Accelerated quasi Monte Carlo integration of the radiative transfer equation

Abstract

Backward Monte Carlo integration of the radiative transfer equation is the technique most easily adapted to complex scattering geometries. However, backward Monte Carlo integration suffers from two disadvantages: the accuracy is often low because the solution calls for the evaluation of high-dimensional integrals, and convergence of the multiple scattering series is slow if the photons are only weakly absorbed by the medium. In this paper, we demonstrate that the errors from both sources can be substantially reduced. First, the multi-dimensional integrals can be evaluated more accurately and more efficiently with quasi Monte Carlo integration, a technique in which photon trajectories are selected to sample the integration domain optimally. Second, the convergence of the multiple scattering series can be accelerated by estimating the rate of decay of the tail of the series. Each of the techniques described in the paper is both robust and applicable to scattering with any geometry.