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.

中文翻译：

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具有 delta-Eddington 型相位函数的辐射传输

辐射传递方程 (RTE) 出现在广泛的应用中，特别是在与光通过生物组织传播相关的生物医学成像应用中。然而，生物介质中的高度前向峰值散射特征使得准确地数值求解 RTE 问题变得非常具有挑战性。克服与高度前向峰值散射相关的困难的一种想法是通过使用 delta-Eddington 相位函数。本文致力于具有一系列 delta-Eddington 型相位函数的 RTE 框架。解释了具有 delta-Eddington 型相位函数的 RTE 在生物医学成像应用中的重要性。问题的数学研究包括解的存在性、唯一性和对问题数据的连续依赖：流入边界值、源函数、吸收系数和散射系数。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.