Effect of the refraction index in the diameter estimation of thin metallic wires

Abstract

The most common technique for diameter measurement of thin metallic cylinders is optical diffractometry. It consists in illuminating the cylinder with a collimated monochromatic light beam, determining the diameter from the location of the minima of the far field diffraction pattern. Babinet principle is normally assumed, being the diffraction pattern of the cylinder equivalent to that of a strip whose width is equal to the cylinder diameter. Due to the three dimensional nature of the cylinder, this model is not valid for accurate measurements. It has been experimentally shown that, when compared to interferometry, Fraunhoffer model presents a systematic overestimation in the cylinder diameter. Rigorous models which assume that the wire presents an infinite conductance have been developed. However, the refraction index of the material has also appeared important for an accurate estimation since it produces a phase shift of the reflected wave by the wire surface, modifying the state of polarization of the incident light beam and, as a consequence, the location of the diffraction minima. In this work we propose a model based on the Geometrical Theory of Diffraction that assumes both the three-dimensional nature and a finite conductance of the wire. Results for several materials are presented, showing that the overestimation of the wire diameter depends on the state of polarization and wavelength of the incident light beam, as well as the diameter and refraction index of the metallic wire.