Abstract
Analytical expressions for sampling the scattering angle from a phase function in Monte Carlo simulations of light propagation are available only for a limited number of phase functions. Consequently, numerical sampling methods based on tabulated values are often required instead. By using Monte Carlo simulated reflectance, we compare two existing and propose an improved numerical sampling method and show that both the number of the tabulated values and the numerical sampling method significantly influence the accuracy of the simulated reflectance. The provided results and guidelines should serve as a good starting point for conducting computationally efficient Monte Carlo simulations with numerical phase function sampling.
Highlights
One of the central mechanisms of light propagation in turbid media such as biological tissue is scattering
We show that the accuracy of the Monte Carlo (MC) simulated reflectance acquired by optical fiber probes at various source-detector separations (SDS) significantly depends on the number of the tabulated cumulative distribution function (CDF) values and the numerical phase function sampling method, and can become significantly degraded, if the tabulated CDF is too sparse
4.1 Influence of the numerical phase function sampling on the Monte Carlo (MC) simulated reflectance
Summary
One of the central mechanisms of light propagation in turbid media such as biological tissue is scattering. In terms of Monte Carlo (MC) simulations, which are often used for modeling the light propagation [1,2], scattering is described by the scattering coefficient and scattering angle typically drawn from the inverse cumulative distribution of the phase function. The Henyey-Greenstein (HG) phase function [9] is most commonly used in the biomedical community since it offers an analytical inverse of the cumulative distribution function (CDF), which is convenient for sampling the scattering angles by a random number drawn from a uniform distribution. In order to use these types of phase functions in the MC simulations, the phase functions have to be numerically sampled For this purpose, Toublanc has proposed a method for computing the scattering angle from tabulated evenly spaced scattering angles that through the CDF correspond to a random number drawn from a uniform distribution [16]. It is very difficult to properly repeat the experiments conducted in those studies
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