Fisher-information-based analysis of a phase-diversity-speckle imaging system

The question of just how much to defocus the second image in the conventional two-channel phase-diversity speckle imaging technique may be addressed in a number of ways. Fisher information furnishes a useful metric for optimizing the choice of defocus as a functional of the object class, operating conditions, and the imaging task. Approximate closed-form expressions for the Fisher information relative to object parameters, rather than the pupil phase, are derived and discussed for phase-diversity-speckle imaging under conditions of strong turbulence and additive Gaussian noise. As an application of our general information-theoretic approach, the optimization of defocus when the imaging task is to estimate the midfrequency power spectrum of the object is discussed.