Correspondence between Continuous and Discrete 2-flux Models for Reflectance and Transmittance of Diffusing Layers

This article provides a theoretical junction between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The KubelkaMunk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogenous layer (continuous 2-flux model). On the other hand, Kubelka’s layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (discrete 2-flux model). The compatibility of these two models is shown. In particular, the Kubelka-Munk reflectance and transmittance expressions are retrieved, using Kubelka’s layering model, with mathematical arguments using infinitely thin sublayers. A new approach to KubelkaMunk expressions is thus obtained, giving, moreover, a kind of physical interpretation of the Kubelka-Munk theory.