Surface Reflection: Physical and Geometrical Perspectives

Machine vision can greatly benefit from the development of accurate reflectance models. There are two approaches to the study of reflection: physical and geometrical optics. While geometrical models may be construed as mere approximations to physical models, they possess simpler mathematical forms that often render them more usable than physical models. However, geometrical models are applicable only when the wavelength of incident light is small compared to the dimensions of the surface imperfections. Therefore, it is incorrect to use these models to interpret or predict reflections from smooth surfaces, and only physical models are capable of describing the underlying reflection mechanism. This paper is directed towards unifying physical and geometrical approaches to describe reflection from surfaces that may vary from smooth to rough. More specifically, we consider the Beckmann-Spizzichino (physical optics) model and the Torrance-Sparrow (geometrical optics) model. We have chosen these two models in particular as they have been reported to fit experimental data very well. Each model is described in detail, and the conditions that determine the validity of the model are clearly stated. From studying the behaviors of both models, we propose a model comprising three reflection components: the diffuse lobe, the specular lobe, and the specular spike. The dependencies of the three components on the surface roughness and the angles of incidence and reflection are analyzed in detail.