Photon path length distributions for an isotropically scattering planar medium

The optical path length concept is employed to determine path length distributions by an approximate numerical inversion of the Laplace transform. Six-term or 13-term closed-form representations of the hemispherical reflectance and transmittance optical path length distributions are presented. The mean path lengths and the distributions integrated over path length are found to be in excellent agreement with known results for a scattering optical depth range of 0.001 to 50.0. Any absorption feature of a medium is easily included in a scattering calculation using the results presented. Internal directional heat flux optical path length distributions are shown to exhibit the effects of higher orders of scattering.