The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics

Monte Carlo (MC) simulations are often at the heart of the testing procedure in biomedical optics. One of the critical points in MC simulations is to define the new photon direction after each scattering event. One of the most popular solutions is to use the Henyey-Greenstein phase function or some linear combinations of it. In this note, we demonstrate that randomly generating the angle defining the new direction of a photon after a collision, by means of the Henyey-Greenstein phase function, is not equivalent to generating the cosine of this angle, as is classically done. In practice, it is demonstrated that for a nearly isotropic medium (asymmetry parameter g approximately 0) this discrepancy is not large, however for an anisotropic medium as is typically found in vivo (e.g. g = 0.98) the two methods give completely different results.