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Fast and accurate new Monte Carlo simulation for light propagation through turbid media

The design of a new semi-analytical Monte Carlo simulation is discussed in detail in this paper. This model uses two stages. In the first stage, the simulation itself, the contribution of each scattering event to the total reflectance and transmittance is evaluated. Thus the photon energy decreases more rapidly during its random walk and fewer steps are required to obtain a given accuracy. The reduced number of necessary steps makes it possible to store all events positions and energies. In the second stage, the results of the first stage can be used to calculate analytically any desired result. Examples are given for scattering slabs of isotropic or anisotropic scatterers when collimated beam incidence is used. Reflections at the boundaries are taken into account. The results obtained with this new method and classical Monte Carlo methods are identical. However, the convergence of our new model is much better and, because of the separation in two stages, any quantity related to the problem can be easily calculated afterwards without recomputing the simulation.