Exact analytical solutions and corresponding Monte Carlo models for the problem of light transport in turbid media with continuous absorption and discrete scattering at the single scattering approximation

Although the radiative transport theory is widely used in various biomedical, ocean, and atmospheric optic problems, there are few light transport problems that can be solved analytically. Therefore, Monte Carlo (MC) numerical simulations are used in most practical applications. In this study, light transport problems in continuously absorbing and discretely scattering media for pencil-like incident beams were considered theoretically using the single scattering approximation. Strict and closed-form analytical solutions to these problems were derived and compared with МС numerical results. Two sets of probabilistic parameters for the MC algorithm were explored. The first was the classical set for media with continuous absorption and smooth scattering, while the second was the newly substantiated set for media with continuous absorption and discrete scattering corresponding to the analytical medium's model. It was shown that if the same model was used in MC simulations and the analytical approach, all of the results were identical. A divergence up to 10% between the obtained analytics and MC results in the case of continuous absorption and smooth scattering was observed.