A stratified model for scattering from multilayer coatings due to roughness of inhomogeneous interfaces is introduced in the paper. It assumes that a rough interface between two media of multilayer coatings consists of a series of very thin, homogeneous sub-layers and that there is an exponential increase in refractive indices of those sub-layers. Matrix method was used to deduce the formulation for calculating the total integrated scattering (TIS). ZrO<sub>2</sub> coatings were deposited on BK7 glass by electron beam evaporation, and their scattering properties were measured and calculated by the scatterometer, the stratified scattering model and the existing uncorrelated surface roughness model, respectively. It is shown that the calculated results based on predictions of the stratified scattering model are in closer correspondence with the experimental data than that obtained with uncorrelated surface roughness model.
A total integrated scattering (TIS) instrument is presented. Its basic structure, theory foundation, and measurement principle are introduced. The surface root mean square (rms) roughness of single silver films on BK7 glass substrates is measured by employing this instrument. The results agree well with the data obtained by the optical profilometer and the atomic force microscope (AFM).