Extracting fiber length distributions from dual-beard fibrographs with the Levenberg–Marquardt algorithm

Fiber length is a critical cotton fiber property that impacts yarn strength, yarn evenness, and ultimately fabric strength and appearance. In this paper, a new fiber fibrograph method was presented for accurate measurements of fiber length distributions (FLDs). The method, called the dual-beard fibrograph (DBF), was based on the transmission image of a combed sample with two tapered fiber ends/beards, and the approximation of the fibrograph with a series of triangular base functions. A desktop scanner was used to generate the transmission image of a dual-beard sample, and essential image-processing algorithms were utilized to mitigate image differences originating from variations in the scanning condition (e.g., brightness, resolution) and the sample condition (e.g., weight, orientation). The fibrograph approximation was implemented by minimizing a cost function that contains the sum of squared errors between the DBF and the ensemble of the weighted triangular base functions, and the regularization term that stabilizes the optimization with the Levenberg–Marquardt algorithm. The minimization eventually determined the optimal weights of the triangular base functions, which defined the FLDs of the scanned image. Important length measurements currently used in the industry can be easily calculated from the FLD. It was found that the DBF could correctly detect fiber lengths cut from 5 to 10 mm, respectively, and it could measure the short fiber content change after a known number of short fibers was added to an existing sample. When compared with an existing fiber testing instrument, the DBF was able to output more reasonable cotton length distributions.