A two-scale roughness model for the gloss of coated paper

A model for gloss is developed for surfaces with two-scale random roughness where one scale lies in the wavelength region (microroughness) and the other in the geometrical optics limit (macroroughness). A number of important industrial materials such as coated and printed paper and some paints exhibit such two-scale rough surfaces. Scalar Kirchhoff theory is used to describe scattering in the wavelength region and a facet model used for roughness features much greater than the wavelength. Simple analytical expressions are presented for the gloss of surfaces with Gaussian, modified and intermediate Lorentzian distributions of surface slopes, valid for gloss at high angle of incidence. In the model, gloss depends only on refractive index, rms microroughness amplitude and the FWHM of the surface slope distribution, all of which may be obtained experimentally. Model predictions are compared with experimental results for a range of coated papers and gloss standards, and found to be in fair agreement within model limitations.