Empirical colorant mixture models

The color behavior of unconventional colorant systems and certain other mixtures cannot be described adequately by available theory. In such cases alternative approaches to formulation and shading need to be developed. In this article we investigate empirical models using Scheffé polynomials to describe color response surfaces for three‐ and four‐component olorant mixtures. We describe experimental designs that allow the efficient estimation of the coefficients of high‐order polynomial models over the full mixture‐design space and that also allow estimation of lower‐order models over subspace mixture regions. The experimental designs are applied to real colorant systems, and the accuracy of color response prediction from linear, quadratic, cubic, and quartic polynomial models is compared to that of theoretical models. The color response surfaces are visualized by preparing contour plots that depict color variation over a compositional region. These maps allow one to observe the relationship between color and composition, to assess the color gamut available with a given colorant set, and to estimate the formula or adjustments required to match a given color position. The effective use of model predictions to perform a sensitivity analysis on the compositional variables is also demonstrated in the context of manufacturing process control.