The method of phase diversity consists of making two measurements of the image of an unknown extended object at two settings of focus and using these images in a certain least squares error metric to estimate the wave aberration function of an incoherent optical imaging system. In this proposal this concept is generalized to include other methods of introducing "diversity" through the introduction of known perturbations in the systems coherent transfer function (CTF). The resulting method, which includes the usual method of phase diversity as a special case, is called the method of generalized phase diversity. It is proposed to use the method of generalized phase diversity to estimate the "state" of a phased array telescope for the purpose of either correcting (realigning) the elements of the telescope or post processing imagery generated by the (misaligned) system to yield improved image quality. The research calls for an investigation into various schemes for introducing generalized phase diversity, the development of algorithms for estimating the state of an optical system using this method, and the test and evaluation of the developed algorithms in a computer simulation study.
