Predicting the Reflectance of Paper Dyed with Ink Mixtures by Describing Light Scattering as a Function of Ink Absorbance

We consider the problem of predicting the spectral reflec-tance 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. INTRODUCTION Ink jet printers use multiple inks which, thanks to half-toning, enable producing a wide color gamut. Pixel dot sizes are variable and can be chosen so as to produce lighter or stronger tones. Selecting the dot size for each ink and each pixel, combined with half-toning, yields a very rich set of color rendering options. In order to better assess this potential , one of the challenges is to predict the reflectance spectra for any combination of pixel dot size and half-tone dot surface coverage. Spectral prediction of the reflectance of color half-tone prints is a difficult problem, mainly due to the interaction of ink and paper. When ink is deposited on a porous paper, part of it penetrates the paper and part of it remains on the surface. The ink concentration as a function of depth within the paper is unknown. Creating exact models of the reflectances of mixtures of multi-ink half-tones with variable pixel dot sizes is therefore difficult. As a first step toward the goal of predicting the reflec-tance of ink mixtures within the paper, we consider a simplified setup where the ink concentration within the paper is assumed to be uniform. The paper is immersed for 30 min in a colored solution with a predetermined ratio of inks and then dried. By considering each ink separately at different concentrations, we establish a link between the ink absor-bance and the ink concentration. This allows us to deduce