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

Abstract

Unclear light propagation in mixed fibers has resulted in unachievable masses of primary fibers, in particular thin two-mixed fiber assemblies for decades. Hereby, a modified mixed medium addition theorem of the Kubelka-Munk transmission model is proposed to address this issue. This theorem was constructed by introducing a transfer function in the common ones on scattering coefficients, and such a transfer function takes both the mass proportion of each component and the reflectivity of mixed material into consideration. This opens up a new avenue for understanding the possible light mechanism of color mixed fiber assemblies. The proposed method demonstrated excellent accuracy in determining the primary masses of 48 specimens, with an average mean absolute error of only 2.23 mg. In comparison, the Lambert-Beer law yielded a much higher average mean absolute error of 8.66 for all types of blended samples. Such superiority was particularly obvious in white-black mixed samples, probably due to its comprised reflectance. In brief, this proposed theorem shows a high-quality prediction accuracy level in fiber mass and can be expanded to detect and control mixed fibers, as well as fiber length and uniformity detection through further study.