A method is described for computing optical properties of surfaces with a sparse distribution of submicroscopic bumps, pits, or foreign particles on or imbedded in them. The particles are assumed to be approximate figures of revolution about an axis normal to the surface. Surface and particle are assumed to have uniform, isotropic values of refractive index. Such foreign particles or roughness are equivalent in optical properties to a thin flat film of uniaxial material with its optic axis normal to the surface. The thickness of the equivalent film is arbitrarily made equal to the volume per unit area of all particles or bumps or pits. The principal values of refractive index of this equivalent film are determined by the shape of the particles and any surface irregularity associated with them, and by the refractive indices of particles and substrate, but not by particle size if size is small compared to wavelength of incident radiation. A recent experimental observation that silver tarnish in the form of isolated particles on a flat substrate gives about the same ellipsometric perturbation as would be expected from a flat film of the same refractive index and density appears to be only a rough approximation. Even that approximation would fail if the substrate were not metallic or if the tarnish particles were embedded in the surface. Differences of optical constants derived from measurements on thick and very thin films are explained.
DWIGHT W. BERREMAN, "Reflectance and Ellipsometry When Submicroscopic Particles Bestrew a Surface," J. Opt. Soc. Am. 60, 499-505 (1970)