An Illumination Model for a System of Isotropic Substrate- Isotropic Thin Film with Identical Rough Boundaries

A new physically-based illumination model describing the interaction of light with a system composed of an isotropic substrate coated by an isotropic film with geometrically identical statistical rough boundaries (ITF) is presented. This model divides the intensity reflected from the system into three components: specular, directional-diffuse and uniform diffuse intensity. The formulas for the intensity reflected coherently (specular) and incoherently (directional-diffuse) from the system are derived within the framework of the scalar diffraction theory. Assuming that the slopes on the boundaries of the film are small, a first-order expansion of the reflection coefficient is used in the evaluation of the Helmholtz-Kirchhoff integral which allows to calculate the previous intensities. The consistency of the model is evaluated numerically and appraised visually by comparison with classic approximations.