Calculation method of a random beard fibrogram based on the derived Kubelka–Munk theory

The random beard image method is a newly developed fiber length measurement method with the advantages of speed, reliability and low cost. This paper proposed the methods of acquiring an accurate and stable fibrogram from the transmission image with the random beard image method based on the derived Kubelka–Munk theory. In the dual-beard preparation process, the optical properties of the short fiber region in the beard were changed by the napping effect. To solve this problem, an imitating experiment with five types of wool fibers was designed to obtain the optical coefficient of the maximum value of the fibrograms of 1.03. To eliminate the random error of the sample, the symmetry principle was adopted to determine the start line of the dual-fibrogram, and the weighted smoothing average fibrogram from two dual-beards is used as the final fibrogram. In addition, upon testing 20 types of wool fiber samples by the random beard image method and the international standard instrument Almeter100, the waviness coefficient of 1.10 was determined. A Z-test and Bland–Altman plot were also applied to verify the accuracy and repeatability of the random beard image method. The results show that under the significance level α = 0.05, the accuracy and the repeatability of the two methods are at the same level. This method sets the foundation for measuring the fiber length distribution parameters, especially the short fiber content.