Statistics of remnant speckles in an adaptively corrected imaging system

Understanding the statistics of remnant speckles in the halo of an adaptively-corrected point-spread function is critically important to using adaptive optics in high-dynamic-range searches for faint companions. It has been clear for some time that photon (Poisson) statistics alone do not adequately account for noise in the halo, as the coherent nature of speckles gives them a temporal persistence that leads to a much larger noise contribution, termed speckle noise. I consider in this paper the physical mechanism for speckle formation, and show that residual speckles, in the case of highly corrected adaptive optics systems, tend to be pinned to secondary maxima (Airy rings) in the underlying diffraction-limited point-spread function, affecting their spatial distribution in an important way. Further, in current practical adaptive optics systems, the structure of the Airy rings will shift over relatively short time scales in response to flexure-induced non-common-path errors, modifying the temporal evolution of the statistics of the speckle distribution as well.