Extension of the Williams-Clapper model to stacked nondiffusing colored coatings with different refractive indices

Abstract

We propose a model for predicting the reflectance and transmittance of multiple stacked nonscattering coloring layers that have different refractive indices. The model relies on the modeling of the reflectance and transmittance of a bounded coloring layer, i.e., a coloring layer and its two interfaces with neighboring media of different refractive indices. This model is then applied to deduce the reflectance of stacked nonscattering layers of different refractive indices superposed with a reflecting diffusing background that has its own refractive index. The classical Williams-Clapper model becomes a special case of the proposed stacked layer model.