We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.
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