Statistics – Computation
Scientific paper
Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phdt........58k&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF ILLINOIS AT CHICAGO, 1987.Source: Dissertation Abstracts International, Volume: 50-02, Section: B,
Statistics
Computation
Scientific paper
The problem of multiple scattering of polarized radiation in an inhomogeneous, anisotropically scattering, plane-parallel random medium is formulated using a vector radiative transfer approach. Incoherent scattering is assumed and the Stokes representation of the polarized radiation is used to describe the multiple scattered polarimetric field in the medium. The formulation is based on a Green's matrix procedure which allows decoupling of the scattering properties of the medium from the polarized radiative source(s). Four sets of Fredholm integral equations of the second kind governing the source matrices in the medium are obtained. The method of invariant imbedding is used to replace these integral equations with their equivalent Cauchy initial -value problems which are amenable to efficient numerical computation. From the symmetry properties of the single scattering process, various symmetry relationships governing the polarized radiative field in the entire imhomogeneous multiple scattering medium are derived, and their utility in the theoretical development and numerical implementation of the Green's matrix formulation is outlined. The computational aspects as well as various applications of the present approach are considered and discussed.
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