On the validity of two-flux and four-flux models for light scattering in translucent layers: angular distribution of internally reflected light at the interfaces

Abstract

Optical characterization and appearance prediction of translucent materials are required in many fields of engineering such as computer graphics, dental restorations or 3D printing technologies. In the case of strongly scattering materials, flux transfer models like the Kubelka-Munk model (2-flux) or the Maheu’s 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 rely on the assumption of lambertian fluxes at any depth within the material, they fail to model the internal reflectance at the interfaces, penalizing the accuracy of the optical parameter extraction. The aim of this 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 scattering on light propagation. It turns out that the light angular distribution at the bordering interfaces is often far from being lambertian, and that the internal reflectance may vary significantly according to the layer’s thickness, refractive index, scattering and absorption coefficients and scattering anisotropy. This work enables to better understand the impact of scattering within a translucent layer and also invites to revisit the well-known Saunderson correction used in 2- or 4-flux models.