Simulation of the optical behavior of rough identical multilayers

This paper presents a new analytical BRDF model allowing the simulation of the optical behavior of a kind of multilayers formed of homogeneous and isotropic thin films with identically rough boundaries. The boundaries are supposed to be locally smooth and the roughness is generated by a stationary Gaussian process characterized by two parameters: RMS height (sigma) and the correlation length (tau) . The BRDF is composed of three terms: specular, directional-diffuse and uniform diffuse. The expressions for the coherent (specular) and incoherent (directional diffuse) components of the BRDF are derived in the framework of the Kirchhoff theory of diffraction. By means of the Abeles [1] formalism and using the small-slope assumption, we derive a first order expansion for the amplitude reflection coefficient of the multilayer system. Replacing the reflection coefficient by this approximate formula in the Helmholtz-Kirchhoff integral allows us to evaluate both the coherent and incoherent components of the BRDF. This model was integrated into a spectral ray tracing algorithm to produce pictures of composite multilayer materials which will be displayed and commented hereafter. We also provide a visual evaluation of the model, studying the effect of a variation of the parameters (number of layers, composition of the multilayer, surface parameters.)