Two-flux and multiflux matrix models for colored surfaces

This paper presents various extensions of the so-called two-flux models for prediction of reflectance and transmittance of diffusing media, i.e. the Kubelka-Munk model, introduced in [HDI062], and the extension of Kubelka-Munk for stacks of diffusing layers. A first matrix formulation of the Kubelka-Munk differential equations leads to a matrix framework based on transfer matrices, which can be extended to stacks of diffusing layers, stacks of nonscattering films, and stacks of scattering and non-scatterings films as a generalization of the WilliamsClapper model for prediction of the reflectance of paper photographs, each of these configurations being illustrated through various examples. This paper also exposes the limits of the two flux approach and shows that the matrix formalism extends in a straightforward manner to multiflux models, where the size of the matrices is increased.