Rayleigh-Sommerfeld Fraunhofer Diffraction

TL;DR

This paper provides a comprehensive analysis of Fraunhofer diffraction using the Rayleigh-Sommerfeld integral, minimizing approximations to clarify the role of Fourier transforms and derive the Guoy phase shift.

Contribution

It offers a complete description of Fraunhofer diffraction without the common inclination factor approximation, enhancing theoretical understanding.

Findings

Exact role of Fourier transform in diffraction clarified

Derivation of Guoy phase shift from first principles

Minimal approximation approach improves theoretical accuracy

Abstract

Treatments of Fraunhofer diffraction normally approximate the inclination factor in the diffraction integral by 1, but this is not necessary. In this paper, the Rayleigh-Sommerfeld diffraction integral is used and a complete description of Fraunhofer diffraction is given, with the minimum possible number of approximations made. A focused wave is examined before, at, and after its focal point to elucidate the exact role of the Fourier transform in describing Fraunhofer diffraction and to derive the Guoy phase shift.