Fresnel diffraction from curved fiber snippets with application to fiber diameter measurement

Fiber curvature is examined for its effect on apparent measured fiber diameter in a double-diffraction-based instrument that is in widespread use in the wool industry. The development uses a two-dimensional Fresnel diffraction model. The magnitude of the effect is studied for 2-mm-long snippets of various diameters from 8 to 50 µm and with radii of curvature of 1 m (straight), 600 µm, 280 µm, 200 µm, and 160 µm. The two-dimensional Fresnel model gives rise to deeply nested vector integrations that make computations with a straightforward approach exceedingly time consuming and impractical. A number of simplifying techniques are used to facilitate and speed up the numerical computations, thereby permitting investigations to be carried out on a personal computer.