Monte Carlo simulations in anomalous radiative transfer: a tutorial

TL;DR

This tutorial explains how to implement Monte Carlo simulations for anomalous radiative transfer, emphasizing non-classical photon step descriptions to accurately model light propagation in complex media.

Contribution

It introduces a Monte Carlo approach tailored for anomalous radiative transfer, highlighting non-classical photon steps and their importance for invariance properties.

Findings

Non-classical photon steps are crucial for accurate ART simulations.

The method preserves invariance properties in light propagation.

Simplifies classical Monte Carlo codes for biomedical optics.

Abstract

Anomalous radiative transfer (ART) theory is a generalization of classical radiative transfer theory. The present tutorial wants to show how Monte Carlo (MC) codes describing photons transport in anomalous media can be implemented. It is shown that the heart of the method consists in suitably describing, in a "non-classical" manner, photons steps starting from fixed light sources or from boundaries separating regions of the medium with different optical properties. To give a better intuition of the importance of these particular photon step lengths, it is also shown numerically that the described approach is essential to preserve the invariance property for light propagation. An interesting byproduct of the MC method for ART, is that it allow us to simplify the structure of "classical" MC codes, utilized e.g. in biomedical optics.