In this paper, some explicit analytical solutions for single-scattered radiance in a half-space medium under consideration of a reflecting boundary are derived. We consider both a unidirectional beam source as well as an isotropic point source. In addition to direct applications within optical tomography and computer graphics, the obtained solutions are also needed when solving the radiative transport equation after the separation of the unscattered and single-scattered contribution. Comparisons between the derived analytical solutions and the Monte Carlo method display excellent agreement.

中文翻译：

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基于辐射输运理论的半无限介质中单散射辐射的解

本文推导了考虑反射边界的半空间介质中单散射辐射的一些显式解析解。我们既考虑了单向波束源又考虑了各向同性的点源。除了在光学层析成像和计算机图形学中的直接应用之外，在分离未散射和单散射分量之后求解辐射输运方程时，还需要获得的解决方案。派生的分析解决方案与蒙特卡洛方法之间的比较显示出极好的一致性。