Radiative transfer with delta-Eddington-type phase functions

Weimin Han, Feixiao Long, Wenxiang Cong, Xavier Intes and Ge Wang

Applied Mathematics and Computation, 2017, vol. 300, issue C, 70-78

Abstract: The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. This paper is devoted to an RTE framework with a family of delta-Eddington-type phase functions. Significance in biomedical imaging applications of the RTE with delta-Eddington-type phase functions are explained. Mathematical studies of the problems include solution existence, uniqueness, and continuous dependence on the problem data: the inflow boundary value, the source function, the absorption coefficient, and the scattering coefficient. Numerical results are presented to show that employing a delta-Eddington-type phase function with properly chosen parameters provides accurate simulation results for light propagation within highly forward-peaked scattering media.

Keywords: Radiative transfer equation; Generalized delta-Eddington phase function; Existence; Uniqueness; Continuous dependence (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:300:y:2017:i:c:p:70-78

DOI: 10.1016/j.amc.2016.12.001

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