Speckle Statistics in Adaptively Corrected Images

Abstract

Imaging observations are generally affected by a fluctuating background of speckles, a particular problem when detecting faint stellar companions at small angular separations. These speckles can be created by both short-lived atmospheric aberrations and slowly changing distortions in the optical system. Over the course of a long-exposure image, the combination of many independent realizations of speckle patterns forms a halo in the point-spread function (PSF) of characteristic scale Δθ ~ λ/r₀ (where r₀ is the coherence length in the pupil). While adaptive optics can increase the achievable image contrast, speckle noise remains a major source of random error, which decreases the sensitivity of companion detection observations near the diffraction limit. Knowing the distribution of the speckle intensities at a given location in the image plane is therefore important for understanding the noise limits of companion detection. The speckle noise limit in a long-exposure image is characterized by the intensity variance and the speckle lifetime. In this paper we address the former quantity through the distribution function of speckle intensity. Previous theoretical work has predicted a form for this distribution function at a single location in the image plane. We developed a fast readout mode to take short exposures of stellar images corrected by adaptive optics at the ground-based UCO/Lick Observatory, with integration times of 5 ms and a time between successive frames of 14.5 ms (λ = 2.2 μm). These observations temporally oversample and spatially Nyquist sample the observed speckle patterns. We show, for various locations in the image plane, that the observed distribution of speckle intensities is consistent with the predicted form. In addition, we demonstrate a method by which I_c and I_s can be mapped over the image plane. As the quantity I_c is proportional to the PSF of the telescope free of random atmospheric aberrations, this method can be used for PSF calibration and reconstruction.