Phase-Gradient Speckle-Image Reconstruction: Discrete-Photon Case

The phase-gradient algorithm (PG) determines the phase of a stellar object's spatial spectrum by estimating the derivatives of the phase directly from the speckle images, and then integrating. A photon-address version of the PG has been successfully implemented for use at very low light levels. Computation of image-domain, cross-correlation functions is simply a matter of generating the 2D histograms of address differences, and bias terms are eliminated by omitting all photon self-correlation products. In a series of comparisons with a photon-address, Knox-Thompson algorithm, PG proved to have greater computational efficiency, to be more robust and to yield images with lower noise.