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NASA NTRS1985

Comments on techniques for spectral deconvolution

Current observational questions in asteroseismology require high spectral resolution that can be only be obtained with observations spanning many days or months. The primary constraint in the full utilization of single mid-latitude observing sites is the presence of diurnal data gaps. Several methods for removing the effect of these gaps in the spectral obtained from velocity observations have been suggested. In the case of data coverage of less than 50%, none of the methods considered has been successful at unambiguously recovering the true spectrum from test spectra with realistic complexity. The limitations of these methods and their applicability to the helioseismology problem is discussed.

Scherrer, P. H.↗
NASA NTRS1987

Deconvolution of spectra for intimate mixtures

Visible to near infrared reflectance spectra of macroscopic mixtures have been shown to be linear combinations of the reflections of the pure mineral components in the mixture. However, for microscopic mixtures the mixing systematics are in general nonlinear. The systematics may be linearized by conversion of reflectance to single scattering albedo (w), where the equations which relate reflectance to w depend on the method of data collection. Several proposed mixing models may be used to estimate mineral abundances from the reflectance spectra of intimate mixtures. These models are summarized and a revised model is presented. A noniterative (linear) least squares approach was used for curve fitting and the data, measured as bi-directional reflectance with incidence and emergence angles of 30 and 0 deg were converted to w by a simplified version of Hapke's equation for bi-directional reflectance. This model was tested with two mixture series composed of 45 to 75 micron particles: an anorthite-enstatite series and an olivine-magnetite series. The data indicate that the simplified Hapke's equation may be used to convolve reflectance spectra into mineral abundances if appropriate endmembers are known or derived from other techniques. For surfaces that contain a significant component of very low albedo material, a somewhat modified version of this technique will need to be developed. Since the abundances are calculated using a noniterative approach, the application of this method is especially efficient for large spectral data sets, such as those produced by mapping spectrometers.

Mustard, John F.↗
NASA NTRS1986

Comments on techniques for spectral deconvolution

Current observational questions in asteroseismology require high spectral resolution that can only be obtained with observations spanning many days or months. The primary constraint in the full utilization of single mid-latitude observing sites is the presence of diurnal data gaps. Several methods for removing the effect of these gaps in the spectral obtained from velocity observations have been suggested. In the case of data coverage of less than 50 percent, none of the methods considered has been successful at unambiguously recovering the true spectrum from test spectra with realistic complexity. The limitations of these methods and their applicability to the helioseismology problem is discussed.

Scherrer, Philip H.↗
NASA NTRS1986

Instrument-induced spatial crosstalk deconvolution algorithm

An algorithm has been developed which reduces the effects of (deconvolves) instrument-induced spatial crosstalk in satellite image data by several orders of magnitude where highly precise radiometry is required. The algorithm is based upon radiance transfer ratios which are defined as the fractional bilateral exchange of energy betwen pixels A and B.

Wright, Valerie G.↗
NASA NTRS1988

Deconvolution results for wide field-of-view radiometer measurements of reflected solar radiation

The measurement of reflected solar radiation by spacecraft wide-field-of-view radiometers is considered analytically, and the method proposed by Smith (1987) for the solution of the discretized governing equations is described and demonstrated. The theoretical basis of the singular-value decomposition method (partitioning the albedo field into observable and unobservable components) is outlined; its application to Nimbus 7 ERB data is explained in detail; and numerical results are presented in graphs and maps and briefly characterized.

Smith, G. Louis↗
NASA NTRS1987

Deconvolution of a pre-outburst picture of SN 1987A

The block iterative method (Young 1971) of algebraic image restoration is applied to a photographic plate of the field around SN 1987A obtained 4 yr before outburst by Chu at the CTIO 4-m telescope. By setting appropriate constraints for the solution on a pixel-by-pixel basis, the image of a starfield centered on Sk -69 202, the precursor to the supernova, is restored. It is found that this star has two companions, which others (e.g., Walborn et al., 1987 and West et al., 1987) have also noted and designated as Star 2 and Star 3. Also found is marginal evidence for Star 4, a weak source at theta = 222 deg, r = 1.9 arcsec. Correction for the contributions of these companions yields an estimate of the magnitude for Sk -69 202 alone of V = 12.37.

Heap, Sara R.↗
NASA NTRS1989

Maximum entropy deconvolution of the optical jet of 3C 273

The technique of maximum entropy image restoration is applied to the problem of deconvolving the point spread function from a deep, high-quality V band image of the optical jet of 3C 273. The resulting maximum entropy image has an approximate spatial resolution of 0.6 arcsec and has been used to study the morphology of the optical jet. Four regularly-spaced optical knots are clearly evident in the data, together with an optical 'extension' at each end of the optical jet. The jet oscillates around its center of gravity, and the spatial scale of the oscillations is very similar to the spacing between the optical knots. The jet is marginally resolved in the transverse direction and has an asymmetric profile perpendicular to the jet axis. The distribution of V band flux along the length of the jet, and accurate astrometry of the optical knot positions are presented.

Evans, I. N.↗
NASA NTRS1990

Deconvolution of wide-field-of-view measurements of reflected solar radiation

Wide-field-of-view (WFOV) radiometers have been flown as part of the Earth Radiation Budget instrument on the Nimbus 6 and 7 spacecraft and as part of the Earth Radiation Budget Experiment (ERBE) instruments aboard the ERBE spacecraft and also the NOAA 9 and 10 operational spacecraft. The measurement is the integral of the reflected solar flux distribution at the top of the earth-atmosphere system over the field-of-view of the radiometer. This paper develops the solution to this two-dimensional integral equation for the albedo distribution in terms of the measurements.

Smith, G. Louis↗
NASA NTRS1990

Formulation of a minimum variance deconvolution technique for compensation of pneumatic distortion in pressure sensing devices

Increasingly, aircraft system designs require that aerodynamic parameters derived from pneumatic measurements be employed as control-system feedbacks. Such high frequency pressure measurements' accuracy is compromised by pressure distortion due to frictional attenuation and pneumatic resonance within the sensing system. A pneumatic distortion model is here formulated and reduced to a low-order state-variable model which retains most of the full model's dynamic characteristics. This reduced-order model is coupled with standard results from minimum variance estimation theory to develop an algorithm to compensate for pneumatic-distortion effects.

Whitmore, Stephen A.↗
NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗
NASA NTRS1988

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 2

This thesis reviews the technique established to clear channels in the Power Spectral Estimate by applying linear combinations of well known window functions to the autocorrelation function. The need for windowing the auto correlation function is due to the fact that the true auto correlation is not generally used to obtain the Power Spectral Estimate. When applied, the windows serve to reduce the effect that modifies the auto correlation by truncating the data and possibly the autocorrelation has on the Power Spectral Estimate. It has been shown in previous work that a single channel has been cleared, allowing for the detection of a small peak in the presence of a large peak in the Power Spectral Estimate. The utility of this method is dependent on the robustness of it on different input situations. We extend the analysis in this paper, to include clearing up to three channels. We examine the relative positions of the spikes to each other and also the effect of taking different percentages of lags of the auto correlation in the Power Spectral Estimate. This method could have application wherever the Power Spectrum is used. An example of this is beam forming for source location, where a small target can be located next to a large target. Other possibilities extend into seismic data processing. As the method becomes more automated other applications may present themselves.

Ioup, George E.↗
NASA NTRS1993

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution. Appendix 7

Because of the interesting science which can be performed using a satellite attached by a very long tether to a mother vehicle in orbit, such as the Space Shuttle, NASA will deploy TSS-1 (Tethered Satellite System) in 1992. A very long tether (20 km in this case) has the possibility of undergoing oscillations of several different types, or modes, and higher harmonics of these modes. The purpose of this document is to describe a method for detecting the amplitude, frequency, and phase (and predicting future motion in the steady state) of these modes, in particular, the skiprope mode, using tethered satellite dynamics measurements. Specifically the rotation rate data about two orthogonal axes, calculated from output from satellite gyroscopes, are used. The data of interest are the satellite pitch and roll rate measurements. NASA has determined to use two methods to diagnose skiprope properties and predict future values. One of these, a Fourier transform domain approach, is the subject of this notebook. The main program and all subroutines are described along with the test plan for evaluating the Frequency Domain Skiprope Observer.

Ioup, George E.↗
NASA NTRS1992

On Capaciflector sensor data interpretation using the constrained deconvolution algorithm

The Capaciflector, a capacitive proximity sensor, is being developed by NASA for collision avoidance. Capaciflector provides a single output value as measure of altered base frequency. This value is a characteristic of an external object in the sensor's field of view. An attempt is made to use the Capaciflector for imaging with operating range from 1 to 2 inches. By positional arangement of sensors in a grid pattern and electronic activation of sensors over the grid one at a time an object characteristic image is obtained. The article describes the Capaciflector experimental imaging system and preliminary results obtained by the system.

Campbell, Charles E., Jr.↗
NASA NTRS1993

Measurement of intact-core length of atomizing liquid jets by image deconvolution

The investigation of liquid jet breakup and spray development is critical to the understanding of combustion phenomena in liquid propellant rocket engines. Much work has been done to characterize low-speed liquid jet breakup and dilute sprays, but atomizing jets and dense sprays have yielded few quantitative measurements due to their high liquid load fractions and hence their optical opacity. Focus was on a characteristic of the primary breakup process of round liquid jets, namely the length of the intact-liquid core. The specific application considered is that of shear-coaxial-type rocket engine injectors in which liquid oxygen is injected through the center post while high velocity gaseous hydrogen is injected through a concentric annulus, providing a shear force to the liquid jet surface. Real-time x ray radiography, capable of imaging through the dense two-phase region surrounding the liquid core, is used to make the measurements. The intact-liquid-core length data were obtained and interpreted using two conceptually different methods to illustrate the effects of chamber pressure, gas-to-liquid momentum ratio, and cavitation.

Woodward, Roger↗
NASA NTRS1993

A new technique for deconvolution of data from instruments that make integral measurements, e.g. RIMS on DE-1

A general method for deconvolving an unknown function from integral measurements is described and applied to data from the instrument Retarding Ion Mass Spectrometer (RIMS) aboard the spacecraft Dynamics Explorer 1 (DE-1). The principal features of the method are: (1) it uses objective criteria based upon fundamental statistical principles, i.e. Bayesian statistics; (2) it provides for insertion of prior knowledge in a non-prejudicial, explicit manner through the choice of breakpoints that determine the bicubic spline expansion functions; (3) it prevents random fluctuations from controlling the fit to the data through the use of singular value decomposition and the elimination of small singular values; and (4) it guards agianst the introduction of spurious features into the result by including a penalty function and using the principle of generalized cross validation. Illustrative examples from RIMS data for H(+) and O(+) show that the method provides enhanced accuracy and detail in deconvolving the ion phase space density.

Perez, J. D.↗
NASA NTRS2003

Vertical Distribution of Shallow Water in the Distinguishable Regions at Low and High Latitudes of Mars: Neutron Data Deconvolution of HEND

High Energy Neutron Detector (HEND) is the part of Gamma-Ray Spectrometer suite onboard NASA Mars Odyssey orbiter [1-4]. During 16 months of mapping stage of Odyssey mission HEND has accumulated the set of maps of neutron emission of Mars at more than seven decades of energies range from the Cadmium threshold of 0.4 eV up to 15 MeV. These maps present very large variations of neutrons at different regions of Mars and they also show quite strong changes along Martian seasons.

I G Mitrofanov↗