Reflectance and transmittance model for recto-verso halftone prints

We propose a spectral prediction model for predicting the reflectance and transmittance of recto-verso halftone prints. A recto-verso halftone print is modeled as a diffusing substrate surrounded by two inked interfaces in contact with air (or with another medium). The interaction of light with the print comprises three components: (a) the attenuation of the incident light penetrating the print across the inked interface, (b) the internal reflectance and internal transmittance that accounts for the substrate's intrinsic reflectance and transmittance and for the multiple Fresnel internal reflections at the inked interfaces, and (c) the attenuation of light exiting the print across the inked interfaces. Both the classical Williams-Clapper and Clapper-Yule spectral prediction models are special cases of the proposed recto-verso reflectance and transmittance model. We also extend the Kubelka-Munk model to predict the reflectance and transmittance of recto-verso halftone prints. The extended Kubelka-Munk model is compatible with the proposed recto-verso reflectance and transmittance model. In the case of a homogeneous substrate, the recto-verso model's internal reflectance and transmittance can be expressed as a function Kubelka-Munk's scattering and absorption parameters, or the Kubelka-Munk's scattering and absorption parameters can be inferred from the recto-verso model's internal reflectance and transmittance, deduced from spectral measurements. The proposed model offers new perspectives both for spectral transmission and reflection predictions and for characterizing the properties of printed diffuse substrates.