9 October 1995 General solution to an inverse problem for the diffusion approximation of the radiative transfer equation
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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, 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); doi: 10.1117/12.224155; https://doi.org/10.1117/12.224155
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