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

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Abstract

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.

© 1996 Optical Society of America

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