A semi-empirical reflectance/scatterance model has evolved over the years to represent a diverse set of materials from coated substrates to optical windows. This model separates the BRDF/BSDF into four basic components, specular, near-specular, diffuse, and Lambertian (random diffuse) terms. The specular and near-specular components employ a Gaussian phase function and the Fresnel power reflection coefficient. The Lambertian component uses Kubelka-Munk theory for the total integrated reflectance and transmittance. The model features wavelength, angle, and full hemispherical dependencies. It is applied to a variety of samples, from painted surfaces to transparent windows, with good success. This parameterized modeling approach is attractive because algorithms that use the model can be computationally efficient. Previous work has only considered in-plane effects. The present paper now explicitly takes into account the out-of-plane contribution and improves the total integrated factors.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.