Lookup table-based sampling of the phase function for Monte Carlo simulations of light propagation in turbid media

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.

Imaging sub-diffuse optical properties of cancerous and normal skin tissue using machine learning-aided spatial frequency domain imaging

“…In this method, the phase function’s inverse CDF equation used for inverse transform sampling is replaced with an inverse CDF look-up table using methods similar to those introduced by Naglič et al. 32 In order to allow for simulation across a wide range of the phase function parameters and , our look-up table is generated with the modified Henyey-Greenstein 23 (MHG) function when and fall within MHG’s valid range ( 31 ) and is otherwise generated with the GK. 51 We approximated GK’s valid range to be and 38 (Supplement 1 in the Supplementary Material ), so our method cannot sample phase functions with .…”

“… 20 , 21 Secondarily, the semi-empirical equation was developed using data simulated with the modified-Henyey Greenstein phase function approximation, 26 whose domain 31 does not fully encompass the range of optical properties seen in biological tissue. 2 , 21 , 26 , 32 – 35 …”

“…Moreover, Naglič et al.’s model was trained on data simulated using the Gegenbauer kernel (GK) phase function approximation, whose domain 38 also does not cover the full range of optical properties seen in biological tissue. 2 , 21 , 26 , 32 – 35 …”

On sampling of scattering phase functions

“…4. Further acceleration, as shown in Algorithm 2, can be made if we select the values of the CDF to be uniform on [0, 1], [17,18]. By using such a setting, the index of subintervals can be found more easily.…”

“…As an approximate sampling method, the performance of the tabulated method is dependent on the number of interpolation points. However, to sample realistic phase functions (with peaks near the forward and backward directions) accurately, a considerably greater number of points are required to obtain a reliable result [18]. Poor sampling near forward and backward directions has a large negative impact on the simulation accuracy of radiation transport [19,18].…”