Estimation-Theoretic Approach to the Deconvolution of Atmospherically Degraded Images With Wavefront

ABSTRACT Deconvolution from wavefront sensing (or self-referenced speckle holography) has previously beenproposed 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 processingthe image and wavefront-sensor data in which the method of maximum-likelihood estimation is usedto simultaneously estimate the object intensity and phase errors directly from the detected imagesand wavefront-sensor data. This technique is demonstrated to work well in a situation for which thewavefront sensor's lenslet diameters are such that their images are not simply spots of light translatedaccording to the local slope of the phase errors, but are instead an array of small, interfering speckle l)atterfls. 1 INTRODUCTION The Potential light-gathering and resolving powers of a telescope become greater as the size of itsaperture increases. However, if the telescope is used to view objects through a randomly inhomoge-neous medium such as the Earth's turbulent atmosphere, the resolving power of the telescope can beseverely reduced. For example, a telescope with an aperture whose diameter is 6 m can have its re-solving power degraded by a factor of 30 when used to form long-exposure images through moderateturbulence. This loss of resolution is a result of time-varying phase errors that corrupt the incomingoptical field. Without some form of correction, these turbulence-induced phase errors can severelyliniit the resolving power of any telescope, but with correction, the resolving power can be restored.Over the past twenty-five years, a variety of imaging techniques has been proposed to overcomethe effects of atmospheric turbulence. All of these techniques rely on the fac.t that short exposure