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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.
Advanced research results on the seismology of the Sun and distant stars is presented. Topics presented include: (1) detection of global convective wave flows; (2) observation of low degree p-mode oscillations; and (3) techniques for spectral deconvolution.
Ultrasonic test system input-output characteristics were investigated by directly coupling the transmitting and receiving transducers face to face without a test specimen. Some of the fundamentals of digital signal processing were summarized. Input and output signals were digitized by using a digital oscilloscope, and the digitized data were processed in a microcomputer by using digital signal-processing techniques. The continuous-time test system was modeled as a discrete-time, linear, shift-invariant system. In estimating the unit-sample response and frequency response of the discrete-time system, it was necessary to use digital filtering to remove low-amplitude noise, which interfered with deconvolution calculations. A digital bandpass filter constructed with the assistance of a Blackman window and a rectangular time window were used. Approximations of the impulse response and the frequency response of the continuous-time test system were obtained by linearly interpolating the defining points of the unit-sample response and the frequency response of the discrete-time system. The test system behaved as a linear-phase bandpass filter in the frequency range 0.6 to 2.3 MHz. These frequencies were selected in accordance with the criterion that they were 6 dB below the maximum peak of the amplitude of the frequency response. The output of the system to various inputs was predicted and the results were compared with the corresponding measurements on the system.
Amplifier gain and collimator hole size variations across the field of view, amplifier/filter efficiency, variations in effective collimator hole size and angular response with photon energy, dead-time, and hard X-ray plate transmission, are among the factors for which instrumental corrections have to be incorporated to effect reliable correction and deconvolution of images from the SMM satellite's Hard X-ray Imaging Spectrometer (HXIS). Attention is given to the substantial Poisson noise in these energy bands. The maximum entropy deconvolution/correction routine developed for establishing the spatial structure reliably inferrable from HXIS data is presented, together with the results of the application of this routine to the three impulsive flares reported by Duijemian et al. (1982) from April 10, May 21, and November 5, 1980.
Spatial scans of IRC + 10216 and NGC 7027 were made at 50 and 100 microns using a diffraction-limited slit. Maximum entropy deconvolution techniques were applied to the data and, in effect, the structure of these sources was probed down to a scale far smaller than previously achieved at these wavelengths. IRC + 10216 was unresolved on a spatial scale of several arcsecs and a low upper limit to either the dust-gas ratio or the bulk emissivity of the grains was implied for the large molecular envelope surrounding the star. NGC 7027 was easily resolved in the scans, with far-infrared emission distribution corresponding closely with the distribution of ionized gas and shorter wavelength infrared emission.
Deconvolution algorithm assists in analysis of x-ray spectra from scanning electron microscopes, electron microprobe analyzers, x-ray fluorescence spectrometers, and like. New algorithm automatically deconvolves x-ray spectrum, identifies locations of spectral peaks, and selects chemical elements most likely producing peaks. Technique based on similarities between zero- and second-order terms of Taylor-series expansions of Gaussian distribution and of damped sinusoid. Principal advantage of algorithm: no requirement to adjust weighting factors or other parameters when analyzing general x-ray spectra.
A restoration of the 37, 21, 18, 10.7, and 6.6 GHz satellite imagery from the scanning multichannel microwave radiometer (SMMR) aboard Nimbus-7 to 22.2 km resolution is attempted using a deconvolution method based upon nonlinear programming. The images are deconvolved with and without the aid of prescribed constraints, which force the processed image to abide by partial a priori knowledge of the high-resolution result. The restored microwave imagery may be utilized to examine the distribution of precipitating liquid water in marine rain systems.
Electron-attachment cross sections are reported in the electron energy range 0-160 meV, and at energy resolutions of 7.0 and 7.5 meV (FWHM), for the molecules CF2Cl2 (dichlorodifluoromethane), c-C4F6 (perfluorocyclobutene), c-C4F8 (perfluorocyclobutane), and c-C7F14 (perfluoromethylcyclohexane). Use is made of the Kr photoionization method. Measured attachment lineshapes are deconvoluted from the spectral slit function, and are converted to cross sections by normalization through thermal attachment-rate constants. Comparisons are made with attachment cross sections derived from several independent sets of swarm-measured rate constants, and with collisional ionization (high-Rydberg attachment) data.
High angular resolution scans at 42 and 95 microns have been obtained of the far-infrared source associated with S106. Using maximum entropy deconvolution techniques it is found that the far-IR-emitting dust appears to be distributed in a toroidal shape around the central star.This result is similar to the morphology implied to millimeter line and continuum mapping on a variety of size scales.
For automation and robotics in the Space Station era, NASA's Johnson Space Center is pursuing several means of synthetic vision. The optical correlator is one such means. The deformable mirror device will form the basis of the first correlator in this project. In-house and contracted effort is being used. Initial in-house activities will concentrate on an impulse deconvolution technique and on a programmable retina for spatial remappings of an image prior to correlation. The retina will permit a form of edge extraction and other primitive operations. Additionally, it will be used as a research tool for assisting persons with low vision.
High-resolution visible and near-infrared diffuse reflectance spectra of mafic silicates can be deconvolved to yield quantitative information concerning mineral mixture properties, and the results can be directly applied to remotely sensed data. Spectral reflectance measurements of laboratory mixtures of olivine, orthophyroxene, and clinopyroxene with known chemistries, phase abundances, and particle size distributions have been utilized to develop correlations between spectral properties and the physicochemical parameters of the samples. A large number of mafic silicate spectra were measured and examined for systematic variations in spectral properties as a function of chemistry, phase abundance, and particle size. Three classes of spectral parameters (ratioed, absolute, and wavelength) were examined for any correlations. Each class is sensitive to particular mafic silicate properties. Spectral deconvolution techniques have been developed for quantifying, with varying degrees of accuracy, the assemblage properties (chemistry, phase abundance, and particle size).
Reduction of data acquired from the HELIOS Solar Wind Plasma Wave Experiments on HELIOS 1 and 2 was continued. Production of 24 hour survey plots of the HELIOS 1 plasma wave data were continued and microfilm copies were submitted to the National Space Science Data Center. Much of the effort involved the shock memory from both HELIOS 1 and 2. This data had to be deconvoluted and time ordered before it could be displayed and plotted in an organized form. The UNIVAX 418-III computer was replaced by a DEC VAX 11/780 computer. In order to continue the reduction and analysis of the data set, all data reduction and analysis computer programs had to be rewritten.
Several techniques useful in the analysis of data from coded-mask telescopes are presented. Methods of handling changes in the instrument pointing direction are reviewed and ways of using FFT techniques to do the deconvolution considered. Emphasis is on techniques for optimally-coded systems, but it is shown that the range of systems included in this class can be extended through the new concept of 'partial cycle averaging'.
The problem of deconvolution of the point source response function (PSF) for two-dimensional imaging infrared arrays is addressed. A variety of phenomena can lead to PSF degradation, ranging from atmospheric turbulence to the array itself. The maximum entropy algorithm is used to demonstrate that substantial image quality improvements are possible in the case of a PSF which is degraded by electronic rather than optical smearing. This result implies that IR arrays need not have perfect or even very good pixel-pixel crosstalk rejection ratios for use in astronomy.
Far-infrared slit scans across NGC 1068 are used to better define the contribution of the active nucleus, starburst disk, and extended spiral arms in the luminous output of this bright Seyfert 2 galaxy. The decomposition of the emission from the bright, inner 3 kpc of this galaxy suggests that at 50 microns, about half the emission is from star formation in a starburst disk and half from the compact, centrally heated circumnuclear cloud. The 100-micron profile of the starburst disk is asymmetric with respect to the nucleus. This appears to be the result of an extraordinary star-forming complex about a kiloparsec away from the center. With the application of maximum entropy deconvolution to the scans, evidence is found for 100-micron emission from the extended spiral arms of the galaxy. The far-infrared emission from the starburst region is distinguished from that of the extended spiral arms. In terms of both total luminosity and surface brightness, the extended spiral arms of NGC 1068 are at the bright end of the range of far-infrared emission from quiescent, noninteracting spirals.
A radiance value of a target pixel recorded by a remote sensor can be decomposed into three components: (1) attenuated target signature, (2) pure atmospheric radiation, and (3) the contribution made by the ground through the atmospheric scattering process. Given the meteorological and optical parameters of a layer-structured atmosphere, its transmittance and radiance distribution can be accurately calculated with a plane-parallel radiative transfer model. For a uniform surface, the ground contribution can be obtained by comparing radiances for an atmosphere over a black but nonemitting surface and the same atmosphere with an underlying ground of given albedo or temperature. For an inhomogeneous surface, the first two components remain the same as long as the surface is a plane. The third may be estimated using the locally averaged top-of-atmosphere radiance. An atmospheric point spread function is calculated by a Monte Carlo approach and is used for retrieving the ground signature through a deconvolution procedure.
Careful deconvolution of spatially resolved IUE ultraviolet spectra shows that only two of the three stars detected in plate material before 1987 are now present near the site of SN 1987A. The separation, magnitudes, and spectra of these two are consistent with their identification as star 2 and star 3 of the Sanduleak -69 deg 202 trio. The clear implication is that star 1, the 12th mag B3 I star, has disappeared, and it may be identified as the progenitor of SN 1987A.
High-resolution far-infrared observations of the galaxy NGC 4945 have been obtained from the Kuiper Airborne Observatory. Using new observational techniques and nonlinear deconvolution routines, it is found that virtually all of the far-infrared luminosity originates from a nuclear source no larger than 12 arcsec x 9 arcsec (225 pc x 170 pc) in extent. This size constraint, coupled with the far-infrared dust temperature, indicates that the source is deeply embedded in dust: the lower limit for the 100 micron optical depth is 0.35, which is by far the largest yet measured in an external galaxy. Published optical spectra of NGC 4945 reveal a heavily obscured nonthermal source which exhibits broad line profiles typical of a Seyfert 2 active nucleus; it is concluded that the far-infrared emission is probably due to thermal radiation from dust grains surrounding the nonthermal nuclear source. A compact cluster of massive young stars may also contribute to the infrared luminosity, but the evidence for such star-forming activity is weak.