An Optical Algorithm for Relative Thickness of Each Monochrome Component in Multilayer Transparent Mixed Films

Abstract

A modification of the two-flux Kubelka-Munk (K-M) model was proposed to describe the energy conservation of scattered light in colored mixed material with a defined scattered photometric, which is applied for the relative quantity distribution of each colored monochrome component in mixed material. A series of systematical experiments demonstrated a higher consistency with the reference quantity distribution than the common Lambert-Beer (L-B) law. Its application in the fibrogram of each component for measuring the cotton fiber’s length was demonstrated to be good, extending its applicability to white and dark colored blended fibers, the length of which is harder to measure using L-B law.

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

“…This attempt was useful and has never been carried out before. To date, relevant research studies of the K-M model mainly focused on the usage of its reflectance equations, including the regressed functional relationship between optical thickness and mass of a particular composition of soil, 24,45 color, 19,20 and proportion prediction 33,37 of blending fibers with infinite thickness or inks on papers. Among them, only the first case had the opportunity to be adopted for thin materials.…”

“…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. 37 The scattering coefficient was obtained on K-M transmission law by multiple actual thickness, 38,39 and the results exhibited a high consistency between the predicted relative masses and the actual ones, better than the L-B model. 37 However, this method cannot be directly applied in mixed fibers blended with primaries at different ratios, which calls for further study in both the optical theory of K-M law and the turbid addition theorem.…”

“…37 The scattering coefficient was obtained on K-M transmission law by multiple actual thickness, 38,39 and the results exhibited a high consistency between the predicted relative masses and the actual ones, better than the L-B model. 37 However, this method cannot be directly applied in mixed fibers blended with primaries at different ratios, which calls for further study in both the optical theory of K-M law and the turbid addition theorem.…”