Resolution limits for deconvolved images

The limits imposed by photon statistics on the resolution attainable by deconvolving seeing-broadened astronomical images are investigated. By analogy with the classical Rayleigh limit for diffraction-limited images, resolution is defined as the separation of the equal component double star that can be just resolved by deconvolution. An approximate analytic theory is given that predicts the dependence of resolution thus defined on the number of detected photons, and this theory is tested by deconvolution experiments on synthetic images. The disparity for restored images between the Rayleigh criterion of resolution and the effective seeing inferred from the angular diameters of deconvolved single stars is stressed.