A cross-correlation approach to astronomical speckle imaging

Summary form only given. The problem of reconstructing finite support objects from images degraded by a propagation through a turbulent atmosphere has been treated. A method for reconstructing the cross-correlating short exposure images of the object with short exposure images of a reference star has been developed. This makes it possible to obtain both magnitude and phase information about the Fourier transform of the object intensity up to the diffraction limit of the telescope. The derivation assumes that the complex amplitude of light that has propagated through the atmosphere has Gaussian statistics in the telescope pupil. In this approach the object intensity is the solution of a Fredholm integral equation of the first type with a positive semidefinite rotationally symmetric kernel. Furthermore, the low-pass nature of the instantaneous point spread function of the atmosphere/telescope and the finite spatial extent of the recorded short exposure images imply that the object intensity cannot be exactly reconstructed without some a priori information