Optical reflectance and transmittance of a multilayer coating affected by refractive-index inhomogeneity, interface roughness, and thickness wedge

A theoretical model to evaluate normal-incidence specular, direct, hemispherical, and diffuse reflectance and transmittance of a single layer affected by refractive-index inhomogeneity along the growth axis, roughness, and thickness wedge was introduced in recent papers. In the present work, the model is extended to the case of a multilayer optical coating. To that purpose, suitable transfer matrices that account for layer-index inhomogeneity and random deviations of the interfaces from smooth planes are introduced, and statistical averages are applied to the resulting amplitude and intensity coefficients. Eventually, thickness wedge is included as a deterministic average on the intensity coefficients.