Doctoral Dissertations

Abstract

"This thesis considers three-dimensional radiative transfer in an anisotropically scattering medium exposed to spatially varying radiation. The solution procedure used is the integral transform method. The first step in this process is the application of an integral transform to reduce the three-dimensional transport equation to a one-dimensional form. Next, Ambarzumian’s method is used to rewrite the governing equations in a form suitable for numerical evaluation. The resulting equations require integration over the polar and azimuthal angle; hence, the equations are in a double-integral form. Finally, spatially varying results are constructed with an inverse transform.

The first four sections deal with a semi-infinite medium. First, the scalar (neglecting polarization) problem is considered. A nonlinear integral equation for the generalized reflection function is developed and solved. A comparison is made to results from the single-integral approach. Next, vector (including polarization) radiative transfer is considered, and a nonlinear integral equation for the generalized reflection matrix is obtained. Results are presented for the backscattered radiation due to a polarized beam normally incident on a Rayleigh scattering medium. Comparisons are made to the uniform loading problem and to the scalar problem. The error in the scalar approximation can be as high as 20%. Far from the beam, the degree of linear polarization is inversely proportional to the optical radius squared, while the degree of circular polarization drops off at a faster rate.

The next two sections deal with a plane-parallel medium. First, scalar radiative transfer is considered and nonlinear integral and integro-differential equations for the generalized reflection and transmission functions are studied. A similar approach is then applied to vector radiative transfer. Equations for the generalized reflection and transmission matrices are obtained and solved for a Rayleigh scattering medium. The effects of polarization are more pronounced at small optical thicknesses; the error in the scalar approximation can be greater than 30%.

The appendices consider isotropic scattering. A double-integral equation for the generalized H-function is obtained for a semi-infinite medium, while coupled, double-integral equations for generalized X - and Y- functions are derived for a finite medium"--Abstract, page iv.

Advisor(s)

Crosbie, A. L. (Alfred L.)

Committee Member(s)

Look, Dwight C., 1938-
Nelson, Harlan F., 1938-2005
Edwards, D. R.
Hall, Leon M., 1946-

Department(s)

Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering

Publisher

University of Missouri--Rolla

Publication Date

Spring 2001

Journal article titles appearing in thesis/dissertation

  • Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: Generalized reflection function
  • Radiation backscattered from a semi-infinite, Rayleigh scattering medium exposed to a polarized laser beam, Part I: Generalized reflection matrix
  • Radiation backscattered from a semi-infinite, Rayleigh scattering medium exposed to a polarized laser beam, Part II: Spatially varying reflection matrix
  • Radiation backscattered from a semi-infinite, Rayleigh scattering medium exposed to a polarized laser beam, Part III: Spatially varying stokes parameters
  • Three-dimensional radiative transfer in an anisotropically scattering, plane-parallel medium: Generalized reflection and transmission functions
  • Three-dimensional vector radiative transfer in a finite medium exposed to spatially varying, polarized radiation: Generalized reflection and transmission matrices

Pagination

xxi, 444 pages

Note about bibliography

Includes bibliographical references.

Rights

© 2001 Donald William Mueller, Jr., All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Thesis Number

T 7872

Print OCLC #

47154087

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