In the smooth-surface limit, the angular distribution of the light scattered from a surface maps the power spectral density of its residual surface roughness. This result is essentially independent of the scattering theory used and the statistical properties of the surface roughness. The power spectral densities of engineering surfaces are generally broad and increase with increasing spatial wavelength. As a result, practical surface finish parameters are not intrinsic properties of the surface, but depend, with varying degrees of sensitivity, on the bandwidth limits inherent in their measurement or dictated by their application. These issues are discussed with reference to two classes of finish parameters: those related to the central moments of the scattering spectrum, and those related to the coefficients in the expansion of the shape of the spectrum in inverse powers of the scattering angle. The significance of "1/02" scattering in this context is emphasized. A shot model of surface roughness is then introduced to gain further insight into the relationship between scattering and surface features. In this model inverse power terms are related to "edge" scattering effects from critical points in various types of elemental microdefects. The relationship between this view and electronic noise is pointed out; in particular, the correspondence between "1/02" scattering and "1/f" or flicker-noise phenomena.
E. L. Church,
H. A. Jenkinson,
J. M. Zavada,
"Relationship between Surface Scattering and Microtopographic Features," Optical Engineering 18(2), 182125 (1 April 1979). https://doi.org/10.1117/12.7972337