Search NASA⌕ Search

SEARCH · Search NASA

Results for “BORN APPROXIMATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Variance of phase fluctuations of waves propagating through a random medium

As an electromagnetic wave propagates through a random scattering medium, such as a forest, its energy is attenuated and random phase fluctuations are induced. The magnitude of the random phase fluctuations induced is important in estimating how well a Synthetic Aperture Radar (SAR) can image objects within the scattering medium. The two-layer random medium model, consisting of a scattering layer between free space and ground, is used to calculate the variance of the phase fluctuations induced between a transmitter located above the random medium and a receiver located below the random medium. The scattering properties of the random medium are characterized by a correlation function of the random permittivity fluctuations. The effective permittivity of the random medium is first calculated using the strong fluctuation theory, which accounts for large permittivity fluctuations of the scatterers. The distorted Born approximation is used to calculate the first-order scattered field. A perturbation series for the phase of the received field in the Rytov approximation is then introduced and the variance of the phase fluctuations is also calculated assuming that the transmitter and receiver are in the paraxial limit of the random medium, which allows an analytic solution to be obtained. Results are compared using the paraxial approximation, scalar Green's function formulation, and dyadic Green's function formulation. The effects studied are the dependence of the variance of the phase fluctuations on receiver location in lossy and lossless regions, medium thickness, correlation length and fractional volume of scatterers, depolarization of the incident wave, ground layer permittivity, angle of incidence, and polarization.

Chu, Nelson C.↗
NASA NTRS1993

Electron excitation of the H2(a 3Sigma(g)(+) - b 3Sigma(u)(+)) continuum in the vacuum ultraviolet

The electron excitation function for the H2(a 3Sigma(g)(+) - b 3Sigma(u)(+)) continuum emission has been measured from 11 to 30 eV at 195.0 nm. The emission cross, section data have been combined with electron energy loss cross section measurements to extend the experimental data to 60 eV. The excitation cross section has been estimated by normalizing the data to the electron energy loss cross section at 20 eV and using a model to account for emission from the entire band system. The spin forbidden excitation of the a 3Sigma(g)(+) state is a major dissociative channel of H2 at low energy with a peak cross section of 1.7 +/- 0.85 x 10 exp -17 sq cm at 15.5 eV. The FWHM of the cross section is 7 eV. The high energy dependence of the cross section has a rapid 1/E-cubed fall off with electron energy, E, above 50 eV. A modified Born approximation analysis was applied to the data to provide an analytic model.

Ajello, J. M.↗
NASA NTRS1992

Polarimetric remote sensing of sea ice in the Beaufort Sea

Data were collected in March 1988 with the Jet Propulsion Laboratory (JPL) polarimetric airborne synthetic aperture radar (SAR). Full covariance matrices were obtained from the scattering data with proper consideration of the polarimetric calibration. Images were processed to form the sea ice scenes in the Beaufort sea. These scenes contain various ice types including thin ice, thick first-year ice, and multiyear ice. Sea ice was modeled as a layer random medium and the polarimetric backscattering coefficients were calculated under the distorted Born approximation with effective permittivities obtained from the strong fluctuation theory. Sea ice signatures remotely observed by the JPL SAR over the Beaufort sea ice scenes were interpreted by comparing their behavior at different incident angles with results obtained from the theoretical model.

Nghiem, S. V.↗
NASA NTRS1992

Modeling of SAR returns from a red pine stand

Bright P-band radar returns from red pine forests have been observed on synthetic aperture radar (SAR) images in Bangor, Maine. A plot of red pine trees was selected for the characterization and modeling to understand the cause of the high P-band returns. The red pine stand under study consisted of mature trees. Diameter at breast height (DBH) measurements were made to determine stand density as a function of tree diameter. Soil moisture and bulk density measurements were taken along with ground rough surface profiles. Detailed biomass measurements of the needles, shoots, branches, and trunks were also taken. These site statistics have been used in a distorted Born approximation model of the forest. Computations indicate that the direct-reflected or the double-bounce contributions from the ground are responsible for the high observed P-band returns for HH polarization.

Lang, R. H.↗
NASA NTRS1992

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is used to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. Thermal emissions based on the reciprocity and energy conservation principles are calculated. The effects of the random roughness at the air-ice, and ice-water interfaces are explained by adding the surface scattering to the volume scattering return incoherently. The theoretical model, which has been successfully applied to analyze the radar backscatter data of first-year sea ice, is used to interpret the measurements performed in the Cold Regions Research and Engineering Laboratory's CRRELEX program.

Han, H. C.↗
NASA NTRS1992

L-band radar scattering from grass

A radar system based on a network analyzer has been developed to study the backscatter from vegetation. The radar is operated at L-band. Radar measurements of a grass field were made in 1991. The radar returns from the grass were measured at three incidence angles. Ground truth and canopy parameters such as blade and stem dimensions, moisture content of the grass and the soil, and blade and stem density, were measured. These parameters are used in a distorted Born approximation model to compute the backscatter coefficients from the grass layer. The model results are compared with the radar data.

Chauhan, N.↗
NASA NTRS1993

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Moghaddam, M.↗
NASA NTRS1993

Application of the target decomposition theorem to a polarimetric random media model

With advances in polarimetric radar measurements of land surfaces, the need for understanding the underlying scattering mechanisms and dominant target features has become the focus of many studies. In particular, the maximum use of the polarimetric information to identify and/or separate parameters related to the surface features such as vegetation thickness, structure, water content, and soil surface characteristics will enhance the possibility of using polarimetric radars for monitoring the earth's surface from space. In this paper, Cloude's decomposition theorem is applied to a polarimetric random media model to simulate the radar measurements of vegetated canopies. The vegetated canopies are modeled as a three layer discrete random medium with leaves and branches in the first layer, tree trunks in the second layer, and a half space of homogeneous ground with rough interface as the bottom layer. The distorted born approximation (DBA) has been used to compute full Mueller matrix of the canopy, using canonical dielectric objects such as thin discs and cylinders as leaves, branches, and trunks, respectively. The Mueller matrix and the derived covariance matrix contain information on the second order statistics of radar signals at various polarizations from the canopy. To decompose the covariance matrix to its constituent targets, the eigenvalues and eigenvectors of the covariance matrix are computed in terms of the physical parameters of the canopy. In addition, each eigenvector explicitly shows the scattering mechanisms such as odd and even reflections in the canopy. Cloude's decomposition theorem is applied using the Pauli spin matrices as a basis and an expression for the degree of disorder or the entropy for the vegetated surface is found. Then, the physical parameters estimated from in situ measurements are used in the random media to obtain realistic covariance matrices. As a result, the sensitivity of the eigenvalue spectrums and the coefficients resulting from the target decomposition theorem to the physical parameters of the canopy are examined and the possible use of Cloude's theorem to estimate vegetation and soil parameters is discussed.

Saatchi, Sasan S.↗
NASA NTRS1993

Plasma-screening effects on the electron-impact excitation of hydrogenic ions in dense plasmas

Plasma-screening effects are investigated on electron-impact excitation of hydrogenic ions in dense plasmas. Scaled cross sections Z(exp 4) sigma for 1s yields 2s and 1s yields 2p are obtained for a Debye-Hueckel model of the screened Coulomb interaction. Ground and excited bound wave functions are modified in the screened Coulomb potential (Debye-Hueckel model) using the Ritz variation method. The resulting atomic wave functions and their eigenenergies agree well with the numerical and high-order perturbation theory calculations for the interesting domain of the Debye length not less than 10. The Born approximation is used to describe the continuum states of the projectile electron. Plasma screening effects on the atomic electrons cannot be neglected in the high-density cases. Including these effects, the cross sections are appreciably increased for 1s yields 2s transitions and decreased for 1s yields 2p transitions.

Jung, Young-Dae↗
NASA NTRS1994

Microwave backscattering and emission model for grass canopies

Microwave radar and radiometer measurements of grasslands indicate a substantial reduction in sensor sensitivity to soil moisture in the presence of a thatch layer. When this layer is wet it masks changes in the underlying soil, making the canopy appear warm in the case of passive sensors (radiometer) and decreasing backscatter in the active case (scatterometer). A model for a grass canopy with thatch will be presented in this paper to explain this behavior and to compare with observations. The canopy model consists of three layers: grass, thatch, and the underlying soil. The grass blades are modeled by elongated elliptical discs and the thatch is modeled as a collection of disk shaped water droplets (i.e., the dry matter is neglected). The ground is homogeneous and flat. The distorted Born approximation is used to compute the radar cross section of this three layer canopy and the emissivity is computed from the radar cross section using the Peake formulation for the passive problem. Results are computed at L-band (1.4 GHz) and C-band (4.75 GHz) using canopy parameters (i.e., plant geometry, soil moisture, plant moisture, etc.) representative of Konza Prairie grasslands. The results are compared to C-band scatterometer measurements and L-band radiometer measurements at these grasslands.

TRT-THEORETICAL↗
NASA NTRS1995

Medium-resolution studies of extreme-ultraviolet emission from CO by electron impact

We report medium-resolution (0.025 nm full width at half maximum (FWHM)) electron impact-induced emission spectra of CO for 20, 100, and 200 eV impact energies. The emission spectra correspond to the extreme ultraviolet transitions from the B (sup 1)Sigma(sup +)(0), and E (sup 1)Pi(0) vibronic states to the X (sup 1)Sigma(sup +)(0) ground state. The present measurements are carried out at 20 times higher spectral resolution (to separate the many blended components) compared to our previous measurements, which were at a spectral resolution of 0.5 nm FWHM. The emission cross sections corresponding to the B (sup 1)Sigma(sup +)(0) yields X (sup 1)Sigma(sup +)(0), C (sup 1)Sigma(sup +)(0) yields X (sup 1)Sigma(sup +)(0), and E (sup 1)Pi(0) yields X (sup 1)Sigma(sup +)(0) resonance transitions were measured. In addition, excitation functions (0-1 keV) extending well into the Born region have been measured for the strong transitions (B (sup 1)Sigma(sup +)(0) yields X (sup 1)Sigma(sup +)(0) and C (sup 1)Sigma(sup +)(0)) and oscillator strengths have been determined, using a modified Born approximation analytic fit to the measured excitation function.

Kanik, Isik↗
NASA NTRS1995

Polarimetric scattering from layered media with multiple species of scatterers

Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.

Nghiem, S. V.↗
NASA NTRS1995

Screening Effects on Nonrelativistic Bremsstrahlung in the Scattering of Electrons by Neutral Atoms

Atomic screening effects on nonrelativistic electron-atom bremsstrahlung radiation are investigated using a simple analytic solution of the Thomas-Fermi model for many-electron atoms. The Born approximation is assumed for the initial and final states of the projectile electron. The results show that the screening effect is important in the soft radiation region and is decreasing with increasing radiation. These results help provide correct information about the behavior of bound electrons in the target atom in bremsstrahlung processes.

Jung, Young-Dae↗
NASA NTRS1993

A Model with Ellipsoidal Scatterers for Polarimetric Remote Sensing of Anisotropic Layered Media

This paper presents a model with ellipsoidal scatterers for applications to polarimetric remote sensing of anisotropic layered media at microwave frequencies. The physical configuration includes an isotropic layer covering an anisotropic layer above a homogeneous half space. The isotropic layer consists of randomly oriented spheroids. The anisotropic layer contains ellipsoidal scatterers with a preferential vertical alignment and random azimuthal orientations. Effective permittivities of the scattering media are calculated with the strong fluctuation theory extended to account for the nonspherical shapes and the scatterer orientation distributions. On the basis of the analytic wave theory, dyadic Green's functions for layered media are used to derive polarimetric backscattering coefficients under the distorted Born approximation. The ellipsoidal shape of the scatterers gives rise to nonzero cross-polarized returns from the untilted anisotropic medium in the first-order approximation. Effects of rough interfaces are estimated by an incoherent addition method. Theoretical results and experimental data are matched at 9 GHz for thick first-year sea ice with a bare surface and with a snow cover at Point Barrow, Alaska. The model is then used to study the sensitivity of polarimetric backscattering coefficients with respect to correlation lengths representing the geometry of brine inclusions. Polarimetric signatures of bare and snow-covered sea ice are also simulated based on the model to investigate effects of different scattering mechanisms.

Nghiem, S. V.↗
NASA NTRS1997

High-Resolution Studies of Extreme-Ultraviolet Emission from CO by Electron Impact

We report a high-resolution study (0.0036 nm full width at half maximum) of electron-impact-induced emission spectra of CO at 30-, 75-, and 100-eV electron-impact energies. The spectral features were acquired in optically thin conditions. At the specified resolution, attainable with our 3-m vacuum ultraviolet spectrometer, we observe rotationally resolved emission bands of CO in the extreme ultraviolet, from the vibronic states B (sup 1)sigma(sup +)(0), C (sup 1)sigma(sup+)(0), and E (sup 1)pi(0), to the ground state X (sup 1)sigma(sup +)(0). A simple model of these bands, based on the Honl-London factors and the rotational constants, is constructed and is shown to be in good agreement with the observed spectra. The predissociation yield for the E (sup 1)pi electronic state has been determined, showing that the E state has the largest predissociation cross section of CO for all singlet-state Rydberg series members. The excitation function of the [E (sup 1)pi(0) yields X (sup 1)sigma(sup +)(0)] transition, in the 0-800-eV impact energy range, is measured, permitting determination of the oscillator strength by using a modified Born approximation analytical fit.

Ciocca, Marco↗
NASA NTRS2001

Deep-Focusing Time-Distance Helioseismology

Much progress has been made by measuring the travel times of solar acoustic waves from a central surface location to points at equal arc distance away. Depth information is obtained from the range of arc distances examined, with the larger distances revealing the deeper layers. This method we will call surface-focusing, as the common point, or focus, is at the surface. To obtain a clearer picture of the subsurface region, it would, no doubt, be better to focus on points below the surface. Our first attempt to do this used the ray theory to pick surface location pairs that would focus on a particular subsurface point. This is not the ideal procedure, as Born approximation kernels suggest that this focus should have zero sensitivity to sound speed inhomogeneities. However, the sensitivity is concentrated below the surface in a much better way than the old surface-focusing method, and so we expect the deep-focusing method to be more sensitive. A large sunspot group was studied by both methods. Inversions based on both methods will be compared.

Duvall, T. L., Jr.↗
NASA NTRS2001

Ratio of Sodium to Potassium in the Mercurian Exosphere

Sodium (Na) and Potassium (K) atoms can be seen in the exosphere of Mercury and the Moon because they are extremely efficient at scattering sunlight. These species must be derived from surface materials, so that we might expect the ratio of sodium to potassium to reflect the ratio of these elements in the surface crust. This expectation is approximately born out for the Moon, where the ratio of sodium to potassium in the lunar exosphere averages to be about 6, not too far from the ratio in lunar rocks of 2 to 7. However, the ratio in the Mercury exosphere was found to be in the range 80 to 190, and at least once, as high as 400. The sodium and potassium atoms seen in the Mercury exosphere represent a balance between production from the surface and loss to space. Only if the production efficiencies and loss rates for Na and K were equal, would the ratio of Na to K in the exosphere reflect the ratio in the surface rocks. Since a value of 100 or more for the ratio of sodium to potassium in the surface rocks seems very unlikely, the high values of the observed ratios suggests that either production efficiencies or loss processes for the two elements are not equivalent. It does not seem likely that source processes should be different on the Moon and Mercury by an order of magnitude. This suggests that loss processes rather than source processes are the cause of the difference between the two. The major loss processes for sodium and potassium on Mercury are radiation pressure and trapping of photoions by the solar wind. Radiation pressure can reach 50-70% of surface gravity, and can sweep sodium and potassium atoms off the planet, provided they are sufficiently hot. Photoionization followed by trapping of the ions in the solar wind is the other major loss process. Photoions are accelerated to keV energies in the magnetosphere, and may either intercept the magnetopause, and be lost from the planet, or impact the planetary surface. Ions that impact the surface are neutralized, and are then available for resupply to the exosphere. The loss efficiency depends on characteristics of the magnetosphere that determine the fraction of the ions that are recycled by neutralization on the surface. Over the preceding decade, we have collected sodium and potassium data for Mercury at irregular intervals. We analyzed these data to extract values for the Na/K ratio at a variety of conditions on Mercury. Additional information is contained in the original extended abstract.

Potter, A. E.↗