Relationship of spatial irradiance in scattering medium with a diffuse reflectance coefficient: comparison of the Monte Carlo method with the Kubelka-Munk approximation
V.P. Tsipilev1, I.A. Saidazimov1, V.I. Oleshko1, A.N. Yakovlev2
1National Research Tomsk Polytechnic University, Tomsk, Russia
2T.F. Gorbachev Kuzbass State Technical University, Kemerovo, Russia
Keywords: light scattering, diffuse scattering media, Monte Carlo method, Kubelka-Munk formula, spatial irradiance
Abstract
Spatial irradiance is a defining characteristic of radiation during the thermal impact of a laser beam on biological tissues, powders, and other scattering media. The provides a theoretical consideration of multiple light scattering in the volume of a semi-infinite diffuse scattering medium (DSM). Calculations are made for pressed dielectric powders with refractive indices n = 1.47, 1.72, and 2.00 at a wavelength of 1.06 μm (the first harmonic of a neodymium laser). The diffuse reflectance coefficients ρ(1 - Λ) calculated by the Monte Carlo method and in the Kubelka-Munk approximation are compared. A linear relationship is established between the spatial irradiance in DSM volume and the diffuse reflectance coefficient. The precisions and applicability limits of the original and corrected Kubelka-Munk formulas are determined. A complex relationship is ascertained between the single scattering albedo Λ and the angular dependence of a photon flux incident on the DSM-air interface f (α). In particular, it was shown that for Λ → 1 and isotropy scattering, f (α) = cos(α), where a is the photon incidence angle. The results can be used for the development of methods for determining spatial irradiance and, for example, in laser medicine.
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