Application of K-integrals to radiative transfer in layered media

Abstract: Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals, originally developed for neutron transport analysis. These are certain weighted integrals applied to the angular intensity distribution at the refracting boundaries. The radiative intensity is expressed as the sum of the asymptotic angular intensity distribution valid in the depth of the scattering medium and a transient term valid near the boundary. Integral boundary conditions are obtained from the vanishing of the K-integrals of the boundary transient, yielding simple linear equations for the intensity coefficients (two for a halfspace, four for a slab or an interface), enabling the angular emission intensity and the diffuse reflectance (albedo) and transmittance of the scattering layer to be calculated. The K-integral method is orders of magnitude more accurate than diffusion theory and can be applied to scattering media with a wide range of scattering albedoes. For example, near five figure accuracy is obtained for the diffuse reflectance of scattering layers of refractive index n = 1.5 with single scattering albedo in the range 0.3 to 1