Validity of Hybrid Models for the Bidirectional Reflectance of Coated Rough Surfaces

Abstract

Modeling of the bidirectional reflectance of thin-film coatings on rough surfaces has been an important and challenging problem. In the past, there have been studies that use thin-film optics to take account of the coating-induced interference effects and the geometric optics approximation to model the surface roughness. In an effort to delineate the validity regime of the hybrid method, the predicted bidirectional reflectance is compared with that obtained from the rigorous electromagnetic-wave solution for one-dimensional rough surfaces, considering the effect of coating thickness and roughness parameters. Two hybrid models are implemented using the Monte Carlo ray-tracing algorithm: the surface generation method and microfacet slope method. The former relies on statistically generated surfaces according to the root-mean-square roughness and the autocorrelation length, whereas the latter uses the microfacet whose orientation is stochastically determined, when a ray hits the surface, according to the slope distribution without creating deterministic rough surfaces a priori. The validity regimes of the hybrid models are established for silicon dioxide films on silicon substrates. The advantages and disadvantages of each hybrid model are discussed. Some useful guidelines are provided for the simulation of optical scattering from coated rough surfaces.