Angular reflectance model for ridged specular surfaces, with comprehensive calculation of inter-reflections and...

The color of a surface structured at the mesoscopic scale differs from the one of a flat surface of the same material because of the light inter-reflections taking place in the concavities of the surface, as well as shadowing effects. The color variation arises not only in scattering materials, but also in the absence of scattering, e.g., in metals and clear dielectrics, just as a consequence of multiple specular reflections between neighboring flat facets of the surface. In this paper, we investigate such color variation in the case of an infinitely long V-shaped groove, having in mind the visual appearance of a surface composed of many structures of that sort, all parallel and identical. We develop a full model of multiple specular reflections, accounting for the ray position and orientation and the polarization effects occurring at each reflection. We compare that situation with two approximate models, more usual and easier to compute, where light is assumed to remain unpolarized all along, or where the $p$p- and $s$s-polarized components are treated separately. Spectral reflectances were predicted for various materials and angles of cavities, under diffuse illumination. In most cases, the three models predict very similar bi-hemispherical reflectances, but the hemispherical-directional reflectances can vary noticeably in certain observation directions. This study might help achieve a more physically realistic rendering of dielectric or metallic ridged surfaces in computer graphics.