Light scattering in translucent layers: angular distribution and internal reflections at flat interfaces

Abstract

Optical characterization and appearance prediction of translucent materials is needed in several fields of engineering such as computer graphics, dental restorations or 3D printing technologies. In the case of strongly diffusing materials, flux transfer models like the Kubelka-Munk model (2-flux) or 4-flux model have been successfully used to this aim for decades. However, they lead to inaccurate prediction of the color variations of translucent objects of different thicknesses. Indeed, as they assume Lambertian fluxes at any depth within the material and in particular at the bordering interfaces, they fail to model the internal reflectance at the interfaces, penalizing the accuracy of the optical parameter extraction. The aim of the paper is to investigate the impact of translucency on light angular distribution and corresponding internal reflectances, by the mean of the radiative transfer equation, which describes more rigorously the impact of the scattering on the light propagation. It turns out that the light angular distribution at the bordering interfaces, assumed to be flat, is far from being Lambertian, and the internal reflectance may vary a lot according to the layer’s thickness, refractive index, scattering and absorption coefficients. This work not only enables to better understand the impact of scattering within a translucent layer but also invites to revisit the well-known Saunderson correction used in 2- or 4- flux models.