Implementation of the four-flux model for spectral and color prediction of 2.5D prints

Optical models to predict visual appearance of 2D prints are relatively well-known. Two-flux models, such as the Kubelka-Munk (KM) theory, are the most commonly used and offer good prediction rates. However, most two-flux models assume that the ink layer and the printing support have the same optical indices neglecting their wavelength dependency. An improvement of such constraint would be to include detailed optical indices of the inks in current models. In this paper we compute optical indices of our inks by printing ink stacks of different thicknesses on a transparent support for reflectance and transmittance measurements. Since KM-based models work under limited conditions, we input our computed indices into a more robust model. By taking additional fluxes into account, one can address the limitations of the two-flux approaches. For instance, the four-flux model considers two collimated and two diffuse fluxes propagating upward and downward the layer stack offering better reflectance and transmittance predictions especially when translucent materials are involved. Our four-flux theory including inks optical indices enables us to make spectral predictions of 2.5D prints without any preliminary measurements. The model is fairly accurate with primary colorants since the ΔE94 values do not exceed 1 unit.