We present an efficient phase retrieval approach for imaging systems with high numerical aperture based on the vectorial model of the point spread function. The algorithm is in the class of alternating minimization methods and can be adjusted for applications with either known or unknown amplitude of the field in the pupil. The algorithm outperforms existing solutions for high-numerical-aperture phase retrieval: (1) the generalization of the method of Hanser et al., based on extension of the scalar diffraction theory by representing the out-of-focus diversity applied to the image by a spherical cap, and (2) the method of Braat et al., which assumes through the use of extended Nijboer-Zernike expansion the phase to be smooth. The former is limited in terms of accuracy due to model deviations, while the latter is of high computational complexity and excludes phase retrieval problems where the phase is discontinuous or sparse. Extensive numerical results demonstrate the efficiency, robustness, and practicability of the proposed algorithm in various practically relevant simulations.

中文翻译：

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基于点扩展函数矢量模型的相位检索。

我们基于点扩展函数的矢量模型，为具有高数值孔径的成像系统提出了一种有效的相位检索方法。该算法属于交替最小化方法，可以针对瞳孔中视场已知或未知的应用进行调整。该算法优于现有的用于高数值孔径相位检索的解决方案：（1）Hanser等人方法的推广，它基于标量衍射理论的扩展，通过表示（2）Braat等人的方法，该方法假设通过使用扩展的Nijboer-Zernike展开来使相位平滑。前者由于模型偏差而在准确性方面受到限制，而后者具有很高的计算复杂度，并且排除了相位不连续或稀疏的相位检索问题。大量的数值结果证明了该算法在各种实际相关的仿真中的效率，鲁棒性和实用性。