14 July 1988 Invariant Imbedding For The Solution Of Vector Radiative Transfer In General Plane-Parallel Media
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Abstract
In this paper, we consider the problem of electromagnetic propagation in plane-parallel random media under rather general conditions and obtain solutions for the scattered polarized fields using radiative transport and the Stokes vector representation. More specifically, the plane-parallel medium is inhomogeneous, scatters radiation anisotropically, and has arbitrary boundary conditions. No restriction is placed on the radiative source as to its spatial and directional profiles. A uniform, unidirectional radiation beam incident on the medium from outside constitutes a special case. The formulation is based on the development of the Green's matrix for the scattering medium. The source matrices of this problem satisfy Fredholm integral equations of the second kind. The invariant imbedding technique developed by R. Bellman and co-workers is used to replace these integral equations with the equivalent Cauchy initial-value problems which can be solved using an appropriate quadrature formula and integration scheme. Various applicable symmetry relations for the scattered polarized fields are derived, and their utility in the solution of the initial-value problems is discussed. The Green's matrix approach is particularly useful in remote sensing applications, since it decouples the radiative sources and boundary conditions from media properties. For example, the temperature profile in a snow pack may be inferred by comparing the observed radiative field with the radiative field obtained by convoluting the Green's matrix solution with various trial temperature profiles.
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A M Khounsary, A M Khounsary, A C Coaley, A C Coaley, W J Minkowycz, W J Minkowycz, } "Invariant Imbedding For The Solution Of Vector Radiative Transfer In General Plane-Parallel Media", Proc. SPIE 0927, Wave Propagation and Scattering in Varied Media, (14 July 1988); doi: 10.1117/12.945823; https://doi.org/10.1117/12.945823
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