Cross-compensation of Zernike aberrations in Gaussian optics

TL;DR

This paper introduces a new framework to understand and analyze the cross-compensation effects of Zernike aberrations in Gaussian beams, enhancing the understanding of optical aberrations in imaging and adaptive optics.

Contribution

It presents a novel approach analyzing Zernike mode coupling with Laguerre-Gauss modes, applicable in both low and high aberration regimes, and during 3D beam propagation.

Findings

Explains fundamental cross-compensation of Zernike aberrations.

Analyzes mode coupling during 3D propagation.

Applicable to both low and high aberration regimes.

Abstract

Zernike polynomials are one of the most widely used mathematical descriptors of optical aberrations in the fields of imaging and adaptive optics. Their mathematical orthogonality as well as isomorphisms with experimentally observable aberrations make them a very powerful tool in solving numerous problems in beam optics. However, Zernike aberrations show cross-coupling between individual modes when used in combination with Gaussian beams, an effect that has not been extensively studied. Here we propose a novel framework that is capable of explaining the fundamental cross-compensation of Zernike type aberrations, both in low-aberration and high-aberration regimes. Our approach is based on analysing the coupling between Zernike modes and different classes of Laguerre-Gauss modes which allows investigating aberrated beams not only on a single plane but also during their 3D propagation.