On the resolvent of Milne's integral equation for a spherical,isotropically-scattering medium |
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Authors: | S. Ueno |
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Affiliation: | Department of Electrical Engineering, University of Southern California, Los Angeles, California 90007, U.S.A. |
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Abstract: | Recently, determination of the resolvent kernel of Milne's integral equation for a spherical, isotropically-scattering medium with internal sources has been made by several authors (cf. Heaslet and Warming;(1)Nagirner;(2)Wilson and Sen(3)). In this paper, it is shown how to compute the resolvent kernel of the above Milne's equation in terms of the modified Sobolev's Φ-function, which is reduced to the angular integration of the source function in the diffuse radiation field by a finite slab. In other words, once the X- and Y-functions of a slab with twice the optical radius of the sphere have been computed and a Cauchy system for the source function has been solved, the resolvent kernel under consideration can be determined by integration of the modified Sobolev Φ-function. |
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