This article reports on a project that used an integral equation approach to finding the Kubelka-Munk (KM) diffuse reflectance formula, and it extended the result by finding the apparent path length and total intensity distribution inside an infinite, homogeneous, diffusely reflecting medium with isotropic scattering.
It then expanded the approach to three dimensions to show that the KM formula is correct for total diffuse reflectance when scattering, excitation, and detection are all isotropic. The project obtained simple and exact results for the angular distribution of diffuse reflection and for the total diffuse reflectance when the incident light has an isotropic angular distribution, when it strikes at a single angle of elevation, and when it has the steady-state angular distribution. This work includes some results that employ Chandrasekhar's H function, so it also provides a program for the rapid evaluation of H. (publisher abstract modified)
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