Estimation-theoretic approach to the deconvolution of atmospherically degraded images with wavefront sensor measurements

Deconvolution from wavefront sensing (or self-referenced speckle holography) has previously been proposed as a post-detection processing technique for correcting turbulence-induced wavefront phase-errors in incoherent imaging systems. In this paper, a new methodology is considered for processing the image and wavefront-sensor data in which the method of maximum-likelihood estimation is used to simultaneously estimate the object intensity and phase errors directly from the detected images and wavefront-sensor data. This technique is demonstrated to work well in a situation for which the wavefront sensor's lenslet diameters are such that their images are not simply spots of light translated according to the local slope of the phase errors, but are instead an array of small, interfering speckle patterns.