Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation

Abstract This manuscript presents a short route to justify the widely used Monte Carlo Radiative Transfer (MCRT) algorithm straight from Equation (RTE). In this regard, paper starts deriving probability measure obtained integral formulation of RTE under unidirectional point source in an infinite domain. derivation only requires analytical integration first two terms perturbation expansion. Although derivations have been devised clarify relationship between MCRT and RTE, they tend be rather long elaborate. Considering how simple it is loose probabilistic interpretation photon’s physical propagation process, decay popularity former approaches relating entirely understandable. Unfortunately, all has given false impression that are not closely related, recent works explicitly stated no direct link exists them. work simpler demonstrating emerges statistically sample through Markov chains, further clarifying method’s foundations. compact, proposed does skip any fundamental step, preserving mathematical rigor while giving specific expressions functions. Thus, can help devise efficient ways for different scenarios or when coupling method with other methods traditionally grounded such as Spherical Harmonics Discrete Ordinates methods.