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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.

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At least 145 records · Page 8
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NASA NTRS1975

The role of multiple scattering in one-dimensional radiative transfer

The usual methods of solving the radiative transfer equation yield answers which embrace all orders of scattering and thus shed little light on the underlying physical process. The present analysis examines the contributions of the various orders of scattering to the one dimensional transfer of radiation. In the one dimensional case an exact analytical solution exists and the problem reduces to that of expanding these exact solutions in powers of the albedo for single scattering. Formulas are given which permit the calculation of any order of scattering in an atmosphere of arbitrary optical thickness, particle albedo, and asymmetry parameter. The results should aid in identifying those physical situations where only the lowest orders of scattering play a significant role and where appropriate approximate methods might provide results of acceptable accuracy.

Adamson, D.↗
NASA NTRS1976

Multiple scattering in planetary atmospheres

Certain simple procedures for solving radiative transfer problems in planetary atmospheres are reviewed: the similarity relations relating isotropic to anisotropic scattering, asymptotic results relating known solutions for semi-infinite layers to desired solutions for optical depths, and expansions relating known solutions for conservative scattering to desired solutions for the nearly conservative case. The complications introduced by atmospheric inhomogeneity, surface reflection, and spectral features are also discussed.

Irvine, W. M.↗
NASA NTRS1976

Multiple scattered radiation emerging from Rayleigh and continental haze layers. I - Radiance, polarization, and neutral points

The matrix operator method was used to calculate the polarization of radiation scattered on layers of various optical thicknesses, with results compared for Rayleigh scattering and for scattering from a continental haze. In both cases, there are neutral points arising from the zeros of the polarization of single scattered photons at scattering angles of zero and 180 degrees. The angular position of these Rayleigh-like neutral points (RNP) in the sky shows appreciable variation with the optical thickness of the scattering layer for a Rayleigh phase matrix, but only a small variation for haze L phase matrix. Another type of neutral point exists for non-Rayleigh phase functions that is associated with the zeros of the polarization for single scattering which occurs between the end points of the curve. A comparison of radiances calculated from the complete theory of radiative transfer using Stokes vectors with those obtained from the scalar theory shows that differences of the order of 23% may be obtained for Rayleigh scattering, while the largest difference found for a haze L phase function was of the order of 0.1%.

Kattawar, G. W.↗
NASA NTRS1978

Simplified multiple scattering model for radiative transfer in turbid water

Quantitative analytical procedures for relating selected water quality parameters to the characteristics of the backscattered signals, measured by remote sensors, require the solution of the radiative transport equation in turbid media. Presented is an approximate closed form solution of this equation and based on this solution, the remote sensing of sediments is discussed. The results are compared with other standard closed form solutions such as quasi-single scattering approximations.

Ghovanlou, A. H.↗
NASA NTRS1977

A fast invariant imbedding method for multiple scattering calculations and an application to equivalent widths of CO2 lines on Venus

The invariant imbedding method considered is based on an equation which describes the change in the reflected radiation when an optically thin layer is added to the top of the atmosphere. The equation is used to treat the problem of reflection from a planetary atmosphere as an initial value problem. A fast method is discussed for the solution of the invariant imbedding equation. The speed and accuracy of the new method are illustrated by comparing it with the doubling program published by Hansen and Travis (1974). Computations are performed of the equivalent widths of carbon dioxide absorption lines in solar radiation reflected by Venus for several models of the planetary atmosphere.

Sato, M.↗
NASA NTRS1979

Geometry dependence of optical pulse broadening in multiple scattering media

A Monte Carlo simulation method has been used to evaluate the temporal response at a variety of receivers to an instantaneous laser pulse input to a turbid medium. The results are compared to the description of the ensemble of all transmitted photons for which a diffusion theory was developed. It was shown that the arrival times for all photons transmitted through the cloud are exponentially distributed with a mean time that varies as the product of the cloud thickness and the momentum transfer optical depth. For large optical depths the mean time delay associated with all reflected photons was found to depend only on the cloud thickness. The impulse response function for receivers on the beam axis varied with field of view and for small fields of view it was dominated by single scattering even for optically thick clouds. In these cases, the mean time delay could be up to 10 to the 6th times shorter than that associated with all transmitted photons with a related increase in the maximum modulation frequency.

Thomas, R. W. L.↗
NASA NTRS1979

Multiple scattering and charged-particle - hydrogen-atom collisions

Glauber-approximation scattering amplitudes for charged-particle - hydrogen-atom elastic and inelastic collisions are derived directly in terms of the known particle-electron and particle-proton Coulomb scattering amplitudes and the known hydrogen-atom form factors. It is shown that the particle-hydrogen amplitude contains no single-scattering term. The double-scattering term is obtained as a two-dimensional integral in momentum space. It is demonstrated how the result can be used as the starting point for an alternative and relatively simple derivation, in closed form, of the Glauber particle-hydrogen scattering amplitude for transitions from the ground state to an arbitrary (nlm) state.

Franco, V.↗
NASA NTRS1985

Multiple Scattering Effects in de/dx-E Instruments for Isotopic Composition Studies

The development of cosmic ray telescopes to separate individual isotopes of heavy elements using the dE/dx-vs.-E technique depends on the incorporation of precise trajectory sensing elements into these systems. In typical implementations the particle trajectory is derived from a set of position measurements made prior to a particle's entering the first energy loss detector. The use of the trajectory obtained in this way to correct energy loss signals for the actual pathlengths through the detectors depends on the assumption that the particle trajectory is a straight line. In order to resolve iron isotopes the angles of incidence, theta the particle track must be known rather accurately.

Wiedenbeck, M. E.↗
NASA NTRS1986

Comparative accuracy of selected multiple scattering approximations

Doubling method computational results which have yielded plane albedo, total transmission and fractional absorption for plane-parallel atmospheres composed of cloud droplets are presently compared with data obtained with selected radiative transfer approximations. The relative and absolute accuracies of asymptotic theory for thick layers and delta-Eddington, Meador-Weaver (1980) and Coakley-Chylek (1975) approximations are compared as a function of optical thickness, solar zenith angle, and single scattering albedo. The delta-Eddington approximation is the most accurate for conservative scattering when the solar zenith angle is small, while Meador-Weaver is the most accurate for nonconservative scattering.

King, M. D.↗
NASA NTRS1987

A canopy reflectance model based on an analytical solution to the multiple scattering equation

An approximation to the radiative transfer equation for solar radiation in relatively full, homogeneous plant canopies is presented and solved analytically for solar zenith angles less than 60 deg. The model predicts reflectance at any depth in the canopy and in any direction and may be inverted with bidirectional reflectance measurements. The model was fit to data at two sun angles and two wavebands (visible and NIR) to within the assumed errors on the reflectance data. The calculated albedos are insensitive to achievable measurement errors. Some of the parameter values themselves found by the inversion agree reasonably well with independent measurements, but the uncertainties introduced by the data noise are rather large. However, the agreement is good enough to demonstrate that the model is physically realistic.

Camillo, Peter↗
NASA NTRS1988

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

Stamnes, Knut↗
NASA NTRS1989

Aerosol analysis with the Coastal Zone Color Scanner - A simple method for including multiple scattering effects

A method for studying aerosols over the ocean using Nimbus-7 CZCS data is proposed which circumvents having to perform radiative transfer computations involving the aerosol properties. The method is applied to the CZCS band 4 at 670 nm, and yields the total radiance (L sub t) backscattered from the top of a stratified atmosphere containing both stratospheric and tropospheric aerosols and the the Rayleigh scattered radiance (L sub r). The radiance which the aerosol would produce in the single scattering approximation is retrieved from (L sub t) - (L sub r) with an error of not greater than 5-7 percent.

Gordon, Howard R.↗
NASA NTRS2011

Numerical Simulations of Single and Multiple Scattering by Fractal Ice Clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4<=R<=10 cm and fractal dimensions D(sub f) 2.5 and 3. We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D(sub f) 2.5, but the differences can increase somewhat for D(sub f)3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.

Dlugach, Janna M.↗