Aberration-like cusped focusing in the post-paraxial Talbot effect

TL;DR

This paper analyzes self-imaging beyond the paraxial approximation, revealing aberration-like cusped focusing in the post-paraxial Talbot effect, and shows that such aberrations can arise from improved approximations rather than system imperfections.

Contribution

It provides an analytical description of aberration-like focusing in the post-paraxial regime, expanding understanding of the Talbot effect beyond traditional paraxial limits.

Findings

Aberration-like cusped focusing occurs beyond the paraxial regime.

Such focusing results from improved approximations, not system imperfections.

The structures relate to diffraction cusps but do not exactly replicate them.

Abstract

We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are described analytically using post-paraxial theory. They are shown to relate to, but surprisingly do not precisely replicate, a standard integral representation of a diffraction cusp. Beyond the Talbot effect, this result is significant as it illustrates that the effect of aberration -- as manifested in the replacement of a perfect focus with a cusp-like pattern -- can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.