An experimental study of the correlation between surface roughness and light scattering for rough metallic surfaces

We present an experimental study of the angular distribution of light scattered from several rough metallic surfaces, which cover a range of roughness conditions. The substrate materials are steel or glass; roughened by bead-blasting, grinding, or etching; and aluminum-coated. The measured surface-roughness statistics are filtered by using a composite roughness model. The raw mechanical roughnesses range from 0.21μm to 2.66μm; the high-frequency small-scale roughnesses range from 0.13μm to 0.86μm. The optical wavelength is 550nm, so that the roughness-to-wavelength ratio is of order one. A BRDF model based on the Kirchhoff approximation is used to establish a relationship between surface-height statistics and the angular distribution of the scattered light. Angular distributions calculated with the BRDF model are fit to the measurements. The best-fit roughness statistics from the BRDF model agree closely with those measured for the high-frequency small-scale roughness component. The latter roughness component, which has the highest surface slopes, is thus the primary contributor to the angular distribution of the reflected light. We show that the Kirchhoff approximation can be applied to rough metallic surfaces that have multiple scales of roughness and near-, but not perfect, Gaussian surface-height distributions.