Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media

We extend the applicability of the recently revised Kubelka-Munk (K-M) theory to inhomogeneous optical media by treating inhomogeneous ink penetration of the substrate. We propose a method for describing light propagation in either homogeneous or inhomogeneous layers using series representations for the K-M scattering and absorption coefficients as well as for intensities of the upward and downward light streams. The conventional and matrix expressions for spectral reflectance and transmittance values of optically homogeneous media in the K-M theory are shown to be special cases of the present framework. Three types of ink distribution-homogeneous, linear, and exponential-have been studied. Simulations of spectral reflectance predict a depression of reflectance peaks and reduction of absorption bands characteristic of hue shifts and significant reduction of saturation and, in turn, color gamut.