The Structure of High Strehl Ratio Point‐Spread Functions

We describe the symmetries present in the point-spread function (PSF) of anoptical system either located in space or corrected by an adaptive o to Strehlratios of about 70% and higher. We present a formalism for expanding the PSF toarbitrary order in terms of powers of the Fourier transform of the residualphase error, over an arbitrarily shaped and apodized entrance aperture. Fortraditional unapodized apertures at high Strehl ratios, bright speckles pinnedto the bright Airy rings are part of an antisymmetric perturbation of theperfect PSF, arising from the term that is first order in the residual phaseerror. There are two symmetric second degree terms. One is negative at thecenter, and, like the first order term, is modulated by the perfect image'sfield strength -- it reduces to the Marechal approximation at the center of thePSF. The other is non-negative everywhere, zero at the image center, and can beresponsible for an extended halo -- which limits the dynamic range of faintcompanion detection in the darkest portions of the image. In regimes where oneor the other term dominates the speckles in an image, the symmetry of thedominant term can be exploited to reduce the effect of those speckles,potentially by an order of magnitude or more. We demonstrate the effects ofboth secondary obscuration and pupil apodization on the structure of residualspeckles, and discuss how these symmetries can be exploited by appropriatetelescope and instrument design, observing strategies, and filter bandwidths toimprove the dynamic range of high dynamic range AO and space-basedobservations. Finally, we show that our analysis is relevant to high dynamicrange coronagraphy.Comment: Accepted for publication in ApJ; 20 pages, 4 figure