Analysis of detectable angles of yarn hairiness in optical measurements

Obstructed by the yarn core, the detectable length and the detection rate of a hairy fiber are mainly determined by the geometry of the yarn and the location of the fiber in an optical system. This paper presents a new theoretical method of analyzing detectable angles of yarn hairiness in optical measurements. Firstly, a cylindrical model of the yarn core is constructed by using the yarn diameter, and spiral lines on the cylinder are drawn using the twist angle of the yarn. Secondly, hairy fibers are simulated by short-line segments passing a spiral line and the Z-axis of the model. The yarn model is projected onto a plane under the assumption of a collimated light source, which is the condition similar to that of optical measurements. The yarn model is cut by a plane parallel to the axes of the Cartesian coordinate system (XOY) at the emergence points of hairy fibers. Finally, the relationship between the hairiness length and other factors, such as the test length, yarn diameter and detectable angle (i.e. the angle at which hairy fiber can be detected) is established. It has been demonstrated that the detection angle dictates not only the length of each hairiness but also the rate of detectable hairiness in the scene. Given a detectable angle, the upper and lower limits of detectable hairiness lengths can be predicted. The verification results of the detection rate by three measurement methods indicate that the detection rates of optical measurements have a certain guidance function for correcting the hairiness results of optical measurements.