Single-layer model for surface roughness

Random roughness of an optical surface reduces its specular reflectance and transmittance by the scattering of light. The reduction in reflectance can be modeled by a homogeneous layer on the surface if the refractive index of the layer is intermediate to the indices of the media on either side of the surface. Such a layer predicts an increase in the transmittance of the surface and therefore does not provide a valid model for the effects of scatter on the transmittance. Adding a small amount of absorption to the layer provides a model that predicts a reduction in both reflectance and transmittance. The absorbing layer model agrees with the predictions of a scalar scattering theory for a layer with a thickness that is twice the rms roughness of the surface. The extinction coefficient k for the layer is proportional to the thickness of the layer.