The Optics of the Wool Fiber Diameter Analyzer

Abstract

The optics underlying the operation of the wool fiber diameter analyzer ( FDA ) is explained in terms of the formation of a Fresnel diffraction shadow behind a strip mask. Consequently, the measurement technique is sensitive only to fiber diameter and is independent of internal properties such as color or refractive index. Using an approximate technique, the Huygens-Fresnel theory of diffraction is modified to account for a finite sized source with non-uniform illumination. This allows the FDA optics to be modeled using a new technique of modified Fresnel integrals. The method, which applies a one-dimensional approach to a two-dimensional problem, is computationally simple and gives an accurate description of optical phenomena encoun tered in the FDA. The model provides a powerful design and analysis tool for this class of instrument and has proved useful in elucidating potential sources of error.