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At least 55 records · Page 3

Beyond maximum entropy: Fractal Pixon-based image reconstruction

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Puetter, Richard C.↗

Meteoroid and debris special investigation group; status of 3-D crater analysis from binocular imagery

During the 3 month deintegration of the LDEF, the M&D SIG generated approximately 5000 digital color stereo image pairs of impact related features from all space exposed surfaces. Currently, these images are being processed at JSC to yield more accurate feature information. Work is currently underway to determine the minimum number of data points necessary to parametrically define impact crater morphologies in order to minimize the man-hour intensive task of tie point selection. Initial attempts at deriving accurate crater depth and diameter measurements from binocular imagery were based on the assumption that the crater geometries were best defined by paraboloid. We made no assumptions regarding the crater depth/diameter ratios but instead allowed each crater to define its own coefficients by performing a least-squares fit based on user-selected tiepoints. Initial test cases resulted in larger errors than desired, so it was decided to test our basic assumptions that the crater geometries could be parametrically defined as paraboloids. The method for testing this assumption was to carefully slice test craters (experimentally produced in an appropriate aluminum alloy) vertically through the center resulting in a readily visible cross-section of the crater geometry. Initially, five separate craters were cross-sectioned in this fashion. A digital image of each cross-section was then created, and the 2-D crater geometry was then hand-digitized to create a table of XY position for each crater. A 2nd order polynomial (parabolic) was fitted to the data using a least-squares approach. The differences between the fit equation and the actual data were fairly significant, and easily large enough to account for the errors found in the 3-D fits. The differences between the curve fit and the actual data were consistent between the caters. This consistency suggested that the differences were due to the fact that a parabola did not sufficiently define the generic crater geometry. Fourth and 6th order equations were then fitted to each crater cross-section, and significantly better estimates of the crater geometry were obtained with each fit. Work is presently underway to determine the best way to make use of this new parametric crater definition.

Sapp, Clyde A.↗

Properties of Polycyclic Aromatic Hydrocarbons in the Northwest Photon Dominated Region of NGC 7023. I. PAH Size, Charge, Composition, and Structure Distribution

Polycyclic aromatic hydrocarbon (PAH) emission in the Spitzer Infrared Spectrograph spectral map of the northwest photon dominated region (PDR) in NGC 7023 was analyzed exclusively using PAH spectra from the NASA Ames PAH IR Spectroscopic Database (www.astrochem.org/pahdb). The 5-15 micron spectrum at each pixel is fitted using a non-negative-least-squares fitting approach. The fits are of good quality, allowing decomposition of the PAH emission into four subclasses: size, charge, composition, and hydrogen adjacency (structure). Maps tracing PAH subclass distributions across the region paint a coherent astrophysical picture. Once past some 20 seconds of arc from HD 200775, the emission is dominated by the more stable, large, symmetric, compact PAH cations with smaller, neutral PAHs taking over along the lines-of-sight toward the more distant molecular cloud. The boundary between the PDR and the denser cloud material shows up as a distinct discontinuity in the breakdown maps. Noteworthy is the requirement for PANH cations to fit the bulk of the 6.2 and 11.0 micron features and the indication of PAH photo-dehydrogenation and fragmentation close to HD 200775. Decomposition of the spectral maps into "principal" subclass template spectra provides additional insight into the behavior of each subclass. However, the general applicability of this computationally more efficient approach is presently undetermined. This is the first time the spectra of individual PAHs are exclusively used to fit the 5-15 micron region and analyze the spatial behavior of the aromatic infrared bands, providing fundamental, new information about astronomical PAH subpopulations including their dependence on, and response to, changes in local conditions.

northwest photon↗

Analysis of pressure-broadened ozone spectra in the 3 micron region

The Molecular Spectroscopy Lab at NASA-Langley has been involved in a long term effort to carefully characterize the infrared spectra of small molecules of atmospheric interest, including methane, water vapor, ozone, and their isotopic counterparts. High resolution gas phase infrared spectra are obtained using both a tunable diode laser system, and the McMath Fourier transform spectrometer at the Kitt Peak Solar Observatory. Spectra are obtained at various pressures and temperatures for pure gas samples, and for samples containing mixtures of the species of interest in nitrogen, oxygen, or air. From these spectra, using a nonlinear least squares fitting technique, spectral parameters of position, intensity, and half-width were determined for varying laboratory conditions that approximate atmospheric conditions experienced in remote sensing situations. These parameters are of interest in theoretical studies of these species, as well as in allowing more accurate interpretation of remote sensing data. The current work involves the analysis of a series of McMath FTIR spectra of ozone broadened by mixing with air, nitrogen, or oxygen. Each spectrum covers the region from 2396 to 4057/cm. Each vibrational band is analyzed by first diving its region into small intervals containing a few well isolated absorption lines of reasonable intensity. Each of these small intervals is fit by multiple iterations of the nonlinear least square program until residuals are minimized to a reasonable value which corresponds to the noise level of the measured spectrum. Intervals for the 3 nu(sub 3) ozone band in the region from 3000 to 3060 wavenumbers are being examined.

Prochaska, Eleanor S.↗

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗

Determine Oxidation State of Transition Metals in Molten Salt Corrosion using Electron Energy Loss Spectroscopy

This work utilizes electron energy loss spectroscopy (EELS) to identify oxidation state of alloying elements in Ni-based alloys after exposure to molten chloride salt systems. Pure Ni and Ni 20Cr model alloy were corroded in molten ZnCl2 and KCl-MgCl2 under argon atmosphere at various temperatures. Oxidation states of Cr (Cr3+) and Ni (Ni2+) in the molten salt after corrosion were determined by monitoring changes in the L2,3 edges of corresponding EELS spectra. Oxidation state mapping technique using principal component analysis and multiple linear least squares fitting in HyperSpy Python package was developed.

36 MATERIALS SCIENCE↗

LIF and emission studies of copper and nitrogen

A technique is developed to determine the rotational temperature of nitrogen molecular ion, N2(+), from the emission spectra of B-X transition, when P and R branches are not resolved. Its validity is tested on simulated spectra of the 0-1 band of N2(+) produced under low resolution. The method is applied to experimental spectra of N2(+) taken in the shock layer of a blunt body at distances of 1.91, 2.54, and 3.18 cm from the body. The laser induced fluorescence (LIF) spectra of copper atoms is analyzed to obtain the free stream velocities and temperatures. The only broadening mechanism considered is Doppler broadening. The temperatures are obtained by manual curve fitting, and the results are compared with least square fits. The agreement on the average is within 10 percent.

Akundi, Murty A.↗

Energization and transport of ions of ionospheric origin in the terrestrial magnetosphere

The work of this grant has been predominantly focused on ion outflows from two data sets: Prognoz 7 and Dynamics Explorer. The Prognoz analysis studied ion densities, temperatures, and flow velocities in the magnetotail. The work performed under this contract consisted of developing a program to load the raw data, computing the background subtraction of a strong sun pulse, and using the net count to calculate the low order moments of the distribution function. The study confirms the results of ISEE with regard to the supply of plasma from the cusp as a major source of plasmasheet plasma and goes beyond this to discuss the use of ion velocities as a way to examine the motions of the magnetotail. The abstract of the work to be reported is included as an appendix. The work on the DE/Retarding Ion Mass Spectrometer is separated into two categories: (1) classification of low-energy ion flows from high-latitudes, and (2) studies of the polar wind. Major publications resulting from this work are also included as an appendix to this report. The polar wind is in a category by itself as a result of the thermal escape of hydrogen and helium because of ambipolar diffusion through the heavier, oxygen-dominated topside ionosphere. The analysis of the polar wind reports the flux variability as a function of season, magnetic activity, etc. Much effort has been expended under this grant to complete a follow on study of the thermal structure of the polar wind. Extensive display tools and analysis software have been developed and used in an attempt to carry out this thermal analysis. The present work uses a constrained fit scheme that combines the ion densities and flow velocities derived from Chandler et al. and a spacecraft potential derived from an empirical relation to the total ion density to determine the remaining fit parameter, the ion temperature, via a least squares fit to the RIMS data.

Waite, J. Hunter JR.↗

Determination of Spectral Line Parameters in Selected Portions of the Infrared Spectrum of Water Vapor

Pressure broadening and pressure-induced shift coefficients due to water and nitrogen have been determined for water vapor transitions in the CO2 region of interest to Project HALOE. The temperature dependences of the widths and shifts have also been determined for selected transitions in this region. Results have been compared with values available in the literature. The line parameters have been obtained from the analysis of room temperature recordings of the spectrum of pure water and recordings of the spectra of heated water/nitrogen mixtures. The recordings of the water vapor spectrum were obtained with Fourier Transform Spectrometers at Kitt Peak and at the Justus-Liebig-Universitat Giessen. Up to eighteen spectra have been fitted simultaneously with a multispectrum nonlinear least-squares fitting technique developed by Dr. D. Chris Benner and colleagues.

Albert, Karen Keppler↗

Complex multicomponent spectrum analysis with Deep Neural Network

Here, in this paper, we present the use of deep neural networks to estimate physical parameters from complex optical emission spectra of the D β /H β transition. Specifically, we focus on estimating the radio frequency electric field vector of the lower hybrid wave and isotope ratio within the scrape-off-layer plasma of the WEST tokamak. Fitting the spectral data using a traditional non-linear least squares analysis requires many free parameters and is computationally expensive, rendering the data unusable for real-time control. By implementing relatively small neural networks, the physical parameters can be directly extracted from the spectral data with reasonable accuracy in a few milliseconds. The deep neural network prediction can serve as input for a reduced model using least-squares fitting or for real-time control. We show that deep neural networks can be an effective tool for analyzing complex multicomponent spectra, providing a speedup of more than 10 5 times compared to least residual analysis, with an accuracy of 0.5% for the isotope ratio, and 0.09 kV/cm and 0.38 kV/cm for the RF radial and poloidal electric field respectively.

47 OTHER INSTRUMENTATION↗

Discrete Tchebycheff orthonormal polynomials and applications

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Lear, W. M.↗

A case study demonstration of the soil temperature extrema recovery rates after precipitation cooling at 10-cm soil depth

Since the invention of maximum and minimum thermometers in the 18th century, diurnal temperature extrema have been taken for air worldwide. At some stations, these extrema temperatures were collected at various soil depths also, and the behavior of these temperatures at a 10-cm depth at the Tifton Experimental Station in Georgia is presented. After a precipitation cooling event, the diurnal temperature maxima drop to a minimum value and then start a recovery to higher values (similar to thermal inertia). This recovery represents a measure of response to heating as a function of soil moisture and soil property. Eight different curves were fitted to a wide variety of data sets for different stations and years, and both power and exponential curves were fitted to a wide variety of data sets for different stations and years. Both power and exponential curve fits were consistently found to be statistically accurate least-square fit representations of the raw data recovery values. The predictive procedures used here were multivariate regression analyses, which are applicable to soils at a variety of depths besides the 10-cm depth presented.

Welker, Jean Edward↗

Multi-Spacecraft Observations of Interplanetary Shocks

Using multi-spacecraft observations primarily from ACE and WIND, and from IMP 8 and Geotail when available, the 3-dimensional structure of interplanetary shocks on the hundred Earth radii scale will be discussed. The complete magnetic field, and solar wind ion and electron data sets were used to fit the shocks with a full non-linear least squares fit "Rankine-Hugoniot" technique yielding the local shock surface normals and speeds with associated uncertainties. Multi-spacecraft results reveal that on the distance scale of ACE's L1 halo orbit the shocks deviate significantly from a simple planar geometry. This result has important consequences for the prediction of the exact arrival times of interplanetary shocks at the Earth's magnetosphere, and hence, on the reliability of space weather predictions. It also has implications on the coherence scale of solar wind structures and their evolution from the Sun to Earth.

Szabo, A.↗

Multi-Spacecraft Observations of Interplanetary Shocks

Using multi-spacecraft observations primarily from ACE and WIND and from IMP 8 and Geotail when available, the 3-dimensional structure of interplanetary shocks on the hundred Earth radii scale will be discussed. The complete magnetic field, and solar wind ion and electron data sets were used to fit the shocks with a full non-linear least squares fitting "Rankine-Hugoniot" technique yielding the local shock surface normals and speeds with associated uncertainties. Multi-spacecraft results reveal that on the distance scale of ACE's L1 halo orbit the shocks deviate from a simple planar geometry. This result has important consequences for the prediction of the exact arrival times of interplanetary shocks at the Earth's magnetosphere, and hence, on the reliability of space weather predictions. It also has implications on the coherence scale of solar wind structures and their evolution from the Sun to Earth.

Smith, C. W.↗

Satellite camera image navigation

Pixels within a satellite camera (1, 2) image are precisely located in terms of latitude and longitude on a celestial body, such as the earth, being imaged. A computer (60) on the earth generates models (40, 50) of the satellite's orbit and attitude, respectively. The orbit model (40) is generated from measurements of stars and landmarks taken by the camera (1, 2), and by range data. The orbit model (40) is an expression of the satellite's latitude and longitude at the subsatellite point, and of the altitude of the satellite, as a function of time, using as coefficients (K) the six Keplerian elements at epoch. The attitude model (50) is based upon star measurements taken by each camera (1, 2). The attitude model (50) is a set of expressions for the deviations in a set of mutually orthogonal reference optical axes (x, y, z) as a function of time, for each camera (1, 2). Measured data is fit into the models (40, 50) using a walking least squares fit algorithm. A transformation computer (66 ) transforms pixel coordinates as telemetered by the camera (1, 2) into earth latitude and longitude coordinates, using the orbit and attitude models (40, 50).

Kamel, Ahmed A.↗

A Novel Multiphysics Multiscale Multiporosity Shale Gas Transport Model for Geomechanics/Flow Coupling in Steady and Transient States

Summary A novel multiphysics multiscale multiporosity shale gas transport (M3ST) model was developed to investigate shale gas transport in both transient and steady states. The microscale model component contains a kerogen domain and an inorganic matrix domain, and each domain has its own geomechanical and gas transport properties. Permeabilities of various shale cores were measured in the laboratory using a pulse decay permeameter (PDP) with different pore pressure and confining stress combinations. The PDP-measured apparent permeability as a function of pore pressure under two effective stresses was fitted using the microscale M3ST model component based on nonlinear least squares fitting (NLSF), and the fitted model parameters were able to provide accurate model predictions for another effective stress. The parameters and petrophysical properties determined in the steady state were then used in the transient-state, continuum-scale M3ST model component, which performed history matching of the evolutions of the upstream and downstream gas pressures. In addition, a double-exponential empirical model was developed as a powerful alternative to the M3ST model to fit laboratory-measured apparent permeability under various effective stresses and pore pressures. The developed M3ST model and the research findings in this study provided critical insights into the role of the multiphysics mechanisms, including geomechanics, fluid dynamics and transport, and the Klinkenberg effect on shale gas transport across different spatial scales in both steady and transient states.

Engineering↗

Gaussian quadrature exponential sum modeling of near infrared methane laboratory spectra obtained at temperatures from 106 to 297 K

Transmission measurements made on near-infrared laboratory methane spectra have previously been fit using a Malkmus band model. The laboratory spectra were obtained in three groups at temperatures averaging 112, 188, and 295 K; band model fitting was done separately for each temperature group. These band model parameters cannot be used directly in scattering atmosphere model computations, so an exponential sum model is being developed which includes pressure and temperature fitting parameters. The goal is to obtain model parameters by least square fits at 10/cm intervals from 3800 to 9100/cm. These results will be useful in the interpretation of current planetary spectra and also NIMS spectra of Jupiter anticipated from the Galileo mission.

Giver, Lawrence P.↗

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗