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NASA NTRS2003

Modified Polar-Format Software for Processing SAR Data

HMPF is a computer program that implements a modified polar-format algorithm for processing data from spaceborne synthetic-aperture radar (SAR) systems. Unlike prior polar-format processing algorithms, this algorithm is based on the assumption that the radar signal wavefronts are spherical rather than planar. The algorithm provides for resampling of SAR pulse data from slant range to radial distance from the center of a reference sphere that is nominally the local Earth surface. Then, invoking the projection-slice theorem, the resampled pulse data are Fourier-transformed over radial distance, arranged in the wavenumber domain according to the acquisition geometry, resampled to a Cartesian grid, and inverse-Fourier-transformed. The result of this process is the focused SAR image. HMPF, and perhaps other programs that implement variants of the algorithm, may give better accuracy than do prior algorithms for processing strip-map SAR data from high altitudes and may give better phase preservation relative to prior polar-format algorithms for processing spotlight-mode SAR data.

Chen, Curtis↗

NASA NTRS1977

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

Truman, W. M.↗

NASA NTRS2007

GIFTS SM EDU Level 1B Algorithms

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) SensorModule (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the GIFTS SM EDU Level 1B algorithms involved in the calibration. The GIFTS Level 1B calibration procedures can be subdivided into four blocks. In the first block, the measured raw interferograms are first corrected for the detector nonlinearity distortion, followed by the complex filtering and decimation procedure. In the second block, a phase correction algorithm is applied to the filtered and decimated complex interferograms. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected spectrum. The phase correction and spectral smoothing operations are performed on a set of interferogram scans for both ambient and hot blackbody references. To continue with the calibration, we compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. We now can estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. The correction schemes that compensate for the fore-optics offsets and off-axis effects are also implemented. In the third block, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation. Finally, in the fourth block, the single pixel algorithms are applied to the entire FPA.

Tian, Jialin↗

NASA NTRS1992

Retrieval of aerosol optical properties from multi-angle satellite imagery

Simulation multiangle imagery have been used to investigate the capabilities of a novel method for retrieval of atmospheric aerosol optical properties over land; this method employs spatial contrasts within the imagery and compares the spatial Fourier transforms of the multiangle images at zero and nonzero spatial frequencies. While requiring the definition of a relationship between the angular variation of the Fourier transform of the intrinsic surface angular reflectance at the zero and nonzero frequencies, the method assumes no a priori knowledge about aerosols or surface characteristics. Sensitivities to various aerosol properties are assessed.

Martonchik, John V.↗

NASA NTRS1993

Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams

A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.

Noor, Ahmed K.↗

NASA NTRS2007

GIFTS SM EDU Radiometric and Spectral Calibrations

Tian, J.↗

NASA NTRS2007

GIFTS SM EDU Data Processing and Algorithms

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation.

Tian, Jialin↗

NASA NTRS2007

Digital Signal Processing Techniques for the GIFTS SM EDU

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiance using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes several digital signal processing (DSP) techniques involved in the development of the calibration model. In the first stage, the measured raw interferograms must undergo a series of processing steps that include filtering, decimation, and detector nonlinearity correction. The digital filtering is achieved by employing a linear-phase even-length FIR complex filter that is designed based on the optimum equiripple criteria. Next, the detector nonlinearity effect is compensated for using a set of pre-determined detector response characteristics. In the next stage, a phase correction algorithm is applied to the decimated interferograms. This is accomplished by first estimating the phase function from the spectral phase response of the windowed interferogram, and then correcting the entire interferogram based on the estimated phase function. In the calibration stage, we first compute the spectral responsivity based on the previous results and the ideal Planck blackbody spectra at the given temperatures, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. In the post-calibration stage, we estimate the Noise Equivalent Spectral Radiance (NESR) from the calibrated ABB and HBB spectra. The NESR is generally considered as a measure of the instrument noise performance, and can be estimated as the standard deviation of calibrated radiance spectra from multiple scans. To obtain an estimate of the FPA performance, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is developed based on the pixel performance evaluation. This would allow us to perform the calibration procedures on a random pixel population that is a good statistical representation of the entire FPA. The design and implementation of each individual component will be discussed in details.

Tian, Jialin↗

DOE OSTI2024

Optimal spectral resolution for solids and liquids using FT and other infrared spectrometers: How much resolution do you really need?

In this study we investigate the possibility of using spectral resolutions for infrared measurements of solids and liquids that are not powers of two, e.g. are not at 1, 2, 4, 8, or 16 cm-1 resolution. In almost all reported literature of the last fifty years the resolution used to record for a Fourier transform infrared spectrum has been a power of two. This stems from the fact that 1) the Cooley-Tukey algorithm used to compute such a transform was constructed to use only powers of two and was also driven by 2) the fact that the computing horsepower required to compute the Fourier transform increases as N?log?_2 (N), where N is the number of points in the interferogram (spectrum). For typical spectra, however, the CPU time is no longer a consideration. Our study is based on both liquid and solid spectra, all of which were recorded at 2 cm-1 resolution. There were at total of 70 solids spectra representing 2,472 spectral peaks and 61 liquids spectra (1,765 spectral peaks), each peak being inspected for being singlet / multiplet in nature. Of the 1,765 liquid bands examined, only 27 had widths less than 5 cm-1. Of the 2,472 solid bands examined, only 39 peaks have widths less than 5 cm-1. For liquids, the mean peak width is 24.7 cm-1 but the median peak width is 13.7 cm-1, and, similarly, for solids, the mean peak width is 22.2 cm-1 but the median peak width is 11.2 cm-1. In both cases, solids and liquids, a skewed peak widths distribution was observed, the peak of the distribution representing narrower bands in the 7 to 9 cm-1 FWHM range but displaying a long tail to the very broad bands, with some displaying spectral widths of 100 cm-1 or more. Because one of the most important criteria for successful instrumental design in IR spectroscopy is the spectral resolution, the data were further analyzed showing that a value to resolve 95% of all bands is 5.7 cm-1 for liquids and 5.3 cm-1 for solids; such a resolution would capture the native linewidth (no instrumental broadening) of 95% of all the solids and liquid bands, respectively. Based on the present results we suggest that, when accounting only for intrinsic linewidths an optimized resolution of 6.0 cm-1 will capture 91% of all condensed-phase bands for IR detection of chemical, mineral, and biological materials.

Forland, Brenda M.↗

DOE OSTI2024

Reviews and syntheses: Opportunities for robust use of peak intensities from high-resolution mass spectrometry in organic matter studies

Abstract. Earth's biogeochemical cycles are intimately tied to the biotic and abiotic processing of organic matter (OM). Spatial and temporal variations in OM chemistry are often studied using direct infusion, high-resolution Fourier transform mass spectrometry (FTMS). An increasingly common approach is to use ecological metrics (e.g., within-sample diversity) to summarize high-dimensional FTMS data, notably Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). However, problems can arise when FTMS peak-intensity data are used in a way that is analogous to abundances in ecological analyses (e.g., species abundance distributions). Using peak-intensity data in this way requires the assumption that intensities act as direct proxies for concentrations. Here, we show that comparisons of the same peak across samples (within-peak) may carry information regarding variations in relative concentration, but comparing different peaks (between-peak) within or between samples does not. We further developed a simulation model to study the quantitative implications of using peak intensities to compute ecological metrics (e.g., intensity-weighted mean properties and diversity) that rely on information about both within-peak and between-peak shifts in relative abundance. We found that, despite analytical limitations in linking concentration to intensity, ecological metrics often perform well in terms of providing robust qualitative inferences and sometimes quantitatively accurate estimates of diversity and mean molecular characteristics. We conclude with recommendations for the robust use of peak intensities for natural organic matter studies. A primary recommendation is the use and extension of the simulation model to provide objective guidance on the degree to which conceptual and quantitative inferences can be made for a given analysis of a given dataset. Broad use of this approach can help ensure rigorous scientific outcomes from the use of FTMS peak intensities in environmental applications.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1976

Subresolution imaging - Use of wavelength and angular diversity techniques

The paper demonstrates the possibility of using an illumination system tunable in angle or wavelength to determine the amplitude and height structure of an object within the resolution cell defined by the resolving power of some imaging system. It is noted that since the value of the electric field at a point on the image of an object varies with the wavelength or angle of illumination on the object, the Fourier transform of this variation provides directly the amplitude and phase structure of the object within the resolution cell corresponding to the image point of interest. This Fourier transform is calculated, and it is shown that the transform of the electric-field intensity with respect to the inverse wavelength dimension is simply the autocorrelation of the electric-field variation with wavelength. Practical techniques that can be employed to measure the subresolution detail of an object are briefly discussed.

Jain, A.↗

NASA NTRS1982

Computing the Power-Density Spectrum for an Engineering Model

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.

Dunn, H. J.↗

NASA NTRS1986

Analytical comparison of transient and steady state visual evoked cortical potentials

To better describe the linear-dynamic properties of the human visual-cortical response system, transient and steady state Visual Evoked Response Potentials (VERP) were observed. The stimulus presentation device provided both the evoking stimulus (flickering or pulsing lights) and a video task display. The steady state stimulus was modulated by a complex, ten frequency, sum-of-sines, wave. The transient VERP was the time-locked average of the EEG to a series of narrow light pulses (pulse width of 10 msec). The Fourier transform of the averaged pulses had properties that approximate band limited white noise, i.e., a flat spectrum over the frequency region spanned by the 10 summed sines. The Fourier transform of both the steady state and the transient evoked potentials resulted in transfer that are equivalent and therefore comparable. To investigate the effects of task loading on evoked potentials, a grammatical reasoning task was provided. Results support the relevancy of continued application of a systems engineering approach for describing neurosensory functioning.

Junker, A. M.↗

NASA NTRS1988

The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior

A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.

Bussard, R. W.↗

NASA NTRS1984

A hybrid silicon membrane spatial light modulator for optical information processing

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.

Pape, D. R.↗

NASA NTRS1988

Applications of Digital Image Processing 11

A new technique, digital image velocimetry, is proposed for the measurement of instantaneous velocity fields of time dependent flows. A time sequence of single-exposure images of seed particles are captured with a high-speed camera, and a finite number of the single-exposure images are sampled within a prescribed period in time. The sampled images are then digitized on an image processor, enhanced, and superimposed to construct an image which is equivalent to a multiple exposure image used in both laser speckle velocimetry and particle image velocimetry. The superimposed image and a single-exposure Image are digitally Fourier transformed for extraction of information on the velocity field. A great enhancement of the dynamic range of the velocity measurement is accomplished through the new technique by manipulating the Fourier transform of both the single-exposure image and the superimposed image. Also the direction of the velocity vector is unequivocally determined. With the use of a high-speed video camera, the whole process from image acquisition to velocity determination can be carried out electronically; thus this technique can be developed into a real-time capability.

Cho, Y. -C.↗

NASA NTRS1974

Viewing-angle effects in radar images

A quantitative determination of the effect of viewing angle on the detectability of topographic linears in radar imagery is presented. Variations of azimuth and aspect angles of an imaging radar antenna relative to a topographic linear were simulated using low-angle illumination of controlled linear features on polystyrene sheets. The several model surfaces represented idealized versions of surface types that may be expected in areas of geologic interest. Fourier transform spectra of the radar image simulations were obtained using a coherent-optics system. These spectra were found to correlate with a detectability factor obtained directly from the radar image simulations. Fourier transform spectra of a linear feature observed from multiple viewing angles by a K-band imaging radar were also obtained and a detectability factor was estimated which agreed closely with theoretical predictions.

Eppes, T. A.↗

NASA NTRS1986

Three-Dimensional Radiative-Transfer Equation

Progress made toward interpretation of radiometric observations. Paper discusses equation of radiative transfer in three-dimensional, inhomogeneous, scattering medium illuminated from above and bounded below by laterallyinhomogeneous, reflective plane. Representation of radiation field with full three-dimensional variability derived by use of spatial Fourier transform and matrix-operator techniques developed previously for one-dimensional version of problem. Equations useful for radiometric measurements from aircraft and spacecraft. Although derivations and resulting equations complicated, use of Fourier-transform, matrix-operator approach to solve practical problems simpler than direct solution of complete three-dimensional, linear wave equations.

Martonchik, J. V.↗