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Diffusion of light in turbid media and Kubelka-Munk theory

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arxiv 2303.04065 v2 pith:BDWOODZX submitted 2023-03-07 cond-mat.dis-nn physics.optics

Diffusion of light in turbid media and Kubelka-Munk theory

classification cond-mat.dis-nn physics.optics
keywords kubelka-munkdiffusionequationscoefficientsderiveequationinternallight
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We show that the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media are equivalent to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulas for these coefficients. We show that the Kubelka-Munk equations are the proper radiative-transfer equations for the one-dimensional diffusion problem and comment on previous attempts to derive the Kubelka-Munk equations.

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