spatial dimensions of the scene, and the third dimension is the wavelength. In this way, each spatial pixel in the image has an associated reflectance spectrum. This "big data" image-cube allows for the mining of artists' materials and mapping their distribution across the surface of a work of art. Reflectance hyperspectral imaging, introduced in the 1980s by Goetz and co-workers, led to a revolution in the field of remote sensing of the earth and near planets ( Goetz, F. H.; Vane, G.; Solomon, B. N.; Rock, N. Imaging Spectrometry for Earth Remote Sensing . Science , 1985 , 228 , 1147 - 1152 ). In the subsequent decades, thanks to rapid advances in solid-state sensor technology, reflectance hyperspectral imaging, once only available to large government laboratories, was extended to new fields of application, such as monitoring agri-foods, pharmaceutical products, the environment, and cultural heritage. In the 2000s, the potential of this noninvasive technology for the study of artworks became evident and, consequently, the methodology is becoming more widely used in the art conservation science field. Typically hyperspectral reflectance image-cubes contain millions of spectra. Many of these spectra are similar, making the reduction of the data set size an important first step. Thus, image-processing tools based on multivariate techniques, such as principal component analysis (PCA), automated classification methods, or expert knowledge systems, that search for known spectral features are often applied. These algorithms seek to reduce the large number of high-quality spectra to a common subset, which allow identifying and mapping artists' materials and alteration products. Hence, reflectance hyperspectral imaging is finding its place as the starting point to find sites on polychrome surfaces for spot analytical techniques, such as X-ray fluorescence, Raman spectroscopy, and Fourier transform infrared spectroscopy. Reflectance hyperspectral imaging can also provide image products that are a mainstay in the art conservation field, such as color-accurate images, broadband near-infrared images, and false-color products. This Account reports on the research activity carried out by two research groups, one at the "Nello Carrara" Institute of Applied Physics of the Italian National Research Council (IFAC-CNR) in Florence and the other at the National Gallery of Art (NGA) in Washington, D.C. Both groups have conducted parallel research, with frequent interchanges, to develop multispectral and hyperspectral imaging systems to study works of art. In the past decade, they have designed and experimented with some of the earliest spectral imaging prototypes for museum applications. In this Account, a brief presentation of the hyperspectral sensor systems is given with case studies showing how reflectance hyperspectral imaging is answering key questions in cultural heritage.

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…

Using linear polarization for LWIR hyperspectral sensing of liquid contaminants

NASA Astrophysics Data System (ADS)

Thériault, Jean-Marc; Fortin, Gilles; Lacasse, Paul; Bouffard, François; Lavoie, Hugo

2013-09-01

We report and analyze recent results obtained with the MoDDIFS sensor (Multi-option Differential Detection and Imaging Fourier Spectrometer) for the passive polarization sensing of liquid contaminants in the long wave infrared (LWIR). Field measurements of polarized spectral radiance done on ethylene glycol and SF96 probed at distances of 6.5 and 450 meters, respectively, have been used to develop and test a GLRT-type detection algorithm adapted for liquid contaminants. The GLRT detection results serve to establish the potential and advantage of probing the vertical and horizontal linear hyperspectral polarization components for improving liquid contaminants detection.

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

Trace gas detection in hyperspectral imagery using the wavelet packet subspace

NASA Astrophysics Data System (ADS)

Salvador, Mark A. Z.

This dissertation describes research into a new remote sensing method to detect trace gases in hyperspectral and ultra-spectral data. This new method is based on the wavelet packet transform. It attempts to improve both the computational tractability and the detection of trace gases in airborne and spaceborne spectral imagery. Atmospheric trace gas research supports various Earth science disciplines to include climatology, vulcanology, pollution monitoring, natural disasters, and intelligence and military applications. Hyperspectral and ultra-spectral data significantly increases the data glut of existing Earth science data sets. Spaceborne spectral data in particular significantly increases spectral resolution while performing daily global collections of the earth. Application of the wavelet packet transform to the spectral space of hyperspectral and ultra-spectral imagery data potentially improves remote sensing detection algorithms. It also facilities the parallelization of these methods for high performance computing. This research seeks two science goals, (1) developing a new spectral imagery detection algorithm, and (2) facilitating the parallelization of trace gas detection in spectral imagery data.

Synthesis of Multispectral Bands from Hyperspectral Data: Validation Based on Images Acquired by AVIRIS, Hyperion, ALI, and ETM+

NASA Technical Reports Server (NTRS)

Blonksi, Slawomir; Gasser, Gerald; Russell, Jeffrey; Ryan, Robert; Terrie, Greg; Zanoni, Vicki

2001-01-01

Multispectral data requirements for Earth science applications are not always studied rigorously studied before a new remote sensing system is designed. A study of the spatial resolution, spectral bandpasses, and radiometric sensitivity requirements of real-world applications would focus the design onto providing maximum benefits to the end-user community. To support systematic studies of multispectral data requirements, the Applications Research Toolbox (ART) has been developed at NASA's Stennis Space Center. The ART software allows users to create and assess simulated datasets while varying a wide range of system parameters. The simulations are based on data acquired by existing multispectral and hyperspectral instruments. The produced datasets can be further evaluated for specific end-user applications. Spectral synthesis of multispectral images from hyperspectral data is a key part of the ART software. In this process, hyperspectral image cubes are transformed into multispectral imagery without changes in spatial sampling and resolution. The transformation algorithm takes into account spectral responses of both the synthesized, broad, multispectral bands and the utilized, narrow, hyperspectral bands. To validate the spectral synthesis algorithm, simulated multispectral images are compared with images collected near-coincidentally by the Landsat 7 ETM+ and the EO-1 ALI instruments. Hyperspectral images acquired with the airborne AVIRIS instrument and with the Hyperion instrument onboard the EO-1 satellite were used as input data to the presented simulations.

Thermal stabilization of static single-mirror Fourier transform spectrometers

NASA Astrophysics Data System (ADS)

Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.

2017-05-01

Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

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.

ICER-3D: A Progressive Wavelet-Based Compressor for Hyperspectral Images

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.; Xie, H.; Aranki, N.

2005-01-01

ICER-3D is a progressive, wavelet-based compressor for hyperspectral images. ICER-3D is derived from the ICER image compressor. ICER-3D can provide lossless and lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The three-dimensional wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of hyperspectral data sets, while facilitating elimination of spectral ringing artifacts. Correlation is further exploited by a context modeler that effectively exploits spectral dependencies in the wavelet-transformed hyperspectral data. Performance results illustrating the benefits of these features are 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.

Framework for hyperspectral image processing and quantification for cancer detection during animal tumor surgery.

PubMed

Lu, Guolan; Wang, Dongsheng; Qin, Xulei; Halig, Luma; Muller, Susan; Zhang, Hongzheng; Chen, Amy; Pogue, Brian W; Chen, Zhuo Georgia; Fei, Baowei

2015-01-01

Hyperspectral imaging (HSI) is an imaging modality that holds strong potential for rapid cancer detection during image-guided surgery. But the data from HSI often needs to be processed appropriately in order to extract the maximum useful information that differentiates cancer from normal tissue. We proposed a framework for hyperspectral image processing and quantification, which includes a set of steps including image preprocessing, glare removal, feature extraction, and ultimately image classification. The framework has been tested on images from mice with head and neck cancer, using spectra from 450- to 900-nm wavelength. The image analysis computed Fourier coefficients, normalized reflectance, mean, and spectral derivatives for improved accuracy. The experimental results demonstrated the feasibility of the hyperspectral image processing and quantification framework for cancer detection during animal tumor surgery, in a challenging setting where sensitivity can be low due to a modest number of features present, but potential for fast image classification can be high. This HSI approach may have potential application in tumor margin assessment during image-guided surgery, where speed of assessment may be the dominant factor.

Framework for hyperspectral image processing and quantification for cancer detection during animal tumor surgery

NASA Astrophysics Data System (ADS)

Lu, Guolan; Wang, Dongsheng; Qin, Xulei; Halig, Luma; Muller, Susan; Zhang, Hongzheng; Chen, Amy; Pogue, Brian W.; Chen, Zhuo Georgia; Fei, Baowei

2015-12-01

Hyperspectral imaging (HSI) is an imaging modality that holds strong potential for rapid cancer detection during image-guided surgery. But the data from HSI often needs to be processed appropriately in order to extract the maximum useful information that differentiates cancer from normal tissue. We proposed a framework for hyperspectral image processing and quantification, which includes a set of steps including image preprocessing, glare removal, feature extraction, and ultimately image classification. The framework has been tested on images from mice with head and neck cancer, using spectra from 450- to 900-nm wavelength. The image analysis computed Fourier coefficients, normalized reflectance, mean, and spectral derivatives for improved accuracy. The experimental results demonstrated the feasibility of the hyperspectral image processing and quantification framework for cancer detection during animal tumor surgery, in a challenging setting where sensitivity can be low due to a modest number of features present, but potential for fast image classification can be high. This HSI approach may have potential application in tumor margin assessment during image-guided surgery, where speed of assessment may be the dominant factor.

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.

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…

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.

Texture-adaptive hyperspectral video acquisition system with a spatial light modulator

NASA Astrophysics Data System (ADS)

Fang, Xiaojing; Feng, Jiao; Wang, Yongjin

2014-10-01

We present a new hybrid camera system based on spatial light modulator (SLM) to capture texture-adaptive high-resolution hyperspectral video. The hybrid camera system records a hyperspectral video with low spatial resolution using a gray camera and a high-spatial resolution video using a RGB camera. The hyperspectral video is subsampled by the SLM. The subsampled points can be adaptively selected according to the texture characteristic of the scene by combining with digital imaging analysis and computational processing. In this paper, we propose an adaptive sampling method utilizing texture segmentation and wavelet transform (WT). We also demonstrate the effectiveness of the sampled pattern on the SLM with the proposed method.

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.

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.

Measurements of multiple gas parameters in a pulsed-detonation combustor using time-division-multiplexed Fourier-domain mode-locked lasers.

PubMed

Caswell, Andrew W; Roy, Sukesh; An, Xinliang; Sanders, Scott T; Schauer, Frederick R; Gord, James R

2013-04-20

Hyperspectral absorption spectroscopy is being used to monitor gas temperature, velocity, pressure, and H(2)O mole fraction in a research-grade pulsed-detonation combustor (PDC) at the Air Force Research Laboratory. The hyperspectral source employed is termed the TDM 3-FDML because it consists of three time-division-multiplexed (TDM) Fourier-domain mode-locked (FDML) lasers. This optical-fiber-based source monitors sufficient spectral information in the H(2)O absorption spectrum near 1350 nm to permit measurements over the wide range of conditions encountered throughout the PDC cycle. Doppler velocimetry based on absorption features is accomplished using a counterpropagating beam approach that is designed to minimize common-mode flow noise. The PDC in this study is operated in two configurations: one in which the combustion tube exhausts directly to the ambient environment and another in which it feeds an automotive-style turbocharger to assess the performance of a detonation-driven turbine. Because the enthalpy flow [kilojoule/second] is important in assessing the performance of the PDC in various configurations, it is calculated from the measured gas properties.

Hyperspectral remote sensing of plant pigments.

PubMed

Blackburn, George Alan

2007-01-01

The dynamics of pigment concentrations are diagnostic of a range of plant physiological properties and processes. This paper appraises the developing technologies and analytical methods for quantifying pigments non-destructively and repeatedly across a range of spatial scales using hyperspectral remote sensing. Progress in deriving predictive relationships between various characteristics and transforms of hyperspectral reflectance data are evaluated and the roles of leaf and canopy radiative transfer models are reviewed. Requirements are identified for more extensive intercomparisons of different approaches and for further work on the strategies for interpreting canopy scale data. The paper examines the prospects for extending research to the wider range of pigments in addition to chlorophyll, testing emerging methods of hyperspectral analysis and exploring the fusion of hyperspectral and LIDAR remote sensing. In spite of these opportunities for further development and the refinement of techniques, current evidence of an expanding range of applications in the ecophysiological, environmental, agricultural, and forestry sciences highlights the growing value of hyperspectral remote sensing of plant pigments.

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

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",…

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

HMM for hyperspectral spectrum representation and classification with endmember entropy vectors

NASA Astrophysics Data System (ADS)

Arabi, Samir Y. W.; Fernandes, David; Pizarro, Marco A.

2015-10-01

The Hyperspectral images due to its good spectral resolution are extensively used for classification, but its high number of bands requires a higher bandwidth in the transmission data, a higher data storage capability and a higher computational capability in processing systems. This work presents a new methodology for hyperspectral data classification that can work with a reduced number of spectral bands and achieve good results, comparable with processing methods that require all hyperspectral bands. The proposed method for hyperspectral spectra classification is based on the Hidden Markov Model (HMM) associated to each Endmember (EM) of a scene and the conditional probabilities of each EM belongs to each other EM. The EM conditional probability is transformed in EM vector entropy and those vectors are used as reference vectors for the classes in the scene. The conditional probability of a spectrum that will be classified is also transformed in a spectrum entropy vector, which is classified in a given class by the minimum ED (Euclidian Distance) among it and the EM entropy vectors. The methodology was tested with good results using AVIRIS spectra of a scene with 13 EM considering the full 209 bands and the reduced spectral bands of 128, 64 and 32. For the test area its show that can be used only 32 spectral bands instead of the original 209 bands, without significant loss in the classification process.

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.

Toward optimal spatial and spectral quality in widefield infrared spectromicroscopy of IR labelled single cells.

PubMed

Mattson, Eric C; Unger, Miriam; Clède, Sylvain; Lambert, François; Policar, Clotilde; Imtiaz, Asher; D'Souza, Roshan; Hirschmugl, Carol J

2013-10-07

Advancements in widefield infrared spectromicroscopy have recently been demonstrated following the commissioning of IRENI (InfraRed ENvironmental Imaging), a Fourier Transform infrared (FTIR) chemical imaging beamline at the Synchrotron Radiation Center. The present study demonstrates the effects of magnification, spatial oversampling, spectral pre-processing and deconvolution, focusing on the intracellular detection and distribution of an exogenous metal tris-carbonyl derivative 1 in a single MDA-MB-231 breast cancer cell. We demonstrate here that spatial oversampling for synchrotron-based infrared imaging is critical to obtain accurate diffraction-limited images at all wavelengths simultaneously. Resolution criteria and results from raw and deconvoluted images for two Schwarzschild objectives (36×, NA 0.5 and 74×, NA 0.65) are compared to each other and to prior reports for raster-scanned, confocal microscopes. The resolution of the imaging data can be improved by deconvolving the instrumental broadening that is determined with the measured PSFs, which is implemented with GPU programming architecture for fast hyperspectral processing. High definition, rapidly acquired, FTIR chemical images of respective spectral signatures of the cell 1 and shows that 1 is localized next to the phosphate- and Amide-rich regions, in agreement with previous infrared and luminescence studies. The infrared image contrast, localization and definition are improved after applying proven spectral pre-processing (principal component analysis based noise reduction and RMie scattering correction algorithms) to individual pixel spectra in the hyperspectral cube.

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.

Observation of Passive and Explosive Emissions at Stromboli with a Ground-based Hyperspectral TIR Camera

NASA Astrophysics Data System (ADS)

Smekens, J. F.; Mathieu, G.

2015-12-01

Scientific imaging techniques have progressed at a fast pace in the recent years, thanks in part to great improvements in detector technology, and through our ability to process large amounts of complex data using sophisticated software. Broadband thermal cameras are ubiquitously used for permanent monitoring of volcanic activity, and have been used in a multitude of scientific applications, from tracking ballistics to studying the thermal evolution lava flow fields and volcanic plumes. In parallel, UV cameras are now used at several volcano observatories to quantify daytime sulfur dioxide (SO2) emissions at very high frequency. In this work we present the results the first deployment of a ground-based Thermal Infrared (TIR) Hyperspectral Imaging System (Telops Hyper-Cam LW) for the study of passive and explosive volcanic activity at Stromboli volcano, Italy. The instrument uses a Michelson spectrometer and Fourier Transform Infrared Spectrometry to produce hyperspectral datacubes of a scene (320x256 pixels) in the range 7.7-11.8 μm, with a spectral resolution of up to 0.25 cm-1 and at frequencies of ~10 Hz. The activity at Stromboli is characterized by explosions of small magnitude, often containing significant amounts of gas and ash, separated by periods of quiescent degassing of 10-60 minutes. With our dataset, spanning about 5 days of monitoring, we are able to detect and track temporal variations of SO2 and ash emissions during both daytime and nighttime. It ultimately allows for the quantification of the mass of gas and ash ejected during and between explosive events. Although the high price and power consumption of the instrument are obstacles to its deployment as a monitoring tool, this type of data sets offers unprecedented insight into the dynamic processes taking place at Stromboli, and could lead to a better understanding of the eruptive mechanisms at persistently active systems in general.

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.

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.

[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.

The role of the continuous wavelet transform in mineral identification using hyperspectral imaging in the long-wave infrared by using SVM classifier

NASA Astrophysics Data System (ADS)

Sojasi, Saeed; Yousefi, Bardia; Liaigre, Kévin; Ibarra-Castanedo, Clemente; Beaudoin, Georges; Maldague, Xavier P. V.; Huot, François; Chamberland, Martin

2017-05-01

Hyperspectral imaging (HSI) in the long-wave infrared spectrum (LWIR) provides spectral and spatial information concerning the emissivity of the surface of materials, which can be used for mineral identification. For this, an endmember, which is the purest form of a mineral, is used as reference. All pure minerals have specific spectral profiles in the electromagnetic wavelength, which can be thought of as the mineral's fingerprint. The main goal of this paper is the identification of minerals by LWIR hyperspectral imaging using a machine learning scheme. The information of hyperspectral imaging has been recorded from the energy emitted from the mineral's surface. Solar energy is the source of energy in remote sensing, while a heating element is the energy source employed in laboratory experiments. Our work contains three main steps where the first step involves obtaining the spectral signatures of pure (single) minerals with a hyperspectral camera, in the long-wave infrared (7.7 to 11.8 μm), which measures the emitted radiance from the minerals' surface. The second step concerns feature extraction by applying the continuous wavelet transform (CWT) and finally we use support vector machine classifier with radial basis functions (SVM-RBF) for classification/identification of minerals. The overall accuracy of classification in our work is 90.23+/- 2.66%. In conclusion, based on CWT's ability to capture the information of signals can be used as a good marker for classification and identification the minerals substance.

Supervised target detection in hyperspectral images using one-class Fukunaga-Koontz Transform

NASA Astrophysics Data System (ADS)

Binol, Hamidullah; Bal, Abdullah

2016-05-01

A novel hyperspectral target detection technique based on Fukunaga-Koontz transform (FKT) is presented. FKT offers significant properties for feature selection and ordering. However, it can only be used to solve multi-pattern classification problems. Target detection may be considered as a two-class classification problem, i.e., target versus background clutter. Nevertheless, background clutter typically contains different types of materials. That's why; target detection techniques are different than classification methods by way of modeling clutter. To avoid the modeling of the background clutter, we have improved one-class FKT (OC-FKT) for target detection. The statistical properties of target training samples are used to define tunnel-like boundary of the target class. Non-target samples are then created synthetically as to be outside of the boundary. Thus, only limited target samples become adequate for training of FKT. The hyperspectral image experiments confirm that the proposed OC-FKT technique provides an effective means for target detection.

Biomass modeling of four water intensiveleading world crops using hyperspectral narrowbands in support of HyspIRI Mission

USGS Publications Warehouse

Marshall, Michael T.; Thenkabail, Prasad S.

2014-01-01

New satellite missions are expected to record high spectral resolution information globally and consistently for the first time, so it is important to identify modeling techniques that take advantage of these new data. In this paper, we estimate biomass for four major crops using ground-based hyperspectral narrowbands. The spectra and their derivatives are evaluated using three modeling techniques: two-band hyperspectral vegetation indices (HVIs), multiple band-HVIs (MB-HVIs) developed from Sequential Search Methods (SSM), and MB-HVIs developed from Principal Component Regression. Overall, the two-band HVIs and MB-HVIs developed from SSMs using first derivative transformed spectra in the visible blue and green and NIR explained more biomass variability and had lower error than the other approaches or transformations; however a better search criterion needs to be developed in order to reflect the true ability of the two-band HVI approach. Short-Wave Infrared 1 (1000 to 1700 nm) proved less effective, but still important in the final models.

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.

Recent Advances in Techniques for Hyperspectral Image Processing

NASA Technical Reports Server (NTRS)

Plaza, Antonio; Benediktsson, Jon Atli; Boardman, Joseph W.; Brazile, Jason; Bruzzone, Lorenzo; Camps-Valls, Gustavo; Chanussot, Jocelyn; Fauvel, Mathieu; Gamba, Paolo; Gualtieri, Anthony;

Manifold structure preservative for hyperspectral target detection

NASA Astrophysics Data System (ADS)

Imani, Maryam

2018-05-01

A nonparametric method termed as manifold structure preservative (MSP) is proposed in this paper for hyperspectral target detection. MSP transforms the feature space of data to maximize the separation between target and background signals. Moreover, it minimizes the reconstruction error of targets and preserves the topological structure of data in the projected feature space. MSP does not need to consider any distribution for target and background data. So, it can achieve accurate results in real scenarios due to avoiding unreliable assumptions. The proposed MSP detector is compared to several popular detectors and the experiments on a synthetic data and two real hyperspectral images indicate the superior ability of it in target detection.

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.

Recent developments and applications of hyperspectral imaging for rapid detection of mycotoxins and mycotoxigenic fungi in food products.

PubMed

Xing, Fuguo; Yao, Haibo; Liu, Yang; Dai, Xiaofeng; Brown, Robert L; Bhatnagar, Deepak

2017-08-28

Mycotoxins are the foremost naturally occurring contaminants of food products such as corn, peanuts, tree nuts, and wheat. As the secondary metabolites, mycotoxins are mainly synthesized by many species of the genera Aspergillus, Fusarium and Penicillium, and are considered highly toxic and carcinogenic to humans and animals. Most mycotoxins are detected and quantified by analytical chemistry-based methods. While mycotoxigenic fungi are usually identified and quantified by biological methods. However, these methods are time-consuming, laborious, costly, and inconsistent because of the variability of the grain-sampling process. It is desirable to develop rapid, non-destructive and efficient methods that objectively measure and evaluate mycotoxins and mycotoxigenic fungi in food. In recent years, some spectroscopy-based technologies such as hyperspectral imaging (HSI), Raman spectroscopy, and Fourier transform infrared spectroscopy have been extensively investigated for their potential use as tools for the detection, classification, and sorting of mycotoxins and toxigenic fungal contaminants in food. HSI integrates both spatial and spectral information for every pixel in an image, making it suitable for rapid detection of large quantities of samples and more heterogeneous samples and for in-line sorting in the food industry. In order to track the latest research developments in HSI, this paper gives a brief overview of the theories and fundamentals behind the technology and discusses its applications in the field of rapid detection and sorting of mycotoxins and toxigenic fungi in food products. Additionally, advantages and disadvantages of HSI are compared, and its potential use in commercial applications is reported.

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

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

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

Unsupervised domain adaptation for early detection of drought stress in hyperspectral images

NASA Astrophysics Data System (ADS)

Schmitter, P.; Steinrücken, J.; Römer, C.; Ballvora, A.; Léon, J.; Rascher, U.; Plümer, L.

2017-09-01

Hyperspectral images can be used to uncover physiological processes in plants if interpreted properly. Machine Learning methods such as Support Vector Machines (SVM) and Random Forests have been applied to estimate development of biomass and detect and predict plant diseases and drought stress. One basic requirement of machine learning implies, that training and testing is done in the same domain and the same distribution. Different genotypes, environmental conditions, illumination and sensors violate this requirement in most practical circumstances. Here, we present an approach, which enables the detection of physiological processes by transferring the prior knowledge within an existing model into a related target domain, where no label information is available. We propose a two-step transformation of the target features, which enables a direct application of an existing model. The transformation is evaluated by an objective function including additional prior knowledge about classification and physiological processes in plants. We have applied the approach to three sets of hyperspectral images, which were acquired with different plant species in different environments observed with different sensors. It is shown, that a classification model, derived on one of the sets, delivers satisfying classification results on the transformed features of the other data sets. Furthermore, in all cases early non-invasive detection of drought stress was possible.

[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.

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.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

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

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition

NASA Astrophysics Data System (ADS)

Li, Jin; Liu, Zilong

2017-12-01

Nonnegative tensor Tucker decomposition (NTD) in a transform domain (e.g., 2D-DWT, etc) has been used in the compression of hyper-spectral images because it can remove redundancies between spectrum bands and also exploit spatial correlations of each band. However, the use of a NTD has a very high computational cost. In this paper, we propose a low complexity NTD-based compression method of hyper-spectral images. This method is based on a pair-wise multilevel grouping approach for the NTD to overcome its high computational cost. The proposed method has a low complexity under a slight decrease of the coding performance compared to conventional NTD. We experimentally confirm this method, which indicates that this method has the less processing time and keeps a better coding performance than the case that the NTD is not used. The proposed approach has a potential application in the loss compression of hyper-spectral or multi-spectral images

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.

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.

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.

Multi-objective based spectral unmixing for hyperspectral images

NASA Astrophysics Data System (ADS)

Xu, Xia; Shi, Zhenwei

2017-02-01

Sparse hyperspectral unmixing assumes that each observed pixel can be expressed by a linear combination of several pure spectra in a priori library. Sparse unmixing is challenging, since it is usually transformed to a NP-hard l0 norm based optimization problem. Existing methods usually utilize a relaxation to the original l0 norm. However, the relaxation may bring in sensitive weighted parameters and additional calculation error. In this paper, we propose a novel multi-objective based algorithm to solve the sparse unmixing problem without any relaxation. We transform sparse unmixing to a multi-objective optimization problem, which contains two correlative objectives: minimizing the reconstruction error and controlling the endmember sparsity. To improve the efficiency of multi-objective optimization, a population-based randomly flipping strategy is designed. Moreover, we theoretically prove that the proposed method is able to recover a guaranteed approximate solution from the spectral library within limited iterations. The proposed method can directly deal with l0 norm via binary coding for the spectral signatures in the library. Experiments on both synthetic and real hyperspectral datasets demonstrate the effectiveness of the proposed method.

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.

Real-time implementation of optimized maximum noise fraction transform for feature extraction of hyperspectral images

NASA Astrophysics Data System (ADS)

Wu, Yuanfeng; Gao, Lianru; Zhang, Bing; Zhao, Haina; Li, Jun

2014-01-01

We present a parallel implementation of the optimized maximum noise fraction (G-OMNF) transform algorithm for feature extraction of hyperspectral images on commodity graphics processing units (GPUs). The proposed approach explored the algorithm data-level concurrency and optimized the computing flow. We first defined a three-dimensional grid, in which each thread calculates a sub-block data to easily facilitate the spatial and spectral neighborhood data searches in noise estimation, which is one of the most important steps involved in OMNF. Then, we optimized the processing flow and computed the noise covariance matrix before computing the image covariance matrix to reduce the original hyperspectral image data transmission. These optimization strategies can greatly improve the computing efficiency and can be applied to other feature extraction algorithms. The proposed parallel feature extraction algorithm was implemented on an Nvidia Tesla GPU using the compute unified device architecture and basic linear algebra subroutines library. Through the experiments on several real hyperspectral images, our GPU parallel implementation provides a significant speedup of the algorithm compared with the CPU implementation, especially for highly data parallelizable and arithmetically intensive algorithm parts, such as noise estimation. In order to further evaluate the effectiveness of G-OMNF, we used two different applications: spectral unmixing and classification for evaluation. Considering the sensor scanning rate and the data acquisition time, the proposed parallel implementation met the on-board real-time feature extraction.

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

NASA Technical Reports Server (NTRS)

Kiely, Aaron; Xie, Hua; Klimesh, matthew; Aranki, Nazeeh

2010-01-01

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

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.

Selective principal component regression analysis of fluorescence hyperspectral image to assess aflatoxin contamination in corn

USDA-ARS?s Scientific Manuscript database

Selective principal component regression analysis (SPCR) uses a subset of the original image bands for principal component transformation and regression. For optimal band selection before the transformation, this paper used genetic algorithms (GA). In this case, the GA process used the regression co...

Alteration mineral mapping and metallogenic prediction using CASI/SASI airborne hyperspectral data in Mingshujing area of Gansu Province, NW China

NASA Astrophysics Data System (ADS)

Sun, Yu; Zhao, Yingjun; Qin, Kai; Tian, Feng

2016-04-01

Hyperspectral remote sensing is a frontier of remote sensing. Due to its advantage of integrated image with spectrum, it can realize objects identification, superior to objects classification of multispectral remote sensing. Taken the Mingshujing area in Gansu Province of China as an example, this study extracted the alteration minerals and thus to do metallogenic prediction using CASI/SASI airborne hyperspectral data. The Mingshujing area, located in Liuyuan region of Gansu Province, is dominated by middle Variscan granites and Indosinian granites, with well developed EW- and NE-trending faults. In July 2012, our project team obtained the CASI/SASI hyperspectral data of Liuyuan region by aerial flight. The CASI hyperspectral data have 32 bands and the SASI hyperspectral data have 88 bands, with spectral resolution of 15nm for both. The hyperspectral raw data were first preprocessed, including radiometric correction and geometric correction. We then conducted atmospheric correction using empirical line method based on synchronously measured ground spectra to obtain hyperspectral reflectance data. Spectral dimension of hyperspectral data was reduced by the minimum noise fraction transformation method, and then purity pixels were selected. After these steps, image endmember spectra were obtained. We used the endmember spectrum election method based on expert knowledge to analyze the image endmember spectra. Then, the mixture tuned matched filter (MTMF) mapping method was used to extract mineral information, including limonite, Al-rich sericite, Al-poor sericite and chlorite. Finally, the distribution of minerals in the Mingshujing area was mapped. According to the distribution of limonite and Al-rich sericite mapped by CASI/SASI hyperspectral data, we delineated five gold prospecting areas, and further conducted field verification in these areas. It is shown that there are significant gold mineralized anomalies in surface in the Baixianishan and Xitan prospecting areas. The application of CASI/SASI airborne hyperspectral remote sensing data in the metallogenic prediction of the Mingshujing area has achieved ideal results, indicative of their wide application potential in geological research.

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.

A differential optical absorption spectroscopy method for retrieval from ground-based Fourier transform spectrometers measurements of the direct solar beam

NASA Astrophysics Data System (ADS)

Huo, Yanfeng; Duan, Minzheng; Tian, Wenshou; Min, Qilong

2015-08-01

A differential optical absorption spectroscopy (DOAS)-like algorithm is developed to retrieve the column-averaged dryair mole fraction of carbon dioxide from ground-based hyper-spectral measurements of the direct solar beam. Different to the spectral fitting method, which minimizes the difference between the observed and simulated spectra, the ratios of multiple channel-pairs—one weak and one strong absorption channel—are used to retrieve from measurements of the shortwave infrared (SWIR) band. Based on sensitivity tests, a super channel-pair is carefully selected to reduce the effects of solar lines, water vapor, air temperature, pressure, instrument noise, and frequency shift on retrieval errors. The new algorithm reduces computational cost and the retrievals are less sensitive to temperature and H2O uncertainty than the spectral fitting method. Multi-day Total Carbon Column Observing Network (TCCON) measurements under clear-sky conditions at two sites (Tsukuba and Bremen) are used to derive xxxx for the algorithm evaluation and validation. The DOAS-like results agree very well with those of the TCCON algorithm after correction of an airmass-dependent bias.

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

Hyperspectral imaging for cancer surgical margin delineation: registration of hyperspectral and histological images

NASA Astrophysics Data System (ADS)

Lu, Guolan; Halig, Luma; Wang, Dongsheng; Chen, Zhuo G.; Fei, Baowei

2014-03-01

The determination of tumor margins during surgical resection remains a challenging task. A complete removal of malignant tissue and conservation of healthy tissue is important for the preservation of organ function, patient satisfaction, and quality of life. Visual inspection and palpation is not sufficient for discriminating between malignant and normal tissue types. Hyperspectral imaging (HSI) technology has the potential to noninvasively delineate surgical tumor margin and can be used as an intra-operative visual aid tool. Since histological images provide the ground truth of cancer margins, it is necessary to warp the cancer regions in ex vivo histological images back to in vivo hyperspectral images in order to validate the tumor margins detected by HSI and to optimize the imaging parameters. In this paper, principal component analysis (PCA) is utilized to extract the principle component bands of the HSI images, which is then used to register HSI images with the corresponding histological image. Affine registration is chosen to model the global transformation. A B-spline free form deformation (FFD) method is used to model the local non-rigid deformation. Registration experiment was performed on animal hyperspectral and histological images. Experimental results from animals demonstrated the feasibility of the hyperspectral imaging method for cancer margin detection.

Spectral Reconstruction Based on Svm for Cross Calibration

NASA Astrophysics Data System (ADS)

Gao, H.; Ma, Y.; Liu, W.; He, H.

2017-05-01

Chinese HY-1C/1D satellites will use a 5nm/10nm-resolutional visible-near infrared(VNIR) hyperspectral sensor with the solar calibrator to cross-calibrate with other sensors. The hyperspectral radiance data are composed of average radiance in the sensor's passbands and bear a spectral smoothing effect, a transform from the hyperspectral radiance data to the 1-nm-resolution apparent spectral radiance by spectral reconstruction need to be implemented. In order to solve the problem of noise cumulation and deterioration after several times of iteration by the iterative algorithm, a novel regression method based on SVM is proposed, which can approach arbitrary complex non-linear relationship closely and provide with better generalization capability by learning. In the opinion of system, the relationship between the apparent radiance and equivalent radiance is nonlinear mapping introduced by spectral response function(SRF), SVM transform the low-dimensional non-linear question into high-dimensional linear question though kernel function, obtaining global optimal solution by virtue of quadratic form. The experiment is performed using 6S-simulated spectrums considering the SRF and SNR of the hyperspectral sensor, measured reflectance spectrums of water body and different atmosphere conditions. The contrastive result shows: firstly, the proposed method is with more reconstructed accuracy especially to the high-frequency signal; secondly, while the spectral resolution of the hyperspectral sensor reduces, the proposed method performs better than the iterative method; finally, the root mean square relative error(RMSRE) which is used to evaluate the difference of the reconstructed spectrum and the real spectrum over the whole spectral range is calculated, it decreses by one time at least by proposed method.

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.

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.

Integrating High-Throughput Parallel Processing Framework and Storage Area Network Concepts Into a Prototype Interactive Scientific Visualization Environment for Hyperspectral Data

NASA Astrophysics Data System (ADS)

Smuga-Otto, M. J.; Garcia, R. K.; Knuteson, R. O.; Martin, G. D.; Flynn, B. M.; Hackel, D.

2006-12-01

The University of Wisconsin-Madison Space Science and Engineering Center (UW-SSEC) is developing tools to help scientists realize the potential of high spectral resolution instruments for atmospheric science. Upcoming satellite spectrometers like the Cross-track Infrared Sounder (CrIS), experimental instruments like the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) and proposed instruments like the Hyperspectral Environmental Suite (HES) within the GOES-R project will present a challenge in the form of the overwhelmingly large amounts of continuously generated data. Current and near-future workstations will have neither the storage space nor computational capacity to cope with raw spectral data spanning more than a few minutes of observations from these instruments. Schemes exist for processing raw data from hyperspectral instruments currently in testing, that involve distributed computation across clusters. Data, which for an instrument like GIFTS can amount to over 1.5 Terabytes per day, is carefully managed on Storage Area Networks (SANs), with attention paid to proper maintenance of associated metadata. The UW-SSEC is preparing a demonstration integrating these back-end capabilities as part of a larger visualization framework, to assist scientists in developing new products from high spectral data, sourcing data volumes they could not otherwise manage. This demonstration focuses on managing storage so that only the data specifically needed for the desired product are pulled from the SAN, and on running computationally expensive intermediate processing on a back-end cluster, with the final product being sent to a visualization system on the scientist's workstation. Where possible, existing software and solutions are used to reduce cost of development. The heart of the computing component is the GIFTS Information Processing System (GIPS), developed at the UW- SSEC to allow distribution of processing tasks such as conversion of raw GIFTS interferograms into calibrated radiance spectra, and retrieving temperature and water vapor content atmospheric profiles from these spectra. The hope is that by demonstrating the capabilities afforded by a composite system like the one described here, scientists can be convinced to contribute further algorithms in support of this model of computing and visualization.

Quantitative methods and detection techniques in hyperspectral imaging involving medical and other applications

NASA Astrophysics Data System (ADS)

Roy, Ankita

2007-12-01

This research using Hyperspectral imaging involves recognizing targets through spatial and spectral matching and spectral un-mixing of data ranging from remote sensing to medical imaging kernels for clinical studies based on Hyperspectral data-sets generated using the VFTHSI [Visible Fourier Transform Hyperspectral Imager], whose high resolution Si detector makes the analysis achievable. The research may be broadly classified into (I) A Physically Motivated Correlation Formalism (PMCF), which places both spatial and spectral data on an equivalent mathematical footing in the context of a specific Kernel and (II) An application in RF plasma specie detection during carbon nanotube growing process. (III) Hyperspectral analysis for assessing density and distribution of retinopathies like age related macular degeneration (ARMD) and error estimation enabling the early recognition of ARMD, which is treated as an ill-conditioned inverse imaging problem. The broad statistical scopes of this research are two fold-target recognition problems and spectral unmixing problems. All processes involve experimental and computational analysis of Hyperspectral data sets is presented, which is based on the principle of a Sagnac Interferometer, calibrated to obtain high SNR levels. PMCF computes spectral/spatial/cross moments and answers the question of how optimally the entire hypercube should be sampled and finds how many spatial-spectral pixels are required precisely for a particular target recognition. Spectral analysis of RF plasma radicals, typically Methane plasma and Argon plasma using VFTHSI has enabled better process monitoring during growth of vertically aligned multi-walled carbon nanotubes by instant registration of the chemical composition or density changes temporally, which is key since a significant correlation can be found between plasma state and structural properties. A vital focus of this dissertation is towards medical Hyperspectral imaging applied to retinopathies like age related macular degeneration targets taken with a Fundus imager, which is akin to the VFTHSI. Detection of the constituent components in the diseased hyper-pigmentation area is also computed. The target or reflectance matrix is treated as a highly ill-conditioned spectral un-mixing problem, to which methodologies like inverse techniques, principal component analysis (PCA) and receiver operating curves (ROC) for precise spectral recognition of infected area. The region containing ARMD was easily distinguishable from the spectral mesh plots over the entire band-pass area. Once the location was detected the PMCF coefficients were calculated by cross correlating a target of normal oxygenated retina with the deoxygenated one. The ROCs generated using PMCF shows 30% higher detection probability with improved accuracy than ROCs based on Spectral Angle Mapper (SAM). By spectral unmixing methods, the important endmembers/carotenoids of the MD pigment were found to be Xanthophyl and lutein, while beta-carotene which showed a negative correlation in the unconstrained inverse problem is a supplement given to ARMD patients to prevent the disease and does not occur in the eye. Literature also shows degeneration of meso-zeaxanthin. Ophthalmologists may assert the presence of ARMD and commence the diagnosis process if the Xanthophyl pigment have degenerated 89.9%, while the lutein has decayed almost 80%, as found deduced computationally. This piece of current research takes it to the next level of precise investigation in the continuing process of improved clinical findings by correlating the microanatomy of the diseased fovea and shows promise of an early detection of this disease.

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.

Target oriented dimensionality reduction of hyperspectral data by Kernel Fukunaga-Koontz Transform

NASA Astrophysics Data System (ADS)

Binol, Hamidullah; Ochilov, Shuhrat; Alam, Mohammad S.; Bal, Abdullah

2017-02-01

Principal component analysis (PCA) is a popular technique in remote sensing for dimensionality reduction. While PCA is suitable for data compression, it is not necessarily an optimal technique for feature extraction, particularly when the features are exploited in supervised learning applications (Cheriyadat and Bruce, 2003) [1]. Preserving features belonging to the target is very crucial to the performance of target detection/recognition techniques. Fukunaga-Koontz Transform (FKT) based supervised band reduction technique can be used to provide this requirement. FKT achieves feature selection by transforming into a new space in where feature classes have complimentary eigenvectors. Analysis of these eigenvectors under two classes, target and background clutter, can be utilized for target oriented band reduction since each basis functions best represent target class while carrying least information of the background class. By selecting few eigenvectors which are the most relevant to the target class, dimension of hyperspectral data can be reduced and thus, it presents significant advantages for near real time target detection applications. The nonlinear properties of the data can be extracted by kernel approach which provides better target features. Thus, we propose constructing kernel FKT (KFKT) to present target oriented band reduction. The performance of the proposed KFKT based target oriented dimensionality reduction algorithm has been tested employing two real-world hyperspectral data and results have been reported consequently.

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.

Remote sensing of soil organic matter of farmland with hyperspectral image

NASA Astrophysics Data System (ADS)

Gu, Xiaohe; Wang, Lei; Yang, Guijun; Zhang, Liyan

2017-10-01

Monitoring soil organic matter (SOM) of cultivated land quantitively and mastering its spatial change are helpful for fertility adjustment and sustainable development of agriculture. The study aimed to analyze the response between SOM and reflectivity of hyperspectral image with different pixel size and develop the optimal model of estimating SOM with imaging spectral technology. The wavelet transform method was used to analyze the correlation between the hyperspectral reflectivity and SOM. Then the optimal pixel size and sensitive wavelet feature scale were screened to develop the inversion model of SOM. Result showed that wavelet transform of soil hyperspectrum was help to improve the correlation between the wavelet features and SOM. In the visible wavelength range, the susceptible wavelet features of SOM mainly concentrated 460 603 nm. As the wavelength increased, the wavelet scale corresponding correlation coefficient increased maximum and then gradually decreased. In the near infrared wavelength range, the susceptible wavelet features of SOM mainly concentrated 762 882 nm. As the wavelength increased, the wavelet scale gradually decreased. The study developed multivariate model of continuous wavelet transforms by the method of stepwise linear regression (SLR). The CWT-SLR models reached higher accuracies than those of univariate models. With the resampling scale increasing, the accuracies of CWT-SLR models gradually increased, while the determination coefficients (R2) fluctuated from 0.52 to 0.59. The R2 of 5*5 scale reached highest (0.5954), while the RMSE reached lowest (2.41 g/kg). It indicated that multivariate model based on continuous wavelet transform had better ability for estimating SOM than univariate model.

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.

A two-step framework for the registration of HE stained and FTIR images

NASA Astrophysics Data System (ADS)

Peñaranda, Francisco; Naranjo, Valery; Verdú, Rafaél.; Lloyd, Gavin R.; Nallala, Jayakrupakar; Stone, Nick

2016-03-01

FTIR spectroscopy is an emerging technology with high potential for cancer diagnosis but with particular physical phenomena that require special processing. Little work has been done in the field with the aim of registering hyperspectral Fourier-Transform Infrared (FTIR) spectroscopic images and Hematoxilin and Eosin (HE) stained histological images of contiguous slices of tissue. This registration is necessary to transfer the location of relevant structures that the pathologist may identify in the gold standard HE images. A two-step registration framework is presented where a representative gray image extracted from the FTIR hypercube is used as an input. This representative image, which must have a spatial contrast as similar as possible to a gray image obtained from the HE image, is calculated through the spectrum variation in the fingerprint region. In the first step of the registration algorithm a similarity transformation is estimated from interest points, which are automatically detected by the popular SURF algorithm. In the second stage, a variational registration framework defined in the frequency domain compensates for local anatomical variations between both images. After a proper tuning of some parameters the proposed registration framework works in an automated way. The method was tested on 7 samples of colon tissue in different stages of cancer. Very promising qualitative and quantitative results were obtained (a mean correlation ratio of 92.16% with a standard deviation of 3.10%).

An adaptive band selection method for dimension reduction of hyper-spectral remote sensing image

NASA Astrophysics Data System (ADS)

Yu, Zhijie; Yu, Hui; Wang, Chen-sheng

2014-11-01

Hyper-spectral remote sensing data can be acquired by imaging the same area with multiple wavelengths, and it normally consists of hundreds of band-images. Hyper-spectral images can not only provide spatial information but also high resolution spectral information, and it has been widely used in environment monitoring, mineral investigation and military reconnaissance. However, because of the corresponding large data volume, it is very difficult to transmit and store Hyper-spectral images. Hyper-spectral image dimensional reduction technique is desired to resolve this problem. Because of the High relation and high redundancy of the hyper-spectral bands, it is very feasible that applying the dimensional reduction method to compress the data volume. This paper proposed a novel band selection-based dimension reduction method which can adaptively select the bands which contain more information and details. The proposed method is based on the principal component analysis (PCA), and then computes the index corresponding to every band. The indexes obtained are then ranked in order of magnitude from large to small. Based on the threshold, system can adaptively and reasonably select the bands. The proposed method can overcome the shortcomings induced by transform-based dimension reduction method and prevent the original spectral information from being lost. The performance of the proposed method has been validated by implementing several experiments. The experimental results show that the proposed algorithm can reduce the dimensions of hyper-spectral image with little information loss by adaptively selecting the band images.

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.

Observation of SO2 degassing at Stromboli volcano using a hyperspectral thermal infrared imager

NASA Astrophysics Data System (ADS)

Smekens, Jean-François; Gouhier, Mathieu

2018-05-01

Thermal infrared (TIR) imaging is a common tool for the monitoring of volcanic activity. Broadband cameras with increasing sampling frequency give great insight into the physical processes taking place during effusive and explosive event, while Fourier transform infrared (FTIR) methods provide high resolution spectral information used to assess the composition of volcanic gases but are often limited to a single point of interest. Continuing developments in detector technology have given rise to a new class of hyperspectral imagers combining the advantages of both approaches. In this work, we present the results of our observations of volcanic activity at Stromboli volcano with a ground-based imager, the Telops Hyper-Cam LW, when used to detect emissions of sulfur dioxide (SO2) produced at the vent, with data acquired at Stromboli volcano (Italy) in early October of 2015. We have developed an innovative technique based on a curve-fitting algorithm to quickly extract spectral information from high-resolution datasets, allowing fast and reliable identification of SO2. We show in particular that weak SO2 emissions, such as inter-eruptive gas puffing, can be easily detected using this technology, even with poor weather conditions during acquisition (e.g., high relative humidity, presence of fog and/or ash). Then, artificially reducing the spectral resolution of the instrument, we recreated a variety of commonly used multispectral configurations to examine the efficiency of four qualitative SO2 indicators based on simple Brightness Temperature Difference (BTD). Our results show that quickly changing conditions at the vent - including but not limited to the presence of summit fog - render the establishment of meaningful thresholds for BTD indicators difficult. Building on those results, we propose recommendations on the use of multispectral imaging for SO2 monitoring and routine measurements from ground-based instruments.

Prediction of sweetness and amino acid content in soybean crops from hyperspectral imagery

NASA Astrophysics Data System (ADS)

Monteiro, Sildomar Takahashi; Minekawa, Yohei; Kosugi, Yukio; Akazawa, Tsuneya; Oda, Kunio

Hyperspectral image data provides a powerful tool for non-destructive crop analysis. This paper investigates a hyperspectral image data-processing method to predict the sweetness and amino acid content of soybean crops. Regression models based on artificial neural networks were developed in order to calculate the level of sucrose, glucose, fructose, and nitrogen concentrations, which can be related to the sweetness and amino acid content of vegetables. A performance analysis was conducted comparing regression models obtained using different preprocessing methods, namely, raw reflectance, second derivative, and principal components analysis. This method is demonstrated using high-resolution hyperspectral data of wavelengths ranging from the visible to the near infrared acquired from an experimental field of green vegetable soybeans. The best predictions were achieved using a nonlinear regression model of the second derivative transformed dataset. Glucose could be predicted with greater accuracy, followed by sucrose, fructose and nitrogen. The proposed method provides the possibility to provide relatively accurate maps predicting the chemical content of soybean crop fields.

Hyperspectral imaging of water quality - past applications and future directions.

NASA Astrophysics Data System (ADS)

Ross, M. R. V.; Pavelsky, T.

2017-12-01

Inland waters control the delivery of sediment, carbon, and nutrients from land to ocean by transforming, depositing, and transporting constituents downstream. However, the dominant in situ conditions that control these processes are poorly constrained, especially at larger spatial scales. Hyperspectral imaging, a remote sensing technique that uses reflectance in hundreds of narrow spectral bands, can be used to estimate water quality parameters like sediment and carbon concentration over larger water bodies. Here, we review methods and applications for using hyperspectral imagery to generate near-surface two-dimensional models of water quality in lakes and rivers. Further, we show applications using newly available data from the National Ecological Observation Network aerial observation platform in the Black Warrior and Tombigbee Rivers, Alabama. We demonstrate large spatial variation in chlorophyll, colored dissolved organic matter, and turbidity in each river and uneven mixing of water quality constituents for several kilometers. Finally, we demonstrate some novel techniques using hyperspectral imagery to deconvolve dissolved organic matter spectral signatures to specific organic matter components.

Real-Time Noise Removal for Line-Scanning Hyperspectral Devices Using a Minimum Noise Fraction-Based Approach

PubMed Central

Bjorgan, Asgeir; Randeberg, Lise Lyngsnes

2015-01-01

Processing line-by-line and in real-time can be convenient for some applications of line-scanning hyperspectral imaging technology. Some types of processing, like inverse modeling and spectral analysis, can be sensitive to noise. The MNF (minimum noise fraction) transform provides suitable denoising performance, but requires full image availability for the estimation of image and noise statistics. In this work, a modified algorithm is proposed. Incrementally-updated statistics enables the algorithm to denoise the image line-by-line. The denoising performance has been compared to conventional MNF and found to be equal. With a satisfying denoising performance and real-time implementation, the developed algorithm can denoise line-scanned hyperspectral images in real-time. The elimination of waiting time before denoised data are available is an important step towards real-time visualization of processed hyperspectral data. The source code can be found at http://www.github.com/ntnu-bioopt/mnf. This includes an implementation of conventional MNF denoising. PMID:25654717

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

Analysis of hyperspectral fluorescence images for poultry skin tumor inspection

NASA Astrophysics Data System (ADS)

Kong, Seong G.; Chen, Yud-Ren; Kim, Intaek; Kim, Moon S.

2004-02-01

We present a hyperspectral fluorescence imaging system with a fuzzy inference scheme for detecting skin tumors on poultry carcasses. Hyperspectral images reveal spatial and spectral information useful for finding pathological lesions or contaminants on agricultural products. Skin tumors are not obvious because the visual signature appears as a shape distortion rather than a discoloration. Fluorescence imaging allows the visualization of poultry skin tumors more easily than reflectance. The hyperspectral image samples obtained for this poultry tumor inspection contain 65 spectral bands of fluorescence in the visible region of the spectrum at wavelengths ranging from 425 to 711 nm. The large amount of hyperspectral image data is compressed by use of a discrete wavelet transform in the spatial domain. Principal-component analysis provides an effective compressed representation of the spectral signal of each pixel in the spectral domain. A small number of significant features are extracted from two major spectral peaks of relative fluorescence intensity that have been identified as meaningful spectral bands for detecting tumors. A fuzzy inference scheme that uses a small number of fuzzy rules and Gaussian membership functions successfully detects skin tumors on poultry carcasses. Spatial-filtering techniques are used to significantly reduce false positives.

Properties of the giant H II regions and bar in the nearby spiral galaxy NGC 5430

NASA Astrophysics Data System (ADS)

Brière, É.; Cantin, S.; Spekkens, K.

2012-09-01

In order to better understand the impact of the bar on the evolution of spiral galaxies, we measure the properties of giant H II regions and the bar in the SB(s)b galaxy NGC 5430. We use two complementary data sets, both obtained at the Observatoire du Mont-Mégantic: a hyperspectral data cube from the imaging Fourier transform spectrograph SpIOMM (Spectromètre-Imageur à transformée de Fourier de l-Observatoire du Mont-Mégantic) and high-resolution spectra across the bar from a long-slit spectrograph. We flux-calibrate SpIOMM spectra for the first time, and produce Hα and [N II]λ6584 Å intensity maps from which we identify 51 giant H II regions in the spiral arms and bar. We evaluate the type of activity, the oxygen abundance and the age of the young populations contained in these giant H II regions and in the bar. Thus, we confirm that NGC 5430 does not harbour a strong active galactic nucleus, and that its Wolf-Rayet knot shows a pure H II region nature. We find no variation in abundance or age between the bar and spiral arms, nor as a function of galactocentric radius. These results are consistent with the hypothesis that a chemical mixing mechanism is at work in the galaxy's disc to flatten the oxygen abundance gradient. Using the STARBURST99 model, we estimate the ages of the young populations, and again find no variations in age between the bar and the arms or as a function of radius. Instead, we find evidence for two galaxy-wide waves of star formation, about 7.1 and 10.5 Myr ago. While the bar in NGC 5430 is an obvious candidate to trigger these two episodes, it is not clear how the bar could induce widespread star formation on such a short time-scale.

Linear and Nonlinear Molecular Spectroscopy with Laser Frequency Combs

NASA Astrophysics Data System (ADS)

Picque, Nathalie

2013-06-01

The regular pulse train of a mode-locked femtosecond laser can give rise to a comb spectrum of millions of laser modes with a spacing precisely equal to the pulse repetition frequency. Laser frequency combs were conceived a decade ago as tools for the precision spectroscopy of atomic hydrogen. They are now becoming enabling tools for an increasing number of applications, including molecular spectroscopy. Recent experiments of multi-heterodyne frequency comb Fourier transform spectroscopy (also called dual-comb spectroscopy) have demonstrated that the precisely spaced spectral lines of a laser frequency comb can be harnessed for new techniques of linear absorption spectroscopy. The first proof-of-principle experiments have demonstrated a very exciting potential of dual-comb spectroscopy without moving parts for ultra-rapid and ultra-sensitive recording of complex broad spectral bandwidth molecular spectra. Compared to conventional Michelson-based Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds, with intriguing prospects for spectroscopy of short lived transient species. The resolution improves proportionally to the measurement time. Therefore longer recordings allow high resolution spectroscopy of molecules with extreme precision, since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock. Moreover, since laser frequency combs involve intense ultrashort laser pulses, nonlinear interactions can be harnessed. Broad spectral bandwidth ultra-rapid nonlinear molecular spectroscopy and imaging with two laser frequency combs is demonstrated with coherent Raman effects and two-photon excitation. Real-time multiplex accessing of hyperspectral images may dramatically expand the range of applications of nonlinear microscopy. B. Bernhardt et al., Nature Photonics 4, 55-57 (2010); A. Schliesser et al. Nature Photonics 6, 440-449 (2012); T. Ideguchi et al. arXiv:1201.4177 (2012) T. Ideguchi et al., Optics letters 37, 4498-4500 (2012); T. Ideguchi et al. arXiv:1302.2414 (2013)

Simultaneous Spectral-Spatial Feature Selection and Extraction for Hyperspectral Images.

PubMed

Zhang, Lefei; Zhang, Qian; Du, Bo; Huang, Xin; Tang, Yuan Yan; Tao, Dacheng

2018-01-01

In hyperspectral remote sensing data mining, it is important to take into account of both spectral and spatial information, such as the spectral signature, texture feature, and morphological property, to improve the performances, e.g., the image classification accuracy. In a feature representation point of view, a nature approach to handle this situation is to concatenate the spectral and spatial features into a single but high dimensional vector and then apply a certain dimension reduction technique directly on that concatenated vector before feed it into the subsequent classifier. However, multiple features from various domains definitely have different physical meanings and statistical properties, and thus such concatenation has not efficiently explore the complementary properties among different features, which should benefit for boost the feature discriminability. Furthermore, it is also difficult to interpret the transformed results of the concatenated vector. Consequently, finding a physically meaningful consensus low dimensional feature representation of original multiple features is still a challenging task. In order to address these issues, we propose a novel feature learning framework, i.e., the simultaneous spectral-spatial feature selection and extraction algorithm, for hyperspectral images spectral-spatial feature representation and classification. Specifically, the proposed method learns a latent low dimensional subspace by projecting the spectral-spatial feature into a common feature space, where the complementary information has been effectively exploited, and simultaneously, only the most significant original features have been transformed. Encouraging experimental results on three public available hyperspectral remote sensing datasets confirm that our proposed method is effective and efficient.

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...

ICER-3D Hyperspectral Image Compression Software

NASA Technical Reports Server (NTRS)

Xie, Hua; Kiely, Aaron; Klimesh, matthew; Aranki, Nazeeh

2010-01-01

Software has been developed to implement the ICER-3D algorithm. ICER-3D effects progressive, three-dimensional (3D), wavelet-based compression of hyperspectral images. If a compressed data stream is truncated, the progressive nature of the algorithm enables reconstruction of hyperspectral data at fidelity commensurate with the given data volume. The ICER-3D software is capable of providing either lossless or lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The compression algorithm, which was derived from the ICER image compression algorithm, includes wavelet-transform, context-modeling, and entropy coding subalgorithms. The 3D wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of sets of hyperspectral image data, while facilitating elimination of spectral ringing artifacts, using a technique summarized in "Improving 3D Wavelet-Based Compression of Spectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. Correlation is further exploited by a context-modeling subalgorithm, which exploits spectral dependencies in the wavelet-transformed hyperspectral data, using an algorithm that is summarized in "Context Modeler for Wavelet Compression of Hyperspectral Images" (NPO-43239), which follows this article. An important feature of ICER-3D is a scheme for limiting the adverse effects of loss of data during transmission. In this scheme, as in the similar scheme used by ICER, the spatial-frequency domain is partitioned into rectangular error-containment regions. In ICER-3D, the partitions extend through all the wavelength bands. The data in each partition are compressed independently of those in the other partitions, so that loss or corruption of data from any partition does not affect the other partitions. Furthermore, because compression is progressive within each partition, when data are lost, any data from that partition received prior to the loss can be used to reconstruct that partition at lower fidelity. By virtue of the compression improvement it achieves relative to previous means of onboard data compression, this software enables (1) increased return of hyperspectral scientific data in the presence of limits on the rates of transmission of data from spacecraft to Earth via radio communication links and/or (2) reduction in spacecraft radio-communication power and/or cost through reduction in the amounts of data required to be downlinked and stored onboard prior to downlink. The software is also suitable for compressing hyperspectral images for ground storage or archival purposes.

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.

Quantum computation in the analysis of hyperspectral data

NASA Astrophysics Data System (ADS)

Gomez, Richard B.; Ghoshal, Debabrata; Jayanna, Anil

2004-08-01

Recent research on the topic of quantum computation provides us with some quantum algorithms with higher efficiency and speedup compared to their classical counterparts. In this paper, it is our intent to provide the results of our investigation of several applications of such quantum algorithms - especially the Grover's Search algorithm - in the analysis of Hyperspectral Data. We found many parallels with Grover's method in existing data processing work that make use of classical spectral matching algorithms. Our efforts also included the study of several methods dealing with hyperspectral image analysis work where classical computation methods involving large data sets could be replaced with quantum computation methods. The crux of the problem in computation involving a hyperspectral image data cube is to convert the large amount of data in high dimensional space to real information. Currently, using the classical model, different time consuming methods and steps are necessary to analyze these data including: Animation, Minimum Noise Fraction Transform, Pixel Purity Index algorithm, N-dimensional scatter plot, Identification of Endmember spectra - are such steps. If a quantum model of computation involving hyperspectral image data can be developed and formalized - it is highly likely that information retrieval from hyperspectral image data cubes would be a much easier process and the final information content would be much more meaningful and timely. In this case, dimensionality would not be a curse, but a blessing.

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.

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.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

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.

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.

Parallel ICA and its hardware implementation in hyperspectral image analysis

NASA Astrophysics Data System (ADS)

Du, Hongtao; Qi, Hairong; Peterson, Gregory D.

2004-04-01

Advances in hyperspectral images have dramatically boosted remote sensing applications by providing abundant information using hundreds of contiguous spectral bands. However, the high volume of information also results in excessive computation burden. Since most materials have specific characteristics only at certain bands, a lot of these information is redundant. This property of hyperspectral images has motivated many researchers to study various dimensionality reduction algorithms, including Projection Pursuit (PP), Principal Component Analysis (PCA), wavelet transform, and Independent Component Analysis (ICA), where ICA is one of the most popular techniques. It searches for a linear or nonlinear transformation which minimizes the statistical dependence between spectral bands. Through this process, ICA can eliminate superfluous but retain practical information given only the observations of hyperspectral images. One hurdle of applying ICA in hyperspectral image (HSI) analysis, however, is its long computation time, especially for high volume hyperspectral data sets. Even the most efficient method, FastICA, is a very time-consuming process. In this paper, we present a parallel ICA (pICA) algorithm derived from FastICA. During the unmixing process, pICA divides the estimation of weight matrix into sub-processes which can be conducted in parallel on multiple processors. The decorrelation process is decomposed into the internal decorrelation and the external decorrelation, which perform weight vector decorrelations within individual processors and between cooperative processors, respectively. In order to further improve the performance of pICA, we seek hardware solutions in the implementation of pICA. Until now, there are very few hardware designs for ICA-related processes due to the complicated and iterant computation. This paper discusses capacity limitation of FPGA implementations for pICA in HSI analysis. A synthesis of Application-Specific Integrated Circuit (ASIC) is designed for pICA-based dimensionality reduction in HSI analysis. The pICA design is implemented using standard-height cells and aimed at TSMC 0.18 micron process. During the synthesis procedure, three ICA-related reconfigurable components are developed for the reuse and retargeting purpose. Preliminary results show that the standard-height cell based ASIC synthesis provide an effective solution for pICA and ICA-related processes in HSI analysis.

Toward Improved Hyperspectral Analysis in Semiarid Systems

NASA Astrophysics Data System (ADS)

Glenn, N. F.; Mitchell, J.

2012-12-01

Idaho State University's Boise Center Aerospace Laboratory (BCAL) has processed and applied hyperspectral data for a variety of biophysical sciences in semiarid systems over the past 10 years. HyMap hyperspectral data have been used in most of these studies, along with AVIRIS, CASI, and PIKA-II data. Our studies began with the detection of individual weed species, such as leafy spurge, corroborated with extensive field analysis, including spectrometer data. Early contributions to the field of hyperspectral analysis included the use of: time-series datasets and classification threshold methods for target detection, and subpixel analysis for characterizing weed invasions and post-fire vegetation and soil conditions. Subsequent studies optimized subpixel unmixing performance using spectral subsetting and vegetation abundance investigations. More recent studies have extended the application of hyperspectral data from individual plant species detection to identification of biochemical constituents. We demonstrated field and airborne hyperspectral Nitrogen absorption in sagebrush using combinations of data reduction and spectral transformation techniques (i.e., continuum removal, derivative analysis, partial least squares regression). In spite of these and many other successful demonstrations, gaps still exist in effective species level discrimination due to the high complexity of soil and nonlinear mixing in semiarid shrubland. BCAL studies are currently focusing on complimenting narrowband vegetation indices with LiDAR (light detection and ranging, both airborne and ground-based) derivatives to improve vegetation cover predictions. Future combinations of LiDAR and hyperspectral data will involve exploring the full range spectral information and serve as an integral step in scaling shrub biomass estimates from plot to landscape and regional scales.

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...

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

New algorithm for lossless hyper-spectral image compression with mixing transform to eliminate redundancy

NASA Astrophysics Data System (ADS)

Xie, ChengJun; Xu, Lin

2008-03-01

This paper presents a new algorithm based on mixing transform to eliminate redundancy, SHIRCT and subtraction mixing transform is used to eliminate spectral redundancy, 2D-CDF(2,2)DWT to eliminate spatial redundancy, This transform has priority in hardware realization convenience, since it can be fully implemented by add and shift operation. Its redundancy elimination effect is better than (1D+2D)CDF(2,2)DWT. Here improved SPIHT+CABAC mixing compression coding algorithm is used to implement compression coding. The experiment results show that in lossless image compression applications the effect of this method is a little better than the result acquired using (1D+2D)CDF(2,2)DWT+improved SPIHT+CABAC, still it is much better than the results acquired by JPEG-LS, WinZip, ARJ, DPCM, the research achievements of a research team of Chinese Academy of Sciences, NMST and MST. Using hyper-spectral image Canal of American JPL laboratory as the data set for lossless compression test, on the average the compression ratio of this algorithm exceeds the above algorithms by 42%,37%,35%,30%,16%,13%,11% respectively.

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

Hyperspectral and LiDAR remote sensing of fire fuels in Hawaii Volcanoes National Park.

PubMed

Varga, Timothy A; Asner, Gregory P

2008-04-01

Alien invasive grasses threaten to transform Hawaiian ecosystems through the alteration of ecosystem dynamics, especially the creation or intensification of a fire cycle. Across sub-montane ecosystems of Hawaii Volcanoes National Park on Hawaii Island, we quantified fine fuels and fire spread potential of invasive grasses using a combination of airborne hyperspectral and light detection and ranging (LiDAR) measurements. Across a gradient from forest to savanna to shrubland, automated mixture analysis of hyperspectral data provided spatially explicit fractional cover estimates of photosynthetic vegetation, non-photosynthetic vegetation, and bare substrate and shade. Small-footprint LiDAR provided measurements of vegetation height along this gradient of ecosystems. Through the fusion of hyperspectral and LiDAR data, a new fire fuel index (FFI) was developed to model the three-dimensional volume of grass fuels. Regionally, savanna ecosystems had the highest volumes of fire fuels, averaging 20% across the ecosystem and frequently filling all of the three-dimensional space represented by each image pixel. The forest and shrubland ecosystems had lower FFI values, averaging 4.4% and 8.4%, respectively. The results indicate that the fusion of hyperspectral and LiDAR remote sensing can provide unique information on the three-dimensional properties of ecosystems, their flammability, and the potential for fire spread.

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.

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.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, Charles L.

1996-01-01

An imaging Fourier transform spectrometer (10, 210) having a Fourier transform infrared spectrometer (12) providing a series of images (40) to a focal plane array camera (38). The focal plane array camera (38) is clocked to a multiple of zero crossing occurrences as caused by a moving mirror (18) of the Fourier transform infrared spectrometer (12) and as detected by a laser detector (50) such that the frame capture rate of the focal plane array camera (38) corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer (12). The images (40) are transmitted to a computer (45) for processing such that representations of the images (40) as viewed in the light of an arbitrary spectral "fingerprint" pattern can be displayed on a monitor (60) or otherwise stored and manipulated by the computer (45).

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.

Nondestructive detection of total viable count changes of chilled pork in high oxygen storage condition based on hyperspectral technology

NASA Astrophysics Data System (ADS)

Zheng, Xiaochun; Peng, Yankun; Li, Yongyu; Chao, Kuanglin; Qin, Jianwei

2017-05-01

The plate count method is commonly used to detect the total viable count (TVC) of bacteria in pork, which is timeconsuming and destructive. It has also been used to study the changes of the TVC in pork under different storage conditions. In recent years, many scholars have explored the non-destructive methods on detecting TVC by using visible near infrared (VIS/NIR) technology and hyperspectral technology. The TVC in chilled pork was monitored under high oxygen condition in this study by using hyperspectral technology in order to evaluate the changes of total bacterial count during storage, and then evaluate advantages and disadvantages of the storage condition. The VIS/NIR hyperspectral images of samples stored in high oxygen condition was acquired by a hyperspectral system in range of 400 1100nm. The actual reference value of total bacteria was measured by standard plate count method, and the results were obtained in 48 hours. The reflection spectra of the samples are extracted and used for the establishment of prediction model for TVC. The spectral preprocessing methods of standard normal variate transformation (SNV), multiple scatter correction (MSC) and derivation was conducted to the original reflectance spectra of samples. Partial least squares regression (PLSR) of TVC was performed and optimized to be the prediction model. The results show that the near infrared hyperspectral technology based on 400-1100nm combined with PLSR model can describe the growth pattern of the total bacteria count of the chilled pork under the condition of high oxygen very vividly and rapidly. The results obtained in this study demonstrate that the nondestructive method of TVC based on NIR hyperspectral has great potential in monitoring of edible safety in processing and storage of meat.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

PubMed

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

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.

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.

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.

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.

Fourier transform spectroscopy of cotton and cotton trash

USDA-ARS?s Scientific Manuscript database

Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...

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...

Forest tree species clssification based on airborne hyper-spectral imagery

NASA Astrophysics Data System (ADS)

Dian, Yuanyong; Li, Zengyuan; Pang, Yong

2013-10-01

Forest precision classification products were the basic data for surveying of forest resource, updating forest subplot information, logging and design of forest. However, due to the diversity of stand structure, complexity of the forest growth environment, it's difficult to discriminate forest tree species using multi-spectral image. The airborne hyperspectral images can achieve the high spatial and spectral resolution imagery of forest canopy, so it will good for tree species level classification. The aim of this paper was to test the effective of combining spatial and spectral features in airborne hyper-spectral image classification. The CASI hyper spectral image data were acquired from Liangshui natural reserves area. Firstly, we use the MNF (minimum noise fraction) transform method for to reduce the hyperspectral image dimensionality and highlighting variation. And secondly, we use the grey level co-occurrence matrix (GLCM) to extract the texture features of forest tree canopy from the hyper-spectral image, and thirdly we fused the texture and the spectral features of forest canopy to classify the trees species using support vector machine (SVM) with different kernel functions. The results showed that when using the SVM classifier, MNF and texture-based features combined with linear kernel function can achieve the best overall accuracy which was 85.92%. It was also confirm that combine the spatial and spectral information can improve the accuracy of tree species classification.

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.

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...

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.

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.

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.

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

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

Target Transformation Constrained Sparse Unmixing (ttcsu) Algorithm for Retrieving Hydrous Minerals on Mars: Application to Southwest Melas Chasma

NASA Astrophysics Data System (ADS)

Lin, H.; Zhang, X.; Wu, X.; Tarnas, J. D.; Mustard, J. F.

2018-04-01

Quantitative analysis of hydrated minerals from hyperspectral remote sensing data is fundamental for understanding Martian geologic process. Because of the difficulties for selecting endmembers from hyperspectral images, a sparse unmixing algorithm has been proposed to be applied to CRISM data on Mars. However, it's challenge when the endmember library increases dramatically. Here, we proposed a new methodology termed Target Transformation Constrained Sparse Unmixing (TTCSU) to accurately detect hydrous minerals on Mars. A new version of target transformation technique proposed in our recent work was used to obtain the potential detections from CRISM data. Sparse unmixing constrained with these detections as prior information was applied to CRISM single-scattering albedo images, which were calculated using a Hapke radiative transfer model. This methodology increases success rate of the automatic endmember selection of sparse unmixing and could get more accurate abundances. CRISM images with well analyzed in Southwest Melas Chasma was used to validate our methodology in this study. The sulfates jarosite was detected from Southwest Melas Chasma, the distribution is consistent with previous work and the abundance is comparable. More validations will be done in our future work.

[Mahalanobis distance based hyperspectral characteristic discrimination of leaves of different desert tree species].

PubMed

Lin, Hai-jun; Zhang, Hui-fang; Gao, Ya-qi; Li, Xia; Yang, Fan; Zhou, Yan-fei

2014-12-01

The hyperspectral reflectance of Populus euphratica, Tamarix hispida, Haloxylon ammodendron and Calligonum mongolicum in the lower reaches of Tarim River and Turpan Desert Botanical Garden was measured by using the HR-768 field-portable spectroradiometer. The method of continuum removal, first derivative reflectance and second derivative reflectance were used to deal with the original spectral data of four tree species. The method of Mahalanobis Distance was used to select the bands with significant differences in the original spectral data and transform spectral data to identify the different tree species. The progressive discrimination analyses were used to test the selective bands used to identify different tree species. The results showed that The Mahalanobis Distance method was an effective method in feature band extraction. The bands for identifying different tree species were most near-infrared bands. The recognition accuracy of four methods was 85%, 93.8%, 92.4% and 95.5% respectively. Spectrum transform could improve the recognition accuracy. The recognition accuracy of different research objects and different spectrum transform methods were different. The research provided evidence for desert tree species classification, monitoring biodiversity and the analysis of area in desert by using large scale remote sensing method.

Feature Transformation Detection Method with Best Spectral Band Selection Process for Hyper-spectral Imaging

NASA Astrophysics Data System (ADS)

Chen, Hai-Wen; McGurr, Mike; Brickhouse, Mark

2015-11-01

We present a newly developed feature transformation (FT) detection method for hyper-spectral imagery (HSI) sensors. In essence, the FT method, by transforming the original features (spectral bands) to a different feature domain, may considerably increase the statistical separation between the target and background probability density functions, and thus may significantly improve the target detection and identification performance, as evidenced by the test results in this paper. We show that by differentiating the original spectral, one can completely separate targets from the background using a single spectral band, leading to perfect detection results. In addition, we have proposed an automated best spectral band selection process with a double-threshold scheme that can rank the available spectral bands from the best to the worst for target detection. Finally, we have also proposed an automated cross-spectrum fusion process to further improve the detection performance in lower spectral range (<1000 nm) by selecting the best spectral band pair with multivariate analysis. Promising detection performance has been achieved using a small background material signature library for concept-proving, and has then been further evaluated and verified using a real background HSI scene collected by a HYDICE sensor.

Hyperspectral imaging for the detection of retinal disease

NASA Astrophysics Data System (ADS)

Harvey, Andrew R.; Lawlor, Joanne; McNaught, Andrew I.; Williams, John W.; Fletcher-Holmes, David W.

2002-11-01

Hyperspectral imaging (HSI) shows great promise for the detection and classification of several diseases, particularly in the fields of "optical biopsy" as applied to oncology, and functional retinal imaging in ophthalmology. In this paper, we discuss the application of HSI to the detection of retinal diseases and technological solutions that address some of the fundamental difficulties of spectral imaging within the eye. HSI of the retina offers a route to non-invasively deduce biochemical and metabolic processes within the retina. For example it shows promise for the mapping of retinal blood perfusion using spectral signatures of oxygenated and deoxygenated hemoglobin. Compared with other techniques using just a few spectral measurements, it offers improved classification in the presence of spectral cross-contamination by pigments and other components within the retina. There are potential applications for this imaging technique in the investigation and treatment of the eye complications of diabetes, and other diseases involving disturbances to the retinal, or optic-nerve-head circulation. It is well known that high-performance HSI requires high signal-to-noise ratios (SNR) whereas the application of any imaging technique within the eye must cope with the twin limitations of the small numerical aperture provided by the entrance pupil to the eye and the limit on the radiant power at the retina. We advocate the use of spectrally-multiplexed spectral imaging techniques (the traditional filter wheel is a traditional example). These approaches enable a flexible approach to spectral imaging, with wider spectral range, higher SNRs and lower light intensity at the retina than could be achieved using a Fourier-transform (FT) approach. We report the use of spectral imaging to provide calibrated spectral albedo images of healthy and diseased retinas and the use of this data for screening purposes. These images clearly demonstrate the ability to distinguish between oxygenated and deoxygenated hemoglobin using spectral imaging and this shows promise for the early detection of various retinopathies.

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.

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 investigation of the bio-oil produced by hydrothermal liquefaction of Spirulina platensis using ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Kostyukevich, Yury; Vlaskin, Mikhail; Vladimirov, Gleb; Zherebker, Alexander; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2017-04-01

We report the investigation of the hydrothermal liquefaction products of the Spirulina platensis microalgae by using the Fourier transform ion cyclotron resonance mass spectrometry. The hydrothermal liquefaction produced two fractions: one with boiling temperature below 300℃ and the dense residue that remained in the reactor. It was observed that N 2 and N classes of compounds that dominate in the positive ESI Fourier transform ion cyclotron resonance spectra for both fractions, and that the light fraction is considerably more saturated then the heavy one. The performed hydrogen/deuterium exchange reaction indicated the presence of the onium compounds in the bio-oil.

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.

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.

Object-based habitat mapping using very high spatial resolution multispectral and hyperspectral imagery with LiDAR data

NASA Astrophysics Data System (ADS)

Onojeghuo, Alex Okiemute; Onojeghuo, Ajoke Ruth

2017-07-01

This study investigated the combined use of multispectral/hyperspectral imagery and LiDAR data for habitat mapping across parts of south Cumbria, North West England. The methodology adopted in this study integrated spectral information contained in pansharp QuickBird multispectral/AISA Eagle hyperspectral imagery and LiDAR-derived measures with object-based machine learning classifiers and ensemble analysis techniques. Using the LiDAR point cloud data, elevation models (such as the Digital Surface Model and Digital Terrain Model raster) and intensity features were extracted directly. The LiDAR-derived measures exploited in this study included Canopy Height Model, intensity and topographic information (i.e. mean, maximum and standard deviation). These three LiDAR measures were combined with spectral information contained in the pansharp QuickBird and Eagle MNF transformed imagery for image classification experiments. A fusion of pansharp QuickBird multispectral and Eagle MNF hyperspectral imagery with all LiDAR-derived measures generated the best classification accuracies, 89.8 and 92.6% respectively. These results were generated with the Support Vector Machine and Random Forest machine learning algorithms respectively. The ensemble analysis of all three learning machine classifiers for the pansharp QuickBird and Eagle MNF fused data outputs did not significantly increase the overall classification accuracy. Results of the study demonstrate the potential of combining either very high spatial resolution multispectral or hyperspectral imagery with LiDAR data for habitat mapping.

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.

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.

A technique for phase correction in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

Artsang, P.; Pongchalee, P.; Palawong, K.; Buisset, C.; Meemon, P.

2018-03-01

Fourier transform spectroscopy (FTS) is a type of spectroscopy that can be used to analyze components in the sample. The basic setup that is commonly used in this technique is "Michelson interferometer". The interference signal obtained from interferometer can be Fourier transformed into the spectral pattern of the illuminating light source. To experimentally study the concept of the Fourier transform spectroscopy, the project started by setup the Michelson interferometer in the laboratory. The implemented system used a broadband light source in near infrared region (0.81-0.89 μm) and controlled the movable mirror by using computer controlled motorized translation stage. In the early study, there is no sample the interference path. Therefore, the theoretical spectral results after the Fourier transformation of the captured interferogram must be the spectral shape of the light source. One main challenge of the FTS is to retrieve the correct phase information of the inferferogram that relates with the correct spectral shape of the light source. One main source of the phase distortion in FTS that we observed from our system is the non-linear movement of the movable reference mirror of the Michelson interferometer. Therefore, to improve the result, we coupled a monochromatic light source to the implemented interferometer. We simultaneously measured the interferograms of the monochromatic and broadband light sources. The interferogram of the monochromatic light source was used to correct the phase of the interferogram of the broadband light source. The result shows significant improvement in the computed spectral shape.

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.

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.

Wide spectral-range imaging spectroscopy of photonic crystal microbeads for multiplex biomolecular assay applications

NASA Astrophysics Data System (ADS)

Li, Jianping

2014-05-01

Suspension assay using optically color-encoded microbeads is a novel way to increase the reaction speed and multiplex of biomolecular detection and analysis. To boost the detection speed, a hyperspectral imaging (HSI) system is of great interest for quickly decoding the color codes of the microcarriers. Imaging Fourier transform spectrometer (IFTS) is a potential candidate for this task due to its advantages in HSI measurement. However, conventional IFTS is only popular in IR spectral bands because it is easier to track its scanning mirror position in longer wavelengths so that the fundamental Nyquist criterion can be satisfied when sampling the interferograms; the sampling mechanism for shorter wavelengths IFTS used to be very sophisticated, high-cost and bulky. In order to overcome this handicap and take better usage of its advantages for HSI applications, a new wide spectral range IFTS platform is proposed based on an optical beam-folding position-tracking technique. This simple technique has successfully extended the spectral range of an IFTS to cover 350-1000nm. Test results prove that the system has achieved good spectral and spatial resolving performances with instrumentation flexibilities. Accurate and fast measurement results on novel colloidal photonic crystal microbeads also demonstrate its practical potential for high-throughput and multiplex suspension molecular assays.

Principal Component-Based Radiative Transfer Model (PCRTM) for Hyperspectral Sensors. Part I; Theoretical Concept

NASA Technical Reports Server (NTRS)

Liu, Xu; Smith, William L.; Zhou, Daniel K.; Larar, Allen

2005-01-01

Modern infrared satellite sensors such as Atmospheric Infrared Sounder (AIRS), Cosmic Ray Isotope Spectrometer (CrIS), Thermal Emission Spectrometer (TES), Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) and Infrared Atmospheric Sounding Interferometer (IASI) are capable of providing high spatial and spectral resolution infrared spectra. To fully exploit the vast amount of spectral information from these instruments, super fast radiative transfer models are needed. This paper presents a novel radiative transfer model based on principal component analysis. Instead of predicting channel radiance or transmittance spectra directly, the Principal Component-based Radiative Transfer Model (PCRTM) predicts the Principal Component (PC) scores of these quantities. This prediction ability leads to significant savings in computational time. The parameterization of the PCRTM model is derived from properties of PC scores and instrument line shape functions. The PCRTM is very accurate and flexible. Due to its high speed and compressed spectral information format, it has great potential for super fast one-dimensional physical retrievals and for Numerical Weather Prediction (NWP) large volume radiance data assimilation applications. The model has been successfully developed for the National Polar-orbiting Operational Environmental Satellite System Airborne Sounder Testbed - Interferometer (NAST-I) and AIRS instruments. The PCRTM model performs monochromatic radiative transfer calculations and is able to include multiple scattering calculations to account for clouds and aerosols.

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

Data Field Modeling and Spectral-Spatial Feature Fusion for Hyperspectral Data Classification.

PubMed

Liu, Da; Li, Jianxun

2016-12-16

Classification is a significant subject in hyperspectral remote sensing image processing. This study proposes a spectral-spatial feature fusion algorithm for the classification of hyperspectral images (HSI). Unlike existing spectral-spatial classification methods, the influences and interactions of the surroundings on each measured pixel were taken into consideration in this paper. Data field theory was employed as the mathematical realization of the field theory concept in physics, and both the spectral and spatial domains of HSI were considered as data fields. Therefore, the inherent dependency of interacting pixels was modeled. Using data field modeling, spatial and spectral features were transformed into a unified radiation form and further fused into a new feature by using a linear model. In contrast to the current spectral-spatial classification methods, which usually simply stack spectral and spatial features together, the proposed method builds the inner connection between the spectral and spatial features, and explores the hidden information that contributed to classification. Therefore, new information is included for classification. The final classification result was obtained using a random forest (RF) classifier. The proposed method was tested with the University of Pavia and Indian Pines, two well-known standard hyperspectral datasets. The experimental results demonstrate that the proposed method has higher classification accuracies than those obtained by the traditional approaches.

A Field Portable Hyperspectral Goniometer for Coastal Characterization

NASA Technical Reports Server (NTRS)

Bachmann, Charles M.; Gray, Deric; Abelev, Andrei; Philpot, William; Fusina, Robert A.; Musser, Joseph A.; Vermillion, Michael; Doctor, Katarina; White, Maurice; Georgiev, Georgi

2012-01-01

During an airborne multi-sensor remote sensing experiment at the Virginia Coast Reserve (VCR) Long Term Ecological Research (LTER) site in June 2011 (VCR '11), first measurements were taken with the new NRL Goniometer for Outdoor Portable Hyperspectral Earth Reflectance (GOPHER). GOPHER measures the angular distribution of hyperspectral reflectance. GOPHER was constructed for NRL by Spectra Vista Corporation (SVC) and the University of Lethbridge through a capital equipment purchase in 2010. The GOPHER spectrometer is an SVC HR -1024, which measures hyperspectral reflectance over the range from 350 -2500 nm, the visible, near infrared, and short-wave infrared. During measurements, the spectrometer travels along a zenith quarter -arc track that can rotate in azimuth, allowing for measurement of the bi-directional reflectance distribution function (BRDF) over the whole hemisphere. The zenith arc has a radius of approximately 2m, and the spectrometer scan pattern can be programmed on the fly during calibration and validation efforts. The spectrometer and zenith arc assembly can be raised and lowered along a mast to allow for measurement of uneven terrain or vegetation canopies of moderate height. Hydraulics on the chassis allow for leveling of the instrument in the field. At just over 400 lbs, GOPHER is a field portable instrument and can be transformed into a compact trailer assembly for movement over long distances in the field.

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

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.

Study on Hyperspectral Estimation Model of Total Nitrogen Content in Soil of Shaanxi Province

NASA Astrophysics Data System (ADS)

Liu, Jinbao; Dong, Zhenyu; Chen, Xi

2018-01-01

The development of hyperspectral remote sensing technology has been widely used in soil nutrient prediction. The soil is the representative soil type in Shaanxi Province. In this study, the soil total nitrogen content in Shaanxi soil was used as the research target, and the soil samples were measured by reflectance spectroscopy using ASD method. Pre-treatment, the first order differential, second order differential and reflectance logarithmic transformation of the reflected spectrum after pre-treatment, and the hyperspectral estimation model is established by using the least squares regression method and the principal component regression method. The results show that the correlation between the reflectance spectrum and the total nitrogen content of the soil is significantly improved. The correlation coefficient between the original reflectance and soil total nitrogen content is in the range of 350 ~ 2500nm. The correlation coefficient of soil total nitrogen content and first deviation of reflectance is more than 0.5 at 142nm, 1963nm, 2204nm and 2307nm, the second deviation has a significant positive correlation at 1114nm, 1470nm, 1967nm, 2372nm and 2402nm, respectively. After the reciprocal logarithmic transformation of the reflectance with the total nitrogen content of the correlation analysis found that the effect is not obvious. Rc2 = 0.7102, RMSEC = 0.0788; Rv2 = 0.8480, RMSEP = 0.0663, which can achieve the rapid prediction of the total nitrogen content in the region. The results show that the principal component regression model is the best.

Exploring the impact of wavelet-based denoising in the classification of remote sensing hyperspectral images

NASA Astrophysics Data System (ADS)

Quesada-Barriuso, Pablo; Heras, Dora B.; Argüello, Francisco

2016-10-01

The classification of remote sensing hyperspectral images for land cover applications is a very intensive topic. In the case of supervised classification, Support Vector Machines (SVMs) play a dominant role. Recently, the Extreme Learning Machine algorithm (ELM) has been extensively used. The classification scheme previously published by the authors, and called WT-EMP, introduces spatial information in the classification process by means of an Extended Morphological Profile (EMP) that is created from features extracted by wavelets. In addition, the hyperspectral image is denoised in the 2-D spatial domain, also using wavelets and it is joined to the EMP via a stacked vector. In this paper, the scheme is improved achieving two goals. The first one is to reduce the classification time while preserving the accuracy of the classification by using ELM instead of SVM. The second one is to improve the accuracy results by performing not only a 2-D denoising for every spectral band, but also a previous additional 1-D spectral signature denoising applied to each pixel vector of the image. For each denoising the image is transformed by applying a 1-D or 2-D wavelet transform, and then a NeighShrink thresholding is applied. Improvements in terms of classification accuracy are obtained, especially for images with close regions in the classification reference map, because in these cases the accuracy of the classification in the edges between classes is more relevant.

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.

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.

The Hughes phenomenon in hyperspectral classification based on the ground spectrum of grasslands in the region around Qinghai Lake

NASA Astrophysics Data System (ADS)

Ma, Weiwei; Gong, Cailan; Hu, Yong; Meng, Peng; Xu, Feifei

2013-08-01

Hyperspectral data, consisting of hundreds of spectral bands with a high spectral resolution, enables acquisition of continuous spectral characteristic curves, and therefore have served as a powerful tool for vegetation classification. The difficulty of using hyperspectral data is that they are usually redundant, strongly correlated and subject to Hughes phenomenon where classification accuracy increases gradually in the beginning as the number of spectral bands or dimensions increases, but decreases dramatically when the band number reaches some value. In recent years，some algorithms have been proposed to overcome the Hughes phenomenon in classification, such as selecting several bands from full bands, PCA- and MNF-based feature transformations. Up to date, however, few studies have been conducted to investigate the turning point of Hughes phenomenon (i.e., the point at which the classification accuracy begins to decline). In this paper, we firstly analyze reasons for occurrence of Hughes phenomenon, and then based on the Mahalanobis classifier, classify the ground spectrum of several grasslands which were recorded in September 2012 using FieldSpec3 spectrometer in the regions around Qinghai Lake，a important pasturing area in the north of China. Before classification, we extract features from hyperspectral data by bands selecting and PCA- based feature transformations, and In the process of classification, we analyze how the correlation coefficient between wavebands, the number of waveband channels and the number of principal components affect the classification result. The results show that Hushes phenomenon may occur when the correlation coefficient between wavebands is greater than 94%，the number of wavebands is greater than 6, or the number of principal components is greater than 6. Best classification result can be achieved (overall accuracy of grasslands 90%) if the number of wavebands equals to 3 (the band positions are 370nm, 509nm and 886nm respectively) or the number of principal components ranges from 4 to 6.

Radiometric assessment method for diffraction effects in hyperspectral imagers applied to the earth explorer #8 mission candidate flex

NASA Astrophysics Data System (ADS)

Berlich, R.; Harnisch, B.

2017-11-01

An accurate stray light analysis represents a crucial part in the early design phase of hyperspectral imaging systems, since scattering effects can severely limit the radiometric accuracy performance. In addition to conventional contributors including ghost images and surface scattering, i.e. caused by a residual surface micro-roughness and particle contamination, diffraction effects can result in significant radiometric errors in the spatial and spectral domain of pushbroom scanners. In this paper, we present a mathematical approach that efficiently evaluates these diffraction effects based on a Fourier analysis. It is shown that considering the conventional diffraction at the systems entrance pupil only, significantly overestimates the stray light contribution. In fact, a correct assessment necessitates taking into account the joint influence of the entrance pupil, the spectrometer slit as well as the dispersion element. We quantitatively investigate the corresponding impact on the Instrument Spectral Response Function (ISRF) of the Earth Explorer #8 Mission Candidate FLEX and analyse the expected radiometric error distribution for a typical earth observation scenario requirement.

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.

Hyperspectral imaging for detection of cholesterol in human skin

NASA Astrophysics Data System (ADS)

Milanič, Matija; Bjorgan, Asgeir; Larsson, Marcus; Marraccini, Paolo; Strömberg, Tomas; Randeberg, Lise L.

2015-03-01

Hypercholesterolemia is characterized by high levels of cholesterol in the blood and is associated with an increased risk of atherosclerosis and coronary heart disease. Early detection of hypercholesterolemia is necessary to prevent onset and progress of cardiovascular disease. Optical imaging techniques might have a potential for early diagnosis and monitoring of hypercholesterolemia. In this study, hyperspectral imaging was investigated for this application. The main aim of the study was to identify spectral and spatial characteristics that can aid identification of hypercholesterolemia in facial skin. The first part of the study involved a numerical simulation of human skin affected by hypercholesterolemia. A literature survey was performed to identify characteristic morphological and physiological parameters. Realistic models were prepared and Monte Carlo simulations were performed to obtain hyperspectral images. Based on the simulations optimal wavelength regions for differentiation between normal and cholesterol rich skin were identified. Minimum Noise Fraction transformation (MNF) was used for analysis. In the second part of the study, the simulations were verified by a clinical study involving volunteers with elevated and normal levels of cholesterol. The faces of the volunteers were scanned by a hyperspectral camera covering the spectral range between 400 nm and 720 nm, and characteristic spectral features of the affected skin were identified. Processing of the images was done after conversion to reflectance and masking of the images. The identified features were compared to the known cholesterol levels of the subjects. The results of this study demonstrate that hyperspectral imaging of facial skin can be a promising, rapid modality for detection of hypercholesterolemia.

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.

Single-pixel imaging by Hadamard transform and its application for hyperspectral imaging

NASA Astrophysics Data System (ADS)

Mizutani, Yasuhiro; Shibuya, Kyuki; Taguchi, Hiroki; Iwata, Tetsuo; Takaya, Yasuhiro; Yasui, Takeshi

2016-10-01

In this paper, we report on comparisons of single-pixel imagings using Hadamard Transform (HT) and the ghost imaging (GI) in the view point of the visibility under weak light conditions. For comparing the two methods, we have discussed about qualities of images based on experimental results and numerical analysis. To detect images by the TH method, we have illuminated the Hadamard-pattern mask and calculated by orthogonal transform. On the other hand, the GH method can detect images by illuminating random patterns and a correlation measurement. For comparing two methods under weak light intensity, we have controlled illuminated intensities of a DMD projector about 0.1 in signal-to-noise ratio. Though a process speed of the HT image was faster then an image via the GI, the GI method has an advantage of detection under weak light condition. An essential difference between the HT and the GI method is discussed about reconstruction process. Finally, we also show a typical application of the single-pixel imaging such as hyperspectral images by using dual-optical frequency combs. An optical setup consists of two fiber lasers, spatial light modulated for generating patten illumination, and a single pixel detector. We are successful to detect hyperspectrul images in a range from 1545 to 1555 nm at 0.01nm resolution.

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.

[Estimation of organic matter content of north fluvo-aquic soil based on the coupling model of wavelet transform and partial least squares].

PubMed

Wang, Yan-Cang; Yang, Gui-Jun; Zhu, Jin-Shan; Gu, Xiao-He; Xu, Peng; Liao, Qin-Hong

2014-07-01

For improving the estimation accuracy of soil organic matter content of the north fluvo-aquic soil, wavelet transform technology is introduced. The soil samples were collected from Tongzhou district and Shunyi district in Beijing city. And the data source is from soil hyperspectral data obtained under laboratory condition. First, discrete wavelet transform efficiently decomposes hyperspectral into approximate coefficients and detail coefficients. Then, the correlation between approximate coefficients, detail coefficients and organic matter content was analyzed, and the sensitive bands of the organic matter were screened. Finally, models were established to estimate the soil organic content by using the partial least squares regression (PLSR). Results show that the NIR bands made more contributions than the visible band in estimating organic matter content models; the ability of approximate coefficients to estimate organic matter content is better than that of detail coefficients; The estimation precision of the detail coefficients fir soil organic matter content decreases with the spectral resolution being lower; Compared with the commonly used three types of soil spectral reflectance transforms, the wavelet transform can improve the estimation ability of soil spectral fir organic content; The accuracy of the best model established by the approximate coefficients or detail coefficients is higher, and the coefficient of determination (R2) and the root mean square error (RMSE) of the best model for approximate coefficients are 0.722 and 0.221, respectively. The R2 and RMSE of the best model for detail coefficients are 0.670 and 0.255, respectively.

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)

Hyperspectral imaging with wavelet transform for classification of colon tissue biopsy samples

NASA Astrophysics Data System (ADS)

Masood, Khalid

2008-08-01

Automatic classification of medical images is a part of our computerised medical imaging programme to support the pathologists in their diagnosis. Hyperspectral data has found its applications in medical imagery. Its usage is increasing significantly in biopsy analysis of medical images. In this paper, we present a histopathological analysis for the classification of colon biopsy samples into benign and malignant classes. The proposed study is based on comparison between 3D spectral/spatial analysis and 2D spatial analysis. Wavelet textural features in the wavelet domain are used in both these approaches for classification of colon biopsy samples. Experimental results indicate that the incorporation of wavelet textural features using a support vector machine, in 2D spatial analysis, achieve best classification accuracy.

Compilation of Theses Abstracts

DTIC Science & Technology

2004-12-01

Lieutenant, United States Navy Master of Business Administration–December 2004 Jonathan C. Byrom–Captain, United States Army Master of Business...Hyperspectral Imagery, Principal Components Analysis, Minimum Noise Transform ALTERNATE CONFIGURATIONS FOR BLOCKED-IMPURITY-BAND DETECTORS Jonathan C...Yew Sing Quek –Captain, Republic of Singapore Armed Forces B.E., Nanyang Technological University-Singapore, 1999 Master of Science in Combat

Guided filter and principal component analysis hybrid method for hyperspectral pansharpening

NASA Astrophysics Data System (ADS)

Qu, Jiahui; Li, Yunsong; Dong, Wenqian

2018-01-01

Hyperspectral (HS) pansharpening aims to generate a fused HS image with high spectral and spatial resolution through integrating an HS image with a panchromatic (PAN) image. A guided filter (GF) and principal component analysis (PCA) hybrid HS pansharpening method is proposed. First, the HS image is interpolated and the PCA transformation is performed on the interpolated HS image. The first principal component (PC1) channel concentrates on the spatial information of the HS image. Different from the traditional PCA method, the proposed method sharpens the PAN image and utilizes the GF to obtain the spatial information difference between the HS image and the enhanced PAN image. Then, in order to reduce spectral and spatial distortion, an appropriate tradeoff parameter is defined and the spatial information difference is injected into the PC1 channel through multiplying by this tradeoff parameter. Once the new PC1 channel is obtained, the fused image is finally generated by the inverse PCA transformation. Experiments performed on both synthetic and real datasets show that the proposed method outperforms other several state-of-the-art HS pansharpening methods in both subjective and objective evaluations.

A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA

NASA Astrophysics Data System (ADS)

Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan

2016-11-01

The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.

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...

Study on Hyperspectral Characteristics and Estimation Model of Soil Mercury Content

NASA Astrophysics Data System (ADS)

Liu, Jinbao; Dong, Zhenyu; Sun, Zenghui; Ma, Hongchao; Shi, Lei

2017-12-01

In this study, the mercury content of 44 soil samples in Guan Zhong area of Shaanxi Province was used as the data source, and the reflectance spectrum of soil was obtained by ASD Field Spec HR (350-2500 nm) Comparing the reflection characteristics of different contents and the effect of different pre-treatment methods on the establishment of soil heavy metal spectral inversion model. The first order differential, second order differential and reflectance logarithmic transformations were carried out after the pre-treatment of NOR, MSC and SNV, and the sensitive bands of reflectance and mercury content in different mathematical transformations were selected. A hyperspectral estimation model is established by regression method. The results of chemical analysis show that there is a serious Hg pollution in the study area. The results show that: (1) the reflectivity decreases with the increase of mercury content, and the sensitive regions of mercury are located at 392 ~ 455nm, 923nm ~ 1040nm and 1806nm ~ 1969nm. (2) The combination of NOR, MSC and SNV transformations combined with differential transformations can improve the information of heavy metal elements in the soil, and the combination of high correlation band can improve the stability and prediction ability of the model. (3) The partial least squares regression model based on the logarithm of the original reflectance is better and the precision is higher, Rc2 = 0.9912, RMSEC = 0.665; Rv2 = 0.9506, RMSEP = 1.93, which can achieve the mercury content in this region Quick forecast.

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.

A new approach for fast indexing of hyperspectral image data for knowledge retrieval and mining

NASA Astrophysics Data System (ADS)

Clowers, Robert; Dua, Sumeet

2005-11-01

Multispectral sensors produce images with a few relatively broad wavelength bands. Hyperspectral remote sensors, on the other hand, collect image data simultaneously in dozens or hundreds of narrow and adjacent spectral bands. These measurements make it possible to derive a continuous spectrum for each image cell, generating an image cube across multiple spectral components. Hyperspectral imaging has sound applications in a variety of areas such as mineral exploration, hazardous waste remediation, mapping habitat, invasive vegetation, eco system monitoring, hazardous gas detection, mineral detection, soil degradation, and climate change. This image has a strong potential for transforming the imaging paradigms associated with several design and manufacturing processes. In this paper, we describe a novel approach for fast indexing of multi-dimensional hyperspectral image data, especially for data mining applications. The index exploits the spectral and spatial relationships embedded in these image sets. The index will be employed for knowledge retrieval applications that require fast information interpretation approaches. The index can also be deployed in real-time mission-critical domains, as it is shown to exhibit speed with high degrees of dimensionality associated with the data. The strength of this index in terms of degree of false dismissals and false alarms will also be demonstrated. The paper will highlight some common applications of this imaging computational paradigm and will conclude with directions for future improvement and investigation.

Design of FPGA ICA for hyperspectral imaging processing

NASA Astrophysics Data System (ADS)

Nordin, Anis; Hsu, Charles C.; Szu, Harold H.

2001-03-01

The remote sensing problem which uses hyperspectral imaging can be transformed into a blind source separation problem. Using this model, hyperspectral imagery can be de-mixed into sub-pixel spectra which indicate the different material present in the pixel. This can be further used to deduce areas which contain forest, water or biomass, without even knowing the sources which constitute the image. This form of remote sensing allows previously blurred images to show the specific terrain involved in that region. The blind source separation problem can be implemented using an Independent Component Analysis algorithm. The ICA Algorithm has previously been successfully implemented using software packages such as MATLAB, which has a downloadable version of FastICA. The challenge now lies in implementing it in a form of hardware, or firmware in order to improve its computational speed. Hardware implementation also solves insufficient memory problem encountered by software packages like MATLAB when employing ICA for high resolution images and a large number of channels. Here, a pipelined solution of the firmware, realized using FPGAs are drawn out and simulated using C. Since C code can be translated into HDLs or be used directly on the FPGAs, it can be used to simulate its actual implementation in hardware. The simulated results of the program is presented here, where seven channels are used to model the 200 different channels involved in hyperspectral imaging.

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.

Opto-digital spectrum encryption by using Baker mapping and gyrator transform

NASA Astrophysics Data System (ADS)

Chen, Hang; Zhao, Jiguang; Liu, Zhengjun; Du, Xiaoping

2015-03-01

A concept of spectrum information hidden technology is proposed in this paper. We present an optical encryption algorithm for hiding both the spatial and spectrum information by using the Baker mapping in gyrator transform domains. The Baker mapping is introduced for scrambling the every single band of the hyperspectral image before adding the random phase functions. Subsequently, three thin cylinder lenses are controlled by PC for implementing the gyrator transform. The amplitude and phase information in the output plane can be regarded as the encrypted information and main key. Some numerical simulations are made to test the validity and capability of the proposed encryption algorithm.

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

Methods for performing fast discrete curvelet transforms of data

DOEpatents

Candes, Emmanuel; Donoho, David; Demanet, Laurent

2010-11-23

Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

NASA Astrophysics Data System (ADS)

Feng, Shengtao; Bo, Wanju; Ma, Qingzun; Wang, Zifan

2017-12-01

Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb-Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series.

A novel collinear optical system with annulus mirrors for holographic disc driver

NASA Astrophysics Data System (ADS)

Wang, Ye

2008-12-01

This paper focus on a novel collinear lens system with annulus mirrors for holographic disc driver, both information beam and reference beam are use same laser beam. The expanded and parallel laser beam, center part of it as the information beam then through Fourier transform lens, the beam around center part as a reference beam. On this axis, the ring reference beam reflected by two annulus shaped mirrors, then became a convergent beam, together with the information beam which through the first Fourier transform lens then produce holographic pattern to be write into the holographic disc behind of them, this lens system with two mirrors made the angle between information beam and reference beam more wide, can improved the multiplex level of holographic storage. Pair of Fourier transform lens with advance performance is designed in this paper.

Colorectal Cancer and Colitis Diagnosis Using Fourier Transform Infrared Spectroscopy and an Improved K-Nearest-Neighbour Classifier.

PubMed

Li, Qingbo; Hao, Can; Kang, Xue; Zhang, Jialin; Sun, Xuejun; Wang, Wenbo; Zeng, Haishan

2017-11-27

Combining Fourier transform infrared spectroscopy (FTIR) with endoscopy, it is expected that noninvasive, rapid detection of colorectal cancer can be performed in vivo in the future. In this study, Fourier transform infrared spectra were collected from 88 endoscopic biopsy colorectal tissue samples (41 colitis and 47 cancers). A new method, viz., entropy weight local-hyperplane k-nearest-neighbor (EWHK), which is an improved version of K-local hyperplane distance nearest-neighbor (HKNN), is proposed for tissue classification. In order to avoid limiting high dimensions and small values of the nearest neighbor, the new EWHK method calculates feature weights based on information entropy. The average results of the random classification showed that the EWHK classifier for differentiating cancer from colitis samples produced a sensitivity of 81.38% and a specificity of 92.69%.

FFTDC2: a one-dimensional Fourier transform with forward and inverse data conditioning for non-complex data

USGS Publications Warehouse

Bracken, Robert E.

2004-01-01

A subroutine (FFTDC2) coded in Fortran 77 is described, which performs a Fast Fourier Transform or Discrete Fourier Transform together with necessary conditioning steps of trend removal, extension, and windowing. The source code for the entire library of required subroutines is provided with the digital release of this report. But, there is only one required entry point, the subroutine call to FFTDC2; all the other subroutines are operationally transparent to the user. Complete instructions for use of FFTDC2.F (as well as for all the other subroutines) and some practical theoretical discussions are included as comments at the beginning of the source code. This subroutine is intended to be an efficient tool for the programmer in a variety of production-level signal-processing applications.

Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation.

PubMed

Vladimirov, Gleb; Kostyukevich, Yury; Kharybin, Oleg; Nikolaev, Eugene

2017-08-01

Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

PubMed

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

Interest point detection for hyperspectral imagery

NASA Astrophysics Data System (ADS)

Dorado-Muñoz, Leidy P.; Vélez-Reyes, Miguel; Roysam, Badrinath; Mukherjee, Amit

2009-05-01

This paper presents an algorithm for automated extraction of interest points (IPs)in multispectral and hyperspectral images. Interest points are features of the image that capture information from its neighbours and they are distinctive and stable under transformations such as translation and rotation. Interest-point operators for monochromatic images were proposed more than a decade ago and have since been studied extensively. IPs have been applied to diverse problems in computer vision, including image matching, recognition, registration, 3D reconstruction, change detection, and content-based image retrieval. Interest points are helpful in data reduction, and reduce the computational burden of various algorithms (like registration, object detection, 3D reconstruction etc) by replacing an exhaustive search over the entire image domain by a probe into a concise set of highly informative points. An interest operator seeks out points in an image that are structurally distinct, invariant to imaging conditions, stable under geometric transformation, and interpretable which are good candidates for interest points. Our approach extends ideas from Lowe's keypoint operator that uses local extrema of Difference of Gaussian (DoG) operator at multiple scales to detect interest point in gray level images. The proposed approach extends Lowe's method by direct conversion of scalar operations such as scale-space generation, and extreme point detection into operations that take the vector nature of the image into consideration. Experimental results with RGB and hyperspectral images which demonstrate the potential of the method for this application and the potential improvements of a fully vectorial approach over band-by-band approaches described in the literature.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

DOE PAGES

Xu, Kuan; Austin, Anthony P.; Wei, Ke

2017-12-21

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

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

Xu, Kuan; Austin, Anthony P.; Wei, Ke

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

Beyond Fourier

NASA Astrophysics Data System (ADS)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

Characterization of non-polar aromatic hydrocarbons in crude oil using atmospheric pressure laser ionization and Fourier transform ion cyclotron resonance mass spectrometry (APLI FT-ICR MS).

PubMed

Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten

2008-07-01

We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

NASA Technical Reports Server (NTRS)

Generazio, E. R.

1986-01-01

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Passive Standoff Detection of Chemical Vapors by Differential FTIR Radiometry

DTIC Science & Technology

2001-01-01

8217 utilisation d’un interferometre infrarouge a transformation de Fourier (FTIR) a double entree optimise pour la soustraction optique. En vue de sa mise...Valcartier (DREV) is currently developing a passive Fourier Transform InfraRed (FTIR) technique for the standoff detection and identification of...chemical vapors. A well-known difficulty associated with this technique is that the recorded signal also contains a large amount of unwanted background

Industrial realization of a direct Fourier transform in automated experimental data processing systems

NASA Technical Reports Server (NTRS)

Lyubashevskiy, G. S.

1973-01-01

Fourier processing of automatic signals transforms direct current voltage into a numerical form through bandpass filtration in time-pulse multiplying devices. It is shown that the ratio of the interference energy to the useful signal energy is inversely proportional to the square of the product of the depth of the width modulation and the ratio of the time constant averaging to the cross-multiplied signals.

Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

PubMed

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

An algorithm for the basis of the finite Fourier transform

NASA Technical Reports Server (NTRS)

Santhanam, Thalanayar S.

1995-01-01

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

PubMed

Lange, K

1982-03-01

In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

Parameter Estimation for the Blind Restoration of Blurred Imagery.

DTIC Science & Technology

1986-09-01

17 Noise Process .... ............. 23 Restoration Methods .... .......... 26 Inverse Filter .... ........... 26 Wiener Filter...of Eq. (155) ....... .................... ... 64 Table 2 Restored Pictures and Noise Variances ........ . 69 v 5𔃼 5- viq °,. r -’ .’S’ .N’% N...restoration system. g(x,y) Degraded image. G(u,v) Discrete Fourier Transform of the degraded image. n(x,y) Noise . N(u,v) Discrete Fourier transform of n

Fourier spectroscopy with a one-million-point transformation

NASA Technical Reports Server (NTRS)

Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.

1972-01-01

A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Efficient hyperspectral image segmentation using geometric active contour formulation

NASA Astrophysics Data System (ADS)

Albalooshi, Fatema A.; Sidike, Paheding; Asari, Vijayan K.

2014-10-01

In this paper, we present a new formulation of geometric active contours that embeds the local hyperspectral image information for an accurate object region and boundary extraction. We exploit self-organizing map (SOM) unsupervised neural network to train our model. The segmentation process is achieved by the construction of a level set cost functional, in which, the dynamic variable is the best matching unit (BMU) coming from SOM map. In addition, we use Gaussian filtering to discipline the deviation of the level set functional from a signed distance function and this actually helps to get rid of the re-initialization step that is computationally expensive. By using the properties of the collective computational ability and energy convergence capability of the active control models (ACM) energy functional, our method optimizes the geometric ACM energy functional with lower computational time and smoother level set function. The proposed algorithm starts with feature extraction from raw hyperspectral images. In this step, the principal component analysis (PCA) transformation is employed, and this actually helps in reducing dimensionality and selecting best sets of the significant spectral bands. Then the modified geometric level set functional based ACM is applied on the optimal number of spectral bands determined by the PCA. By introducing local significant spectral band information, our proposed method is capable to force the level set functional to be close to a signed distance function, and therefore considerably remove the need of the expensive re-initialization procedure. To verify the effectiveness of the proposed technique, we use real-life hyperspectral images and test our algorithm in varying textural regions. This framework can be easily adapted to different applications for object segmentation in aerial hyperspectral imagery.

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.

A Quantitative Approach to Scar Analysis

PubMed Central

Khorasani, Hooman; Zheng, Zhong; Nguyen, Calvin; Zara, Janette; Zhang, Xinli; Wang, Joyce; Ting, Kang; Soo, Chia

2011-01-01

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology. PMID:21281794

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

Santa Maria, Odilyn L.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

PubMed Central

Füsti-Molnár, László; Merz, Kenneth M.

2008-01-01

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring. PMID:18624561

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

Off-axis illumination direct-to-digital holography

DOEpatents

Thomas, Clarence E.; Price, Jeffery R.; Voelkl, Edgar; Hanson, Gregory R.

2004-06-08

Systems and methods are described for off-axis illumination direct-to-digital holography. A method of recording an off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis, includes: reflecting a reference beam from a reference mirror at a non-normal angle; reflecting an object beam from an object at an angle with respect to an optical axis defined by a focusing lens; focusing the reference beam and the object beam at a focal plane of a digital recorder to form the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digitally recording the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; Fourier analyzing the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes by transforming axes of the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined as an angle between the reference beam and the object beam; applying a digital filter to cut off signals around an original origin; and then performing an inverse Fourier transform.

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

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

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resultingmore » Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.« less

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.

Fourier transform of the multicenter product of 1s hydrogenic orbitals and Coulomb or Yukawa potentials and the analytically reduced form for subsequent integrals that include plane waves

NASA Technical Reports Server (NTRS)

Straton, Jack C.

1989-01-01

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.

Metric Learning for Hyperspectral Image Segmentation

NASA Technical Reports Server (NTRS)

Bue, Brian D.; Thompson, David R.; Gilmore, Martha S.; Castano, Rebecca

2011-01-01

We present a metric learning approach to improve the performance of unsupervised hyperspectral image segmentation. Unsupervised spatial segmentation can assist both user visualization and automatic recognition of surface features. Analysts can use spatially-continuous segments to decrease noise levels and/or localize feature boundaries. However, existing segmentation methods use tasks-agnostic measures of similarity. Here we learn task-specific similarity measures from training data, improving segment fidelity to classes of interest. Multiclass Linear Discriminate Analysis produces a linear transform that optimally separates a labeled set of training classes. The defines a distance metric that generalized to a new scenes, enabling graph-based segmentation that emphasizes key spectral features. We describe tests based on data from the Compact Reconnaissance Imaging Spectrometer (CRISM) in which learned metrics improve segment homogeneity with respect to mineralogical classes.

Predicting the diurnal blue-sky albedo of soils using their laboratory reflectance spectra and roughness indices

NASA Astrophysics Data System (ADS)

Cierniewski, Jerzy; Ceglarek, Jakub; Karnieli, Arnon; Królewicz, Sławomir; Kaźmierowski, Cezary; Zagajewski, Bogdan

2017-10-01

The objective of this study was to assess the relationship between the hyperspectral reflectance of soils and their albedo, measured under various roughness conditions. 108 soil surface measurements were conducted in Poland and Israel. Each surface was characterised by its diurnal albedo variation in the field as well as by its reflectance spectra obtained in the laboratory. The best fit to the model was achieved by post-processing manipulation of the spectra, namely second derivate transformation. Using a stepwise elimination process, four spectral wavelengths and the roughness index were selected for modelling. The resulting models allowed the albedo of a soil to be predicted for its different roughness states and any solar zenith angle, provided that hyperspectral reflectance data is available.

A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis

NASA Technical Reports Server (NTRS)

Ioup, G. E.

1980-01-01

Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

Program for the analysis of time series. [by means of fast Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Brown, T. J.; Brown, C. G.; Hardin, J. C.

1974-01-01

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

PubMed

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers

NASA Technical Reports Server (NTRS)

Campbell, Joel

2008-01-01

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Generalization and modularization of two-dimensional adaptive coordinate transformations for the Fourier modal method.

PubMed

Küchenmeister, Jens

2014-04-21

The Fourier modal method (FMM) has advanced greatly by using adaptive coordinates and adaptive spatial resolution. The convergence characteristics were shown to be improved significantly, a construction principle for suitable meshes was demonstrated and a guideline for the optimal choice of the coordinate transformation parameters was found. However, the construction guidelines published so far rely on a certain restriction that is overcome with the formulation presented in this paper. Moreover, a modularization principle is formulated that significantly eases the construction of coordinate transformations in unit cells with reappearing shapes and complex sub-structures.

Progress Toward Achieving an IR Radiance Record for Decadal Climate Trending: Fundamental Questions, Challenges, and Assessments

NASA Astrophysics Data System (ADS)

Revercomb, H. E.; Knuteson, R. O.; Tobin, D. C.; Best, F. A.; Taylor, J. K.; Martin, G.; Gero, P. J.; Adler, D.; Pettersen, C.; Mulligan, M.; Thielman, D.

2017-12-01

Infrared radiance spectra can be measured with very high accuracy (0.1 K 3-sigma brightness temperature at scene brightness temperature) and contain a high degree of information about the state of the Earth's climate, including temperature, water vapor, and trace gas profiles, lapse rates, plus cloud and surface properties. How best to make use of existing EOS-AIRS and Suomi NPP/JPSS-CrIS/IASI observations and how to move toward more extensive future observations is a fundamental question that the climate community and world's space agencies need to address. A major step toward achieving climate quality observations was realized through the successes of the operational sounders IASI-A & B on MetOp and the CrIS on Suomi NPP. Both instrument types are expected to continue as part of the Joint Polar Satellite system through at least 2040 (with upgrades to IASI and hopefully to CrIS as well). IASI covers the 0930 time slot and CrIS the 1330 slot for operational weather forecasting applications. This represents a major step toward the unbiased sampling needed for accurate climate trending products. However, there is still a hole at the 0530 dawn/dusk time slot that needs to be filled. The new Chinese hyperspectral sounder, HIRAS, is expected to fulfill this need when FY3E is launched in 2018. In addition to improved sampling, the system of operational Fourier transform sounding instruments offer other measurement accuracy advantages over earlier instruments. This talk will review some of these, including review of CrIS accuracy estimates, discussion of several specific error sources, and the fundamental ability of these instruments to produce well-defined, stable, and largely instrument independent Instrument Line Shape (ILS) functions. In this context, we will address EOS to Suomi NPP spectral radiance continuity issues. Finally, optimizing this system still requires an on-orbit 0.1 K 3-sigma calibration reference that is not susceptible to long-term drifts and that can be used to correct inconsistencies among the different sensors. The new technologies needed to provide this capability have been developed under NASA ESTO and the CLARREO program, and should be flown as soon as possible. For the infrared it is widely accepted that a Fourier transform instrument provides the best possible reference sensor.

Application of the one-dimensional Fourier transform for tracking moving objects in noisy environments

NASA Technical Reports Server (NTRS)

Rajala, S. A.; Riddle, A. N.; Snyder, W. E.

1983-01-01

In Riddle and Rajala (1981), an algorithm was presented which operates on an image sequence to identify all sets of pixels having the same velocity. The algorithm operates by performing a transformation in which all pixels with the same two-dimensional velocity map to a peak in a transform space. The transform can be decomposed into applications of the one-dimensional Fourier transform and therefore can gain from the computational advantages of the FFT. The aim of this paper is the concern with the fundamental limitations of that algorithm, particularly as relates to its sensitivity to image-disturbing parameters as noise, jitter, and clutter. A modification to the algorithm is then proposed which increases its robustness in the presence of these disturbances.

a Signal-Tuned Gabor Transform with Application to Eeg Analysis

NASA Astrophysics Data System (ADS)

Torreão, José R. A.; Victer, Silvia M. C.; Fernandes, João L.

2013-04-01

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

Real-Time Fourier Transformed Holographic Associative Memory With Photorefractive Material

NASA Astrophysics Data System (ADS)

Changsuk, Oh; Hankyu, Park

1989-02-01

We describe a volume holographic associative memory using photorefractive material and conventional planar mirror. Multiple hologram is generated with two angular multiplexed writing beams and Fourier transformed object beam in BaTiO3 crystal at 0.6328 μm. Complete image can be recalled successfully by partial input of original stored image. It is proved that our system is useful for optical implementation of real-time associative memory and location addressable memory.

A hybrid silicon membrane spatial light modulator for optical information processing

NASA Technical Reports Server (NTRS)

Pape, D. R.; Hornbeck, L. J.

1984-01-01

A new two dimensional, fast, analog, electrically addressable, silicon based membrane spatial light modulator (SLM) was developed for optical information processing applications. Coherent light reflected from the mirror elements is phase modulated producing an optical Fourier transform of an analog signal input to the device. The DMD architecture and operating parameters related to this application are presented. A model is developed that describes the optical Fourier transform properties of the DMD.

Metabolic fingerprinting of lichen Usnea baileyi by Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Bakar, Siti Zaharah Abu; Latip, Jalifah; bin Din, Laily; Samsuddin, Mohd Wahid

2014-09-01

The lichen Usnea baileyi collected from different environments was characterised using Fourier transform infrared spectroscopy. This preliminary study was done to determine the effects of different environment populations on U. baileyi chemical composition. Results showed that the absorbance peaks of Golf Course 2 (GCU2) are more intense compared to Taman Awana (TA), Jalan Awana (JA) and Jalan Gohtong (JG). U. baileyi contains of dibenzofurans, depsides, depsidones, xanthones and terpenoids.

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.

PubMed

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method.

Quantum-classical analogies in waveguide arrays: From Fourier transforms to ion-laser interactions

NASA Astrophysics Data System (ADS)

Moya-Cessa, Héctor M.

2018-04-01

By using the fact that infinite and semi-infinite systems of differential equations may be casted as Schrödinger-like equations we show how quantum-classical analogies may be achieved. In particular we show how the analogies of ion-laser, functions of a phase operator and quantised-field-two-level-atom interactions may be emulated. We also show a realization of the fractional discrete Fourier transform.

Apparatus and methods for continuous beam fourier transform mass spectrometry

DOEpatents

McLuckey, Scott A.; Goeringer, Douglas E.

2002-01-01

A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform

NASA Technical Reports Server (NTRS)

Brown, R. D.

1992-01-01

Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.

Using vertical Fourier transforms to invert potential-field data to magnetization or density models in the presence of topography

USGS Publications Warehouse

Phillips, Jeffrey

2014-01-01

A physical property inversion approach based on the use of 3D (or 2D) Fourier transforms to calculate the potential-field within a 3D (or 2D) volume from a known physical property distribution within the volume is described. Topographic surfaces and observations at arbitrary locations are easily accommodated. The limitations of the approach and applications to real data are considered.

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

Beyond MOS and Fibers: Wide-FoV Imaging Fourier Transform Spectroscopy - an Instrumentation Proposal for the Present and Future Mexican Telescopes

NASA Astrophysics Data System (ADS)

Rosales-Ortega, F. F.; Castillo, E.; Sánchez, S. F.; Iglesias-Páramo, J.; Mollá, J. I. M.; Chávez, M.

2016-10-01

In order to extend the current suite of instruments offered in the Observatorio Astrofísico Guillermo Haro (OAGH) in Cananea, Mexico (INAOE), and to explore a second-generation instrument for the future 6.5 m Telescopio San Pedro Martir (TSPM), we propose a prototype instrument that will provide un-biased wide-field (few arcmin) spectroscopic information, with the flexibility of operating at different spectral resolutions (R˜1-104), with a spatial resolution limited by seeing, and therefore to be used in a wide range of astronomical problems. This instrument will make use of the Fourier Transform Spectroscopy technique, which has been proved to be feasible in the optical wavelength range. Here we give the basic technical description of a Fourier transform spectrograph, as well as the technical advantages and weaknesses, and the science cases in which this instrument can be implemented.

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

Determination of layer ordering using sliding-window Fourier transform of x-ray reflectivity data

NASA Astrophysics Data System (ADS)

Smigiel, E.; Knoll, A.; Broll, N.; Cornet, A.

1998-01-01

X-ray reflectometry allows the determination of the thickness, density and roughness of thin layers on a substrate from several Angstroms to some hundred nanometres. The thickness is determined by simulation with trial-and-error methods after extracting initial values of the layer thicknesses from the result of a classical Fast Fourier Transform (FFT) of the reflectivity data. However, the order information of the layers is lost during classical FFT. The order of the layers has then to be known a priori. In this paper, it will be shown that the order of the layers can be obtained by a sliding-window Fourier transform, the so-called Gabor representation. This joint time-frequency analysis allows the direct determination of the order of the layers and, therefore, the use of a more appropriate starting model for refining simulations. A simulated and a measured example show the interest of this method.

A Hyperspectral View of the Crab Nebula

NASA Astrophysics Data System (ADS)

Charlebois, M.; Drissen, L.; Bernier, A.-P.; Grandmont, F.; Binette, L.

2010-05-01

We have obtained spatially resolved spectra of the Crab nebula in the spectral ranges 450-520 nm and 650-680 nm, encompassing the Hβ, [O III] λ4959, λ5007, Hα, [N II] λ6548, λ6584, and [S II] λ6717, λ6731 emission lines, with the imaging Fourier transform spectrometer SpIOMM at the Observatoire du Mont-Mégantic's 1.6 m telescope. We first compare our data with published observations obtained either from a Fabry-Perot interferometer or from a long-slit spectrograph. Using a spectral deconvolution technique similar to the one developed by Čadež et al., we identify and resolve multiple emission lines separated by large Doppler shifts and contained within the rapidly expanding filamentary structure of the Crab. This allows us to measure important line ratios, such as [N II]/Hα, [S II]/Hα, and [S II] λ6717 /[S II] λ6731 of individual filaments, providing a new insight on the SE-NW asymmetry in the Crab. From our analysis of the spatial distribution of the electronic density and of the respective shocked versus photoionized gas components, we deduce that the skin-less NW region must have evolved faster than the rest of the nebula. Assuming a very simple expansion model for the ejecta material, our data provide us with a complete tridimensional view of the Crab.

Mapping TES Aerobreaking Data of The Martian Polar Caps

NASA Astrophysics Data System (ADS)

Altunaiji, E. S.; Edwards, C. S.; Smith, M. D.; AlShamsi, M. R.; AlJanaahi, A. A.

2016-12-01

The purpose of this paper is to create maps of the north and south Mars polar caps using Thermal Emission Spectrometer (TES) aerobreaking surface temperature data in south and north as well as Lambert albedo data in the south. TES is an instrument on board the Mars Global Surveyor (MGS) spacecraft. It has six detectors arranged in a 2x3 array with a nominal spot size of 3 × 6 km; however, given the elliptical nature of the orbit during aerobreaking the footprint can be significantly larger (10s of km), especially over the southern hemisphere. TES is a Fourier transform infrared spectrometer designed to study the Martian surface and atmosphere using thermal infrared emission spectroscopy. It is composed of 2 separate channels, a broadband visible/near-infrared bolometer and hyperspectral thermal infrared spectrometer with a broadband thermal infrared bolometer. TES aerobraking spectra were taken between Mars Year 23, Ls=180° and Mars Year 24, Ls=30°. To determine the footprint location on the surface, geometry is calculated using the Spacecraft Planet Instrument Camera Matrix and Event (SPICE) Toolkit. These data were then binned and mapped to surface in polar stereographic projection. While some early studies focused on these data, we have expanded upon the ranges, generated time-/seasonally-binned data, and re-examined this largely underutilized set of data from TES ultimately extending the record of polar science on Mars.

Detecting the spatial chirp signals by fractional Fourier lens with transformation materials

NASA Astrophysics Data System (ADS)

Chen, J.; Hu, J.

2018-02-01

Fractional Fourier transform (FrFT) is the general form of the Fourier transform and is an important tool in signal processing. As one typical application of FrFT, detecting the chirp rate (CR, or known as the rate of frequency change) of a chirp signal is important in many optical measurements. The optical FrFT that based on graded index lens fails to detect the high CR chirp because the short wave propagation distance of the impulse in the lens will weaken the paraxial approximation condition. With the help of transformation optics, the improved FrFT lens is proposed to adjust the high CR as well as the impulse location of the given input chirp signal. The designed transformation materials can implement the effect of space compression, making the input chirp signal is equivalent to have lower CR, therefore the system can satisfy the paraxial approximation better. As a result, this lens can improve the detection precision for the high CR. The numerical simulations verified the design. The proposed device may have both theoretical and practical values, and the design demonstrates the ability and flexibility of TO in spatial signal processing.

Beyond Fourier.

PubMed

Hoch, Jeffrey C

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

PubMed

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

PubMed

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.