Diffraction as scattering under the Born approximation

TL;DR

This paper introduces a new diffraction calculation method using the Born approximation, providing a general formula for 2D objects that encompasses existing theories without angular approximations.

Contribution

It presents a novel approach to diffraction analysis employing the first order Born approximation, unifying and extending classical diffraction formulas.

Findings

Derives a general diffraction formula for 2D objects using the Born approximation

Shows the new formula encompasses classical theories like Fresnel-Kirchhoff and Rayleigh-Sommerfeld

Discusses the validity of common approximations in diffraction analysis

Abstract

Light diffraction at an aperture is a basic problem that has generated a tremendous amount of interest in optics. Some of the most significant diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas. These theories are based on solving the wave equation using Green's theorem and result in slightly different expressions depending on the particular boundary conditions employed. In this paper, we propose another approach for solving the diffraction by a thin screen, which includes apertures, gratings, transparencies etc. We show that, applying the first order Born approximation to 2D objects, we obtain a general diffraction formula, without angular approximations. We discuss several common approximations and place our results in the context of existing theories.