Validation of Fresnel–Kirchhoff Integral Method for the Study of Volume Dielectric Bodies

Abstract

In this work, we test a nondestructive optical method based on the Fresnel–Kirchhoff integral, which could be applied to different fields of engineering, such as detection of small cracks in structures, determination of dimensions for small components, analysis of composition of materials, etc. The basic idea is to apply the Fresnel–Kirchhoff integral method to the study of the properties of small-volume dielectric objects. In this work, we study the validity of this method. To do this, the results obtained by using this technique were compared to those obtained by rigorously solving the Helmholtz equation for a dielectric cylinder of circular cross-section. As an example of the precision of the method, the Fresnel–Kirchhoff integral method was applied to obtain the refractive index of a hair by fitting the theoretical curve to the experimental results of the diffraction pattern of the hair measured with a CCD camera. In a same manner, the method also was applied to obtain the dimensions of a crack artificially created in a piece of plastic.

Keywords

• scattering
• Fresnel diffraction
• interferometry
• solid mechanics
• optical methods