Reduction of the problem of transport in a finite layer to a problem for a half-space

Physics – Optics

Scientific paper

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Atmospheric Optics, Atmospheric Stratification, Half Spaces, Radiative Transfer, Astrophysics, Atmospheric Scattering, Eigenvalues, Group Theory, Operators (Mathematics), Optical Thickness

Scientific paper

The paper considers the application of Ambartsumian's (1943 and 1960) method of adding layers in radiative transport problems, and shows how to reduce the problem of transport in a finite layer to the corresponding problem in a semi-infinite layer. The problem for a half-space is shown to be, in fact, a problem of determining the eigenfunctions and eigenvalues of the operator G which describes the change in the outgoing frequency or angular distribution when an infinitely thin layer is placed over the semi-infinite medium. The operator G is simply expressed through the Ambartsumian operator phi and can be easily constructed from physical considerations in accordance with a group property of the linear operator Y, which describes the transformation of the primary radiation by the added layer.

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