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Eigenfunction expansions of reduced nonGaussian phase error transition probability density function for first order tracking loop, analyzing spectral properties of Fokker-Planck equation
Light from an incoherently radiating object and background light are focused onto a photosensitive mosaic, the currents from whose elements constitute the data on which is based a least-squares linear estimate of the radiance at points in the object. By comparison of the mean-square error with that given by Wiener filtering theory, the equivalent noise spectral density for use in the latter is shown to consist of a shot-noise term and a term due to the random fluctuations of the incoherent light; the former predominates under most circumstances. Turbulent distortion of the image after passage of the rays through a random-phase screen is also treated from this standpoint.
Optimum bounding filters are derived for a specific version (steady state time-invariant with scalar observations) of the Kalman-Bucy filtering problem with inexactly known system parameters and for the Wiener filtering problem with inexactly known spectral densities. The designed filter obtains a bound on the actual error covariance which is not known, and it also prevents apparent divergence. Conditions are derived for the design of the optimum bounding filter within a permissible class of solutions; this turns out to be the min-max mean-square error filter for an extended class of solutions. The bounding filter can be of lower order than the original system, and a technique is devised for reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance.
Two test sites of different water quality and bottom topography were used to test for maximum water depth penetration using the Skylab S-192 MSS for measurement of nearshore coastal bathymetry. Sites under investigation lie along the Lake Michigan coastline where littoral transport acts to erode sand bluffs and endangers developments along 1,200 miles of shore, and on the west coast of Puerto Rico where unreliable shoal location and depth information constitutes a safety hazard to navigation. The S-192 and S-190A and B provide data on underwater features because of water transparency in the blue/green portion of the spectrum. Depth of 20 meters were measured with the S-192 in the Puerto Rico test site. The S-190B photography with its improved spatial resolution clearly delineates the triple sand bar topography in the Lake Michigan test site. Several processing techniques were employed to test for maximum depth measurement with least error. The results are useful for helping to determine an optimum spectral bandwidth for future space sensors that will increase depth measurements for different water attenuation conditions where a bottom reflection is detectable.
The author has identified the following significant results. In order to choose a design which will be optimal for the largest class of remote sensing problems, a method was developed which attempted to represent the spectral response function from a scene as accurately as possible. The performance of the overall recognition system was studied relative to the accuracy of the spectral representation. The spectral representation was only one of a set of five interrelated parameter categories which also included the spatial representation parameter, the signal to noise ratio, ancillary data, and information classes. The spectral response functions observed from a stratum were modeled as a stochastic process with a Gaussian probability measure. The criterion for spectral representation was defined by the minimum expected mean-square error.
The subcarrier phase recovery is analyzed for the bent-pipe mode of Space Shuttle detached-payload data transmission on the Tracking and Data Relay Satellite System (TDRSS) Ku-band return link. The high-power component of the subcarrier modulation is unrestored payload data, either at baseband or modulating another subcarrier. At the receiver a Costas loop recovers the subcarrier phase. To analyze its performance in the baseband case, we obtain the loop S-curve, the power spectral density of the equivalent noise process, and the loop phase error variance.
Mean absolute intensities (spectral radiance) over 0.1 nm intervals between 225.2 nm and 319.6 nm at disk center and near the limb of the sun (mu = 0.23 + or - 0.04) are derived from the high spectral resolution measurements published by Kohl, Parkinson, and Kurucz. The corresponding limb-to-center ratios and spectral irradiance values are provided. A comparison with existing measurements of solar spectral radiance and spectral irradiance for the most part shows agreement within the estimated error limits, although some narrow band variations may be outside experimental errors. The contribution to the solar constant of the 230-305 nm band is derived to be 19.7 W/square m + or - 12%.
In virtue of the extent to which the visible and near-IR spectral reflectance of minerals that may be encountered on asteroid surfaces is a function of temperature, surface temperature distributions must be taken into account in the mineralogical evaluation of spectral reflectance data obtained from a spatially resolved asteroid surface. Possible errors of this type are presently illustrated for the case of a silicate mineral assemblage measured at the various temperatures that may be encountered over an asteroid surface, in order to allow optimal mineralogical data extraction.
This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve(s), refine existing triangulations based on solution error measures, and partition meshes based on the Cuthill-McKee, spectral, and coordinate bisection strategies.
The static response of sea level to the forcing of atmospheric pressure, the so-called inverted barometer (IB) effect, is investigated using TOPEX/POSEIDON data. This response, characterized by the rise and fall of sea level to compensate for the change of atmospheric pressure at a rate of -1 cm/mbar, is not associated with any ocean currents and hence is normally treated as an error to be removed from sea level observation. Linear regression and spectral transfer function analyses are applied to sea level and pressure to examine the validity of the IB effect. In regions outside the tropics, the regression coefficient is found to be consistently close to the theoretical value except for the regions of western boundary currents, where the mesoscale variability interferes with the IB effect. The spectral transfer function shows near IB response at periods of 30 degrees is -0.84 +/- 0.29 cm/mbar (1 standard deviation). The deviation from = 1 cm /mbar is shown to be caused primarily by the effect of wind forcing on sea level, based on multivariate linear regression model involving both pressure and wind forcing. The regression coefficient for pressure resulting from the multivariate analysis is -0.96 +/- 0.32 cm/mbar. In the tropics the multivariate analysis fails because sea level in the tropics is primarily responding to remote wind forcing. However, after removing from the data the wind-forced sea level estimated by a dynamic model of the tropical Pacific, the pressure regression coefficient improves from -1.22 +/- 0.69 cm/mbar to -0.99 +/- 0.46 cm/mbar, clearly revealing an IB response. The result of the study suggests that with a proper removal of the effect of wind forcing the IB effect is valid in most of the open ocean at periods longer than 20 days and spatial scales larger than 500 km.
A two component Point Doppler Velocimetry (PDV) system has been developed and tested. Improvements were made to an earlier PDV system, in terms of experimental techniques, as well as the data acquisition and reduction software. Measurements of the streamwise and spanwise mean and fluctuating velocities for flows from a rectangular channel and over an NACA 0012 airfoil were made, and the data were compared against hot wire data. The closest to the airfoil surface that PDV measurements could be made was on the order of 0.005 m(0.2", z/c = 0.0169). When the PDV and hot wire data were compared, the time traces for each appeared similar. The mean velocities agreed to within plus or minus 2 m/sec, while the RMS velocities agreed to plus or minus 0.4 m/sec. While the PDV time autocorrelations agreed with those of the hot wire data, the PDV power spectral densities were noisier above 750 Hz. A major source of error in these experiments was determined to be the drifting of the iodine cell stem temperatures. While the stem temperatures were controlled to within plus or minus 0.1 C, this could lead to a frequency shift of as much as 6 MHz, which translates into an error of 1.6 m/sec for the back scatter channel, and up to 6.9 m/sec for the forward scatter channel. These error estimates are consistent with the observed error magnitudes.
Ball Aerospace and Technologies Corporation in Boulder, Colorado, has developed a heliostat facility that will be used to determine the preflight radiometric calibration of Earth-observing sensors that operate in the solar-reflective regime. While automatically tracking the Sun, the heliostat directs the solar beam inside a thermal vacuum chamber, where the sensor under test resides. The main advantage to using the Sun as the illumination source for preflight radiometric calibration is because it will also be the source of illumination when the sensor is in flight. This minimizes errors in the pre- and post-launch calibration due to spectral mismatches. It also allows the instrument under test to operate at irradiance values similar to those on orbit. The Remote Sensing Group at the University of Arizona measured the transmittance of the heliostat facility using three methods, the first of which is a relative measurement made using a hyperspectral portable spectroradiometer and well-calibrated reference panel. The second method is also a relative measurement, and uses a 12-channel automated solar radiometer. The final method is an absolute measurement using a hyperspectral spectroradiometer and reference panel combination, where the spectroradiometer is calibrated on site using a solar-radiation-based calibration.
A purely ab initio potential energy surface (PES) was refined with selected (32)S(16)O2 HITRAN data. Compared to HITRAN, the root-mean-squares error (RMS) error for all J=0-80 rovibrational energy levels computed on the refined PES (denoted Ames-1) is 0.013 cm(exp -1). Combined with a CCSD(T)/aug-cc-pV(Q+d)Z dipole moment surface (DMS), an infrared (IR) line list (denoted Ames-296K) has been computed at 296K and covers up to 8,000 cm(exp -1). Compared to the HITRAN and CDMS databases, the intensity agreement for most vibrational bands is better than 85-90%. Our predictions for (34)S(16)O2 band origins, higher energy (32)S(16)O2 band origins and missing (32)S(16)O2 IR bands have been verified by most recent experiments and available HITRAN data. We conclude that the Ames-1 PES is able to predict (32/34)S(16)O2 band origins below 5500 cm(exp -1) with 0.01-0.03 cm(exp -1) uncertainties, and the Ames-296K line list provides continuous, reliable and accurate IR simulations. The Ka-dependence of both line position and line intensity errors is discussed. The line list will greatly facilitate SO2 IR spectral experimental analysis, as well as elimination of SO2 lines in high-resolution astronomical observations.
Raman imaging is an emerging tool for the analysis of meteorites, as it is capable of describing mineralogy, carbon composition/speciation, and crystal orientation all within a petrographic context. Adequately examining the heterogeneous composition of a meteorite, while maintaining low laser powers needed to prevent damage to meteorite mineralogy and organics, often requires the collection of large Raman images with long collection times on the timescale of days. However, the frequency calibration of the Raman instrument/spectrometer drifts on long timescales resulting in low frequency precision for the Raman spectra comprising a large Raman image. This decrease in frequency precision can compromise the analysis of geological markers that can provide important information on a meteorite sample. We examine, in detail, the change in bandwidth and frequency of the Raman bands and Hg-Ar emission lines in our Raman images as a function of time and laboratory temperature. To overcome the drift in calibration, we utilize a commercial WITec Raman instrument with an internal Hg-Ar calibration lamp to individually calibrate each spectrum in the Raman image. Our instrument, known as “Ratatoskr”, uses a beam splitter in place of the customary mirror to facilitate collection of Hg-Ar calibration lines concurrent with Raman spectra. We show that using the internal calibration we can improve the frequency precision for the spectra in our Raman images from ~±0.15 cm(exp -1) to ~±0.05 cm(exp -1) for Raman spectra collected over multiple days. This is important as it improves measurements of mineral chemistry, latent strain, and other features that are dependent upon accurate peak position determination. We also examine the spectral signal-to-noise ratio needed to minimize the frequency error when fitting bands to Gaussian/Lorentzian profiles. We then use our results to suggest a general method for calibrating the frequency of Raman spectra in large Raman images.
The trade-o↵ between spectral resolution and instrument throughput is analyzed for a compact, uncooled, longwave infrared (LWIR) channeled spectropolarimeter (IRCSP). The IRCSP was developed as a part of the Submm Wave and InfraRed Polarimeters (SWIRP) project out of NASA’s Goddard Spaceflight Center. The IRCSP scientific objective targets measurements of AOLP and DOLP with 1-μm spectral resolution from 8.5 - 12.5 μm in a single snapshot. The geometry of the field stop determines the field of view (FOV) of the IRCSP. This work relates the spectral resolution, instrument throughput, and polarimetric accuracy of a spectro-polarimeter to the FOV. The accuracy of linear Stokes retrievals for low temperature thermal targets are predicted for varying FOV and measurement noise conditions. This work presents a method to quantify the achievable accuracy in AOLP and DOLP as a function of field stop dimensions and signal-to-noise ratio (SNR). While smaller field stops are shown to improve accuracy as the spectral resolution is increased, low SNR is the dominant source of error for the IRCSP prototype. For the IRCSP, a SNR of at least 80 is required to produce DOLP measurements with < 5% error for targets with DOLP < 0.2.
We have analyzed very high quality reflectance spectra of the lunar surface from the University of Hawaii lunar spectral data collection using a spectral mixing model. The spectra analyzed are those of 45 mare sites and 75 highland sites. The spectra were selected on the basis of very high signal to noise ratios based on error bars and point to point scatter, and on quality of removal of telluric water bands. The spectral mixing model used 7 components, not all of which were used in each fit. Four of the components were mineral spectra of the orthopyroxene, a clinopyroxene, an olivine and an anorthite, measured at the Brown University's RELAB. All of the minerals were 45-90 micron splits. Lunar soil contains other components which have the effect of reddening and darkening the soil as well as reducing spectral contrast. In addition, lunar soil contains spectral neutral bright material (likely very fine grained feldspar) which serves to reduce spectral contrast and brighten soils. Early attempts to fit many of the spectra pointed out the need for a component which has a very broad smooth absorption feature centered near 1.1 microns. Glass is a good candidate for this component. For the bright component we used a flat reflectance of 70 percent to represent fine grained feldspar. For the 'glass' component we used a telescopic spectrum of a pyroclastic glass present on the Aristarchus plateau which is characterized by a strong smooth band centered at 1.07 microns. In addition to exhibiting the glass band this spectrum is very red and has a low albedo. On the assumption that the dark component and the red component are agglutinates, which is reasonable but not necessarily true, we sought a dark red component. To derive its properties we modelled the spectrum of an Apollo 16 soil (16xxx) and assumed the dark red component to comprise 60 percent of the soil, appropriate to agglutinate abundance in mature soil. We adjusted the albedo and slope of a straight line representing the dark red component until the contrast and albedo of the model spectrum matched the soil spectrum. The mixing was done after conversion to a single scattering albedo.
A learning program has been developed which combines 'learning by example' with the generate-and-test paradigm to furnish a robust learning environment capable of handling error-prone data. The problem is shown to be capable of learning class descriptions from positive and negative training examples of spectral and directional reflectance data taken from soil and vegetation. The program, which used AI techniques to automate very tedious processes, found the sequence of relationships that contained the most important information which could distinguish the classes.
The radiative kernel approach provides a simple way to separate the radiative response to different climate parameters and to decompose the feedback into radiative and climate response components. Using CERES/MODIS/Geostationary data, we calculated and analyzed the solar spectral reflectance kernels for various climate parameters on zonal, regional, and global spatial scales. The kernel linearity is tested. Errors in the kernel due to nonlinearity can vary strongly depending on climate parameter, wavelength, surface, and solar elevation; they are large in some absorption bands for some parameters but are negligible in most conditions. The spectral kernels are used to calculate the radiative responses to different climate parameter changes in different latitudes. The results show that the radiative response in high latitudes is sensitive to the coverage of snow and sea ice. The radiative response in low latitudes is contributed mainly by cloud property changes, especially cloud fraction and optical depth. The large cloud height effect is confined to absorption bands, while the cloud particle size effect is found mainly in the near infrared. The kernel approach, which is based on calculations using CERES retrievals, is then tested by direct comparison with spectral measurements from Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) (a different instrument on a different spacecraft). The monthly mean interannual variability of spectral reflectance based on the kernel technique is consistent with satellite observations over the ocean, but not over land, where both model and data have large uncertainty. RMS errors in kernel ]derived monthly global mean reflectance over the ocean compared to observations are about 0.001, and the sampling error is likely a major component.