Optical Cross Sections of a Random Layer
In this chapter, cross sections of a random layer and their optical relations are obtained, in terms of cross sections of the two boundaries, from Sect. 3.3.6, and the medium counterpart, S<Stack><Subscript>2</Subscript><Superscript>(0q)</Superscript></Stack>, which can be obtained as a boundary-value solution of the transport equation subject to the conventional condition of no reflection at the boundaries. The contribution from the entire random medium, S<Stack><Subscript>22</Subscript><Superscript>(q/12+23)</Superscript></Stack> thereby constructed based on the equations of Sect. 4.2.1, first, and the resultant cross section of the layer is then obtained. We then apply the diffusion approximation to the medium part of the contribution by introducing an appropriate boundary condition for the diffusion equation. This enables us to obtain specific expressions of the cross sections in terms of a simple boundary-value solution of the diffusion equation. Finally, the boundary conditions are generalized to the case in which media are random on both sides of a rough boundary.
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