High-Precision Benchmarks for the Stochastic Rod

We demonstrate a method to calculate high-precision benchmarks for the reflectance and transmittance of a finite rod with a stochastic cross section, assuming that the attenuation law has a known closed form and both the single-scattering albedo and scattering kernel are deterministic. We introduce new 10-digit values for an existing binary-Markov benchmark (including mean and variance), along with several new benchmarks defined for non-Markov binary mixtures and a continuous-fluctuation model featuring gamma stationary statistics. Furthermore, we reveal that our analysis of scattering in the stochastic rod enables a practical algorithm for identifying the parameters of an 𝑛-ary Markov mixture that most accurately approximates transport in a non-Markov system.