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Zernike polynomials are one of the most widely used mathematical descriptorsof optical aberrations in the fields of imaging and adaptive optics. Theirmathematical orthogonality as well as isomorphisms with experimentallyobservable aberrations make them a very powerful tool in solving numerousproblems in beam optics. However, Zernike aberrations show cross-couplingbetween individual modes when used in combination with Gaussian beams, aneffect that has not been extensively studied. Here we propose a novel frameworkthat is capable of explaining the fundamental cross-compensation of Zerniketype aberrations, both in low-aberration and high-aberration regimes. Ourapproach is based on analysing the coupling between Zernike modes and differentclasses of Laguerre-Gauss modes which allows investigating aberrated beams notonly on a single plane but also during their 3D propagation.

Cross-compensation of Zernike aberrations in Gaussian optics