Validity of thin element approximation in diffractometry of opaque thick objects

Abstract

The Thin Element Approximation (TEA) is widely used in diffraction analyses since it can be applied in efficient plane-to-plane propagation algorithms. While refinements have been developed for dielectric objects to obtain more accurate results, TEA is assumed precise for opaque objects. However, through numerical simulations presented in this work, based on Wave Propagation Method, we analyze the tendency of TEA to overestimate the dimensions of opaque objects in diffractometry. This effect was acknowledged in the case of cylinders, and we obtain similar results for the case of rectangular thick strips. On the other hand, TEA demonstrates a high level of accuracy when applied to objects with thickness concentrated at the center and thin edges, such as the isosceles triangular obstacle. Finally, we analyze objects whose shape is defined using the superellipse function, which is chosen for its versatility in generating objects of equivalent width and maximum thickness but with different shapes just changing a single parameter. Our results highlight the importance of considering the object geometry when employing this approximation in diffraction studies of opaque three-dimensional objects.