利用Cramér-Rao理论研究相位差法的最佳离焦量

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

针对光子数足够多的情况,利用Cramér-Rao理论研究了在选取离焦作为附加像差时,不同的待测波前和目标对最佳离焦量选取的影响。结果表明:在点目标情况下,像差的大小和空间频率对最佳离焦量的影响不大;而在扩展目标情况下,最佳离焦量虽然与待测像差的空间频率关系不明显,但随着待测像差峰谷值的增大而增大。最佳离焦量与目标的结构有关而与其扩展程度关系不大,成像时目标上各点的干扰越大,最佳离焦量越大。

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 defocus does not depend on the spatial frequency of the aberration,it increases as the aberration increases.Besides,the optimum defocus depends on the structure of the object instead of the extent.In the imaging process,when the crosstalk of each point of the object increases,the optimum defocus should be larger.