Zernike mode rescaling extends capabilities of adaptive optics for microscopy

Zernike polynomials are widely used mathematical models of experimentally observed optical aberrations, and they have found widespread use in adaptive optic realizations that are used to correct wavefront aberrations. However, Zernike aberrations lose their orthogonality when used in combination with Gaussian beams and, as a consequence, 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 (i.e. the radius of the beam relative to the active aperture of an active optical element) influences this cross-coupling of Zernike aberrations in a way that is distinct from simple truncation or balancing. Furthermore, we show 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 that would normally require more complex and expensive devices.