The aliasing effect in the discrete Fourier transform inherent will impose a serious detrimental effect on conventional phase retrieval measurement accuracy with under-sampled intensity. In this Letter, we describe a modal-based nonlinear optimization phase retrieval approach that is capable of retrieving wavefront measurements using under-sampled intensities. The extended Nijboer–Zernike theory is introduced to establish an analytic solution between wavefront phase and intensity image, and then nonlinear optimization is further utilized to solve wavefront aberration coefficients from under-sampled intensity data. The feasibility and accuracy of the algorithm are verified by simulations and experiments. This is a promising method that is especially suitable for full field phase recovery of optical systems with a relatively high numerical aperture.

中文翻译：

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基于模态的欠采样数据波前测量非线性优化算法

离散傅里叶变换固有的混叠效应将严重影响具有欠采样强度的常规相位恢复测量精度。在这封信中，我们描述了一种基于模态的非线性优化相位检索方法，该方法能够使用欠采样强度来检索波前测量值。引入扩展的Nijboer–Zernike理论来建立波前相位和强度图像之间的解析解，然后进一步利用非线性优化从欠采样强度数据中求解波前像差系数。通过仿真和实验验证了该算法的可行性和准确性。这是一种有前途的方法，特别适用于具有相对较高数值孔径的光学系统的全场相位恢复。