AI 中文总结
本文通过蒙特卡洛和辐射传输两种方法，研究光子进入平面平行散射平板后的首次通过统计，推导反射率、透射率、吸收率和出射角分布。
AI 中文摘要
一个光子进入平面平行散射平板后执行随机游走，最终从两个面之一逃逸或被吸收。散射分布为Henyey Greenstein相位函数，步长分布为指数分布。本文的核心结果是反射率、透射率、吸收率和出射角分布都可以用游走的首次通过统计来表示。采用两种方法。在蒙特卡洛（MC）方法中，高效生成一个极长的随机游走（多步），不考虑任何边界。该游走与大量目标物体的交集创建了一个物体游走段的集合。MC方法明确依赖于指数分布的无记忆性，使得物体内部第一步和最后一步的部分与游走步长具有相同的长度分布。记录每个游走段的细节，并从游走段数据库中提取任何统计量（达到采样精度）。特别地，从该集合中提取首次通过统计。在本工作中，物体是具有不同位置和厚度的平板。在辐射传输（RT）方法中，将平板划分为薄层，每层中的散射按一阶处理。然后直接在平板上积分RT方程，得到所需的首次通过统计。在RT方法中，反射、透射和吸收达到RT求解器的精度。两种方法在测试的随机游走参数范围内与MC精度一致。
英文摘要
A photon entering a plane parallel scattering slab performs a random walk and eventually escapes through one of the two faces or is absorbed. The standard model employs a Henyey Greenstein phase function (HG) and an exponential step length distribution (Exp). Slab reflectance, transmittance, absorptance, and emergent angular distributions can be calculated in terms of random walk statistics. A central result is that the slab calculations factor into the order resolved first passage statistics of a half space combined with the a factor for the slab thickness. Absorptance is derived from order resolved walk statistics using the absorption rate. Two approaches are used. In the Monte Carlo (MC) approach, an extremely long random walk with many steps is efficiently generated without regard to any boundaries. The intersection of this walk with a large collection of target objects creates an ensemble of excursions of the objects. The MC approach relies explicitly on the memoryless property of Exp so that the portion of the first and last steps inside the object follow the same length distribution as the walk steps. The details of each excursion are recorded and any statistics can be extracted from the database of excursions. In particular, first passage statistics are extracted from this ensemble. In this work the objects are slabs with different positions and thicknesses. In the radiative transfer (RT) approach the slab is divided into thin layers with scattering treated to first order in each layer. The RT equations are then directly integrated over the slab to give the desired first passage statistics, reflectance, transmittance, and absorptance. The two methods agree to the Monte Carlo precision over the tested range of random walk parameters.
Comments13 pages, 10 figures, 2 tables, 16 references
