Coherence versus radiance formulations of surface scattering

Surface scattering can be formulated in terms of coherence functions averaged over surface realizations. The resulting integrals for the average scattered intensity are superficially similar to those derived in conventional formulations like the Kirchhoff, Beckmann, and physical-optics models, but the coherence function is subject to some essential conditions, which are extensions of previously-derived conditions on the radiometric parame- ters of primary, partially-coherent sources and their propagated fields, that significantly influence the resulting scattered-intensity or BRDF solutions. The field approximation that leads to conventional radiance-like models is compared to a field approximation that leads to a particular coherence model of surface scattering, which is reviewed and verified against radiometric and atomic-force microscope (AFM) data due to a standard diffuse-gold reflector, representing apparently the first verified inverse reflectance solution for a non-contrived diffuse rough surface.