  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.
