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Results for “Radiation Scattering Equations”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

The usefulness of Klett's inversion algorthms to simulated satellite Lidar returns

The lidar equation is a special form of the radiative transport equation in single scattering approximation and describes the return signal of a lidar. Klett's algorithm for retrieving the total extinction coefficient profile was developed for application to ground-based lidar returns by a backward integration from the far end to the near end, the range where the incident and backscattered pulse overlap totally. The applicability of Klett's algorithm to satellite backscatter lidar returns was assessed. The simulated data of a 1 J Alexandrite laser operated at about 0.7 micron and at a satellite flight level of 840 km.

Kastner, M.↗
NASA NTRS1989

Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients

The small-angle scattering approximation of the scalar radiative transfer equation (RTE) is examined for the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic RTE can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. Two transfer equations are obtained describing the average radiant intensity and the spatial correlation function of the intensity fluctuations. The average intensity equation is then solved and applied to a simple propagation scenario. An approximate solution is also derived for the equation giving the correlation function. The developed equations can be applied to problems involving short wavelength electromagnetic wave propagation through media possessing the variable characteristics of turbulence and turbidity, such as plasmas, the atmosphere, and the ocean.

Manning, Robert M.↗
NASA NTRS1996

Internal Radiation Effects in Zirconia Thermal Barrier Coatings

Using thermal barrier coatings on combustor liners, turbine vanes, and rotating blades is important for reducing metal temperatures in current and advanced aircraft engines. Zirconia is a common coating material, and it is partially transparent to thermal radiation. Radiation becomes more significant as temperatures are raised for higher efficiency in advanced engines. Calculations are often made with radiation effects neglected inside the coating. The effect of radiation is illustrated here, where an analytical procedure is provided by using the two-flux method for the radiative contribution. A detailed study was made of ceramic thermal barrier coatings for diesel engines, and a two-flux analysis was developed for radiation in semitransparent multilayer composites. These efforts provide the basis for the present analysis where illustrative solutions are obtained for typical conditions in an aircraft engine. The formulation and solution of the exact spectral radiative transfer equations including large scattering, as is characteristic of zirconia, are rather complicated. The two-flux method is used here to provide a simplified method.

Siegel, Robert↗
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 NTRS1973

Matrix operator theory of radiative transfer. I - Rayleigh scattering.

An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.

Plass, G. N.↗
NASA NTRS1974

Energy transfer in volume-reflecting heat shields

An approximate analysis of radiative transfer in highly scattering materials was developed based on the Kubelka-Munk differential equations--a set of two differential equations representing the spatial rate of change of radiative half-fluxes within the scattering media. These approximate solutions of the Kubelka-Munk equations together with analytic solutions for the steady state temperature distribution for two types of boundary conditions are given. These solutions show the influence of back surface reflectance, scattering power, incident radiative flux parameter and boundary conductive flux parameter on overall reflectance and temperature distributions. This radiation field analysis, adapted to spherical geometry, was applied to the evaluation of the thermal performance of teflon and fritted quartz as heat protection materials for entry into the atmosphere of Jupiter.

Weston, K. C.↗
NASA NTRS2015

OSOAA: A Vector Radiative Transfer Model of Coupled Atmosphere-Ocean System for a Rough Sea Surface Application to the Estimates of the Directional Variations of the Water Leaving Reflectance to Better Process Multi-angular Satellite Sensors Data Over the Ocean

In this study, we present a radiative transfer model, so-called OSOAA, that is able to predict the radiance and degree of polarization within the coupled atmosphere-ocean system in the presence of a rough sea surface. The OSOAA model solves the radiative transfer equation using the successive orders of scattering method. Comparisons with another operational radiative transfer model showed a satisfactory agreement within 0.8%. The OSOAA model has been designed with a graphical user interface to make it user friendly for the community. The radiance and degree of polarization are provided at any level, from the top of atmosphere to the ocean bottom. An application of the OSOAA model is carried out to quantify the directional variations of the water leaving reflectance and degree of polarization for phytoplankton and mineral-like dominated waters. The difference between the water leaving reflectance at a given geometry and that obtained for the nadir direction could reach 40%, thus questioning the Lambertian assumption of the sea surface that is used by inverse satellite algorithms dedicated to multi-angular sensors. It is shown as well that the directional features of the water leaving reflectance are weakly dependent on wind speed. The quantification of the directional variations of the water leaving reflectance obtained in this study should help to correctly exploit the satellite data that will be acquired by the current or forthcoming multi-angular satellite sensors.

Ocean surface↗
NASA NTRS1979

On the Angular Variation of Solar Reflectance of Snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations.

Chang, A. T. C.↗
NASA NTRS1981

On the angular variation of solar reflectance of snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks are derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface is considered, and for subsurface multiple scattering an approximate solution of the radiative transfer equation is studied. Solar radiation incident on the snowpack is decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol, and molecular scattering are included in the calculation of incident solar radiation. Illustrative numerical results are given for a case of North American winter atmospheric condition. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation is in qualitative agreement with available observations.

Choudhury, B. J.↗
NASA NTRS1976

Theory of thermal microwave emission from a two-layer medium

Thermal microwave emission from a scattering layer overlying a homogeneous half space is studied with the radiative transfer approach. Scattering models of random medium and discrete spherical scatterers are used. The radiative transfer equations are solved by both the classical method and the invariant imbedding method. The brightness temperatures of the two-layer model exhibit distinguishing features important to microwave passive remote sensing.

Tsang, L.↗
NASA NTRS2001

Remote-Sensing Reflectance and Inherent Optical Properties for Optically Deep Waters: A Revisit

Remote-sensing reflectance (r(rs)) is defined as the ratio of upwelling radiance to downwelling irradiance. Relationships between remote-sensing reflectance and inherent optical properties serve as the basis for ocean-color modeling, as well as for spectral deduction of oceanic constituents through analytical/semi-analytical models of ocean color. A decade ago, a simple and concise formula based on Monte Carlo simulations was developed by relating rrs to a property u, the ratio of backscattering (b(b)) to the sum of absorption (a) and backscattering (u = b(b)/(a+b(b))). This relationship generally ignored the shape differences in phase functions between molecular scattering and particle scattering. In this study, the relationship is updated with separate parameters for molecular and particle scattering, based on the Radiative Transfer Equation through use of Hydrolight numerical solutions. The new approach fits r(rs) better than an earlier traditional formula, for both clear and turbid waters.

Lee, Zhong-Ping↗
NASA NTRS2003

Vector Radiative Transfer Equation for Arbitrarily Shaped and Arbitrarily Oriented Particles: A Microphysical Derivation from Statistical Electromagnetics

We use the concepts of statistical electromagnetics to derive the general radiative transfer equation (RTE) describing multiple scattering of polarized light by sparse discrete random media consisting of arbitrarily shaped and arbitrarily oriented particles. The derivation starts from the volume integral and Lippmann-Schwinger equations for the electric field scattered by a fixed N-particle system and proceeds to the vector form of the Foldy-Lax equations and their approximate far-field version. We then assume that particle positions are completely random and derive the vector RTE by applying the Twersky approximation to the coherent electric field and the Twersky and ladder approximations to the coherency dyad of the diffuse field in the limit N -> infinity. The concluding section discusses the physical meaning of the quantities entering the general vector RTE and the assumptions made in its derivation.

Mishchenko, Michael I.↗
NASA NTRS2018

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Far-field electromagnetic scattering; Absorbing ho↗
NASA NTRS1982

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Sharma, A.↗
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
DOE OSTI2025

Dependent scattering and fractal microstructure determine the transparency of aerogel monoliths

This study reveals how dependent scattering and microstructure significantly affect electromagnetic wave propagation through aerogel monoliths, contributing to their transparency. Light scattering by particle ensembles is considered “dependent” when the scattering properties rely not only on particle size and optical constants but also on their spatial distribution, typically occurring when the average interparticle distance is small in comparison with the wavelength of incident radiation. Addressing dependent scattering requires solving Maxwell’s equations for complex heterogeneous structures, which is computationally demanding and usually limited to sample thicknesses on the same scale as the wavelength. This study combines computer-generated ambigel microstructures of fractal aggregates of polydisperse nanoparticles and the radiative transfer with reciprocal transaction method to predict the transmittance of thick ambigel slabs. Transmittance measurements of ambiently dried aerogel monoliths (ambigels) with porosities from about 50% to 90% closely matched the predicted values for their digital twins. However, ignoring dependent scattering or particle aggregation led to inaccurate predictions. This study validated the computational framework, and its findings offer insights for designing photonic metamaterials and analyzing their interactions with electromagnetic waves.

Yalcin, Refet A. (ORCID:0000000339973494)↗
NASA NTRS1986

The temperature structure in accretion flows onto massive protostars

Radiation transfer problems involved in the infall of dust and gas during star formation are studied. Dust properties are discussed, and modifications of spherical radiative transfer equations are presented that permit forward scattering by dust to be treated for the small size of the star relative to the inner radius of the shell. A procedure for deriving the stellar radiation field incident on the inner edge of the shell is developed. The temperature correction procedure of Cassinelli and Hartmann (1975) for extended stellar atmospheres is modified so that the multitemperature nature of the grains in the cloud may be derived. Temperature distributions for three schematic models in which the density is prespecified are discussed. Radiative acceleration of grains is addressed, showing that the proper mean opacity differs by a large factor from the Rosseland mean opacity that is commonly used. Emergent fluxes for the models are given.

Wolfire, Mark G.↗