Cross-compensation of Zernike aberrations in Gaussian beam optics

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, most notably the recent developments of adaptive optics for correcting beam aberrations. However, Zernike aberrations show cross coupling between individual modes when used in combination with Gaussian beams, which are ubiquitous in most practical applications, 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, in both low-aberration and high-aberration regimes. Our approach is based on analyzing the coupling between Zernike modes and different classes of Laguerre-Gauss modes, which allows investigating aberrated beams not only on a single transverse plane but also during their 3D propagation.