Direct-inverse problems in transport theory. 1. The inverse problem

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Abstract
For the inverse problem treated here we use the results of an experiment which measures the total angular‐dependent column density as compared to the measurement which provides information on the angle integrated spatial‐dependent angular density (or the specific intensity). We use two methods of approach. One, the Legendre expansion method and two a maximal variational principle. In particular we demonstrate how the variational principle yields a very convenient representation of the scattering kernel (or the phase function) in terms of a basis consisting of Case eigenfunctions for the isotropically scattering medium.

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