Abstract
We describe the symmetries present in the point-spread function (PSF) of an optical system either located in space or corrected by an adaptive optics (AO) system to Strehl ratios of about 70% and higher. We present a formalism for expanding the PSF to arbitrary order in terms of powers of the Fourier transform of the residual phase error over an arbitrarily shaped and apodized entrance aperture. For traditional unapodized apertures at high Strehl ratios, bright speckles pinned to the bright Airy rings are part of an antisymmetric perturbation of the perfect PSF, arising from the term that is first order in the residual phase error. There are two symmetric second-degree terms. One is negative at the center and, like the first-order term, is modulated
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