Radiative transfer equation-based color prediction and color adjustment strategies

Abstract

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

Modified addition theorem on Kubelka-Munk transmission law for mass prediction of each primary in two-mixed cotton fiber blends

“…27,28 To date, the K-M theory has mainly focused on color prediction in the textile field using its reflectance law and addition theorem, 5,23,[29][30][31] and was also gradually applied in relative mass prediction using its transmission function in recent years. [32][33][34] For example, Wu and Wang proposed an algorithm to calculate the optical relative surface density of fiber assembly based on K-M theory and obtained stable and accurate results on measuring the fiber length. 35,36 Following this, Wu et al constructed the color-separation algorithm on scattering for the relative thickness distribution of each primary component in mixed films based on the derived K-M transmission equation and mixed medium addition theorem.…”