General solution to an inverse problem for the diffusion approximation of the radiative transfer equation

Vladimir S. Ladyzhets

doi:10.1117/12.224155

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9 October 1995 General solution to an inverse problem for the diffusion approximation of the radiative transfer equation

Vladimir S. Ladyzhets

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Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224155
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

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Vladimir S. Ladyzhets "General solution to an inverse problem for the diffusion approximation of the radiative transfer equation", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); https://doi.org/10.1117/12.224155

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