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Proceedings Paper

General solution to an inverse problem for the diffusion approximation of the radiative transfer equation
Author(s): Vladimir S. Ladyzhets
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Paper Abstract

An inverse problem for the one-speed, time-independent, homogeneous radiative transfer equation (RTE) for the intensity of light propagating in a strongly-scattering medium is investigated. We assume that the equation has a rotationally invariant scattering kernel and the diffusion approximation of the spherical harmonics method can be applied. The problem consists in simultaneous determination of a solution to the RTE and a combination of functions describing media absorption and scattering characteristics. It is shown that strictly following the diffusion approximation assumption brings about a general solution to the problem which, in turn, demonstrates that for any limited domain D, the only data we need to find a unique solution to the inverse problem are angular distributions of light intensity in four points belonging to the boundary (delta) D of the domain D and an angular mean value of the intensity along a curve on (delta) D. Explicit formulas for calculating a solution to the inverse problem are obtained.

Paper Details

Date Published: 9 October 1995
PDF: 11 pages
Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224155
Show Author Affiliations
Vladimir S. Ladyzhets, Florida International Univ. (United States)


Published in SPIE Proceedings Vol. 2570:
Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications
Randall Locke Barbour; Mark J. Carvlin; Michael A. Fiddy, Editor(s)

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