A surface-scattering model satisfying energy conservation and reciprocity

- We are introducing a BSDF that satisfies both reciprocity and energy conservation.
- We are accounting for both collimated (coherent) and diffuse (incoherent) components.
- The near-field absorption in the substrate induced by scatterers has been included.

Roughness scattering models based on Kirchhoff׳s approximation or perturbation theory give a good account of the angular distribution of the scattered intensity but do not satisfy energy conservation and reciprocity rigorously. For applications such as solar cells with rough interfaces producing a quasi isotropic intensity in the multiple scattering regime, an accurate model of the angular pattern is not required. Instead, energy conservation and reciprocity must be satisfied with great accuracy. Here we present a surface scattering model based on analysis of scattering from a layer of particles on top of a substrate in the dipole approximation which satisfies both energy conservation and reciprocity and is thus accurate in all frequency ranges. The model takes into account the absorption in the substrate induced by the particles but does not take into account the near-field interactions between the particles. In arriving at this model, we use the effective-medium approach to show how we can proceed from modeling the electromagnetic scattering from a single particle to modeling the scattering from a layer of particles positioned above a substrate, and finally relate this to the bidirectional scattering distribution function of the substrate.