We consider the problem of predicting the spectral reflectance of paper samples immersed in ink mixtures of varying ink concentrations. Relying on an adapted version of the Kubelka-Munk theory, we predict the reflectances of the samples dyed by ink mixtures. We first derive a method to calculate the effective scattering coefficient of an inked paper sample as a function of its absorbance coefficient. Then we learn from a single sample the reduction in ink concentrations when two inks are mixed. Using these ink concentration reduction factors, we can then predict the reflectances of paper colored by ink mixtures of various nominal concentrations.
Fabrice Rousselle, Mathieu Hébert, Roger Hersch, "Predicting the Reflectance of Paper Dyed with Ink Mixtures by Describing Light Scattering as a Function of Ink Absorbance" in Journal of Imaging Science and Technology, 2010, pp 50501-1 - 50501-8, https://doi.org/10.2352/J.ImagingSci.Technol.2010.54.5.050501