Optimum defocus diversity in phase diversity wave-front sensing using Cramér-Rao theorem

Phase diversity wave-front sensing(PDWFS) is a method for estimating wave-front aberrations from two (or more) images whose pupil phases differ from one another with a known diversity phase. It can be used to estimate wave-front for point source as well as extended source. The accuracy of the estimate is relied on the diversity phase and is always given quantitatively in Cramér-Rao theorem. With defocus is used as the diversity mode, the effect of the object and the aberration on the optimum defocus is studied using Cramér-Rao theorem in this paper when the photons is enough. The results show that the optimum defocus does not depend on the peak-to-valley value or the spatial frequency of the aberration observably in the case of point source. For extended source, although the optimum defo