A modified single-constant Kubelka–Munk model for color prediction of pre-colored fiber blends

The goal of this work is to propose a modified single-constant Kubelka–Munk model for color prediction of pre-colored fiber blends. The original single-constant Kubelka–Munk model follows the Duncan’s additivity theorem, assuming that the optical coefficients of individual components in a turbid media are linear to their respective proportions. However, the linear assumption is invalid for the media of fiber blends due to the interactions between primary fibers, causing inaccurate color prediction of the model. Aiming at improving the accuracy, the single-constant Kubelka–Munk model was modified by employing a new additivity formula. The new additivity formula was established to achieve good linearity of the optical coefficients by modeling interactions between primary fibers as configurations. Cotton fibers blending samples were prepared to assess the color prediction accuracy. The average color difference of the proposed model was 0.91 CIEDE2000 unit, which was significantly better than that of the original model (~ 5.48). The results indicate the proposed model is much more suitable for color prediction of pre-colored fiber blends.