Radiative transfer equation-based color prediction and color adjustment strategies

Abstract

This paper discusses different strategies for color prediction and matching. Although many groups use the two-flux model (i.e., the Kubelka–Munk theory or its extensions), we introduce a solution of the P N approximation for the radiative transfer equation (RTE) with modified Mark boundaries for the prediction of the transmittance and reflectance of turbid slabs with or without a glass layer on top. To demonstrate the capabilities of our solution, we have presented a way to prepare samples with different scatterers and absorbers where we can control and predict the optical properties and discussed three color-matching strategies: the approximation of the scattering and absorption coefficient, the adjustment of the reflectance, and the direct matching of the color value L ∗ a ∗ b ∗ .