  Zernike polynomials are widely used mathematical models of experimentally
observed optical aberrations. Their useful mathematical properties, in
particular their orthogonality, make them a ubiquitous basis set for solving
various problems in beam optics. Thus they have found widespread use in
adaptive optics realizations that are used to correct wavefront aberrations.
However, Zernike aberrations lose their orthogonality when used in combination
with Gaussian beams, which are omnipresent in real-world optical applications.
As a consequence, Zernike aberrations in Gaussian beams start to cross-couple
between each other, a phenomenon that does not occur for Zernike aberrations in
plane waves. Here, we describe how the aberration radius influences this
cross-coupling of Zernike aberrations. Furthermore, we propose that this effect
can actually be harnessed to allow efficient compensation of higher-order
aberrations using only low-order Zernike modes. This finding has important
practical implications, as it suggests the possibility of using adaptive optics
devices with low element numbers to compensate aberrations which would normally
require more complex and expensive devices.
