On high-frequency radiation scattering sensitivity to surface roughness in particulate media

This paper analyzes the sensitivity of high-frequency radiation scattering in particulate media, to particle surface roughness. Ray-tracing theory and computation are employed. Since the magnitude of the Poynting vector ray, the irradiance, is the appropriate quantity to be tracked, the behavior of the reflectance, which controls the ratio of the reflected and incident Poynting vector magnitudes, is of primary concern. The reflectance is a highly nonlinear function of the refractive indices and angle of incidence. The present work first addresses the relationship between a single scatterer's sensitivity to its surface roughness and then the response of a large number of scatterers to the surface roughness. The analysis indicates that, for a single scatterer, the sensitivity of the response to roughness decreases, up to a point, and then increases again, i.e., it is nonmonotone. However, for a system of multiple scatterers, this effect vanishes, due to multiple internal reflections which dominate the overall response characteristics. While it was relatively straightforward to compute the overall sensitivity of a single scattering body, for example a sphere, when multiple reflecting bodies are considered, numerical simulations are necessary because the reflected rays from one rough body will, in turn, be reflected to another rough body, etc. Examples are given for a system of randomly distributed scatterers.