Optical algorithm for calculating the quantity distribution of fiber assembly

Abstract

A modification of the two-flux model of Kubelka-Munk was proposed for the description of light propagating through a fiber-air mixture medium, which simplified fibers' internal reflection as a part of the scattering on the total fiber path length. A series of systematical experiments demonstrated a higher consistency with the reference quantity distribution than the common Lambert law on the fibrogram used in the textile industry did. Its application in the fibrogram for measuring the cotton fiber's length was demonstrated to be good, extending its applicability to the wool fiber, the length of which is harder to measure than that of the cotton fiber.

Algorithm for measuring fiber length distributions of raw cotton and combed wool using dual-beard image method

“…Next, the dual-beard transmittance at each pixel was calculated by dividing the grayscales by 255, and converted into the dual-beard areal density at each pixel using the optical algorithm introduced in our previous publications. 33 The summation of the areal densities of the pixels in a column could be considered as the dual-beard linear density at that column. Computing the linear densities of all columns and normalizing them would generate the relative linear density curve as shown in Figure 1.…”

“…[28][29][30][31] A new imaging method, called dual-beard imaging method (DBI) has been developed for fiber length measurement. 14,15,32,33 In this method, the specimen is not a traditional aligned beard but a dual-beard, a new invented specimen style which is much simpler and faster to be prepared than the traditional aligned one. Based on the image processing technology, the DBI has already been able to rapidly detect several parameters such as mean length, coefficient of variation, modal length, quality length (UHML, upper half mean length), and short fiber content (SFC).…”

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

“…Taking the reflection and scattering as the fiber assembly scattering effect, the author has deduced the relative density distribution algorithm based on the Kubelka-Munk transmission equation, which is adapted to different types of fiber assemblies, such as cotton and wool. 29 Assume that the transmission gray image of the layer assemblies is a matrix with the size of m  n pixels. Then, Equation (1) was used to calculate the optical mass of fibers of this point…”

“…However, these two methods all have large biases that need an experience correction table, which is only adapted to cotton fibers. In 2016, Wu and Wang 29 deduced the Kubelka-Munk derivation theory to calculate the optical area density of the fiber assembly based on the Kubelka-Munk theory. 30,31 It was found that the optical area densities with this method had good consistency with the real value.…”

“…The accuracy of this derived Kubelka-Munk equation was higher than that of the Beer-Lambert law for wool and cotton fibers. 29,30 However, designed for verifying the trueness of this theory preliminarily, it was measured from 1 cm away from the napping line. The fineness, waviness coefficient, fiber length distribution, smoothing and modification theory were not considered.…”