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

• Published in: Journal of quantitative spectroscopy & radiative transfer Vol. 271; p. 107741
• Main Authors: Tarasov, Andrey P., Persheyev, Saydulla, Rogatkin, Dmitry A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2021
• Subjects: Analytical solution; Biological tissue; Discrete scattering; Light transport; Monte Carlo; Single scattering; Biological tissue; Single scattering; Discrete scattering; Monte Carlo; Analytical solution; Light transport
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/j.jqsrt.2021.107741

•Light transport in turbid media with continuous absorption and discrete scattering under pencil-like beam illumination was considered theoretically using single scattering approximation.•Exact closed-form analytical solutions were obtained for 2D and 3D spatial cases.•Connections between obtained analytical solutions for different spatial cases were indicated.•Monte Carlo modelling results were compared with the analytical solutions.•Small divergence between obtained analytical results and the results for continuous absorbing and smooth scattering media was observed.•Revised Monte Carlo parameters were suggested to reach the analytical results. 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.