Zernike expansion is an important tool for aberration retrieval in the optical field. The Zernike coefficients in the expansion can be solved in a linear system from those focal region intensity images, which can be modeled by the extended Nijboer–Zernike approach. Here we point out that those coefficients usually follow from different prior distributions, and especially, their variances could be dramatically diverse. To incorporate the prior information, we further introduce customized penalties to those Zernike coefficients and adopt a global adaptive generative adjustment algorithm for estimating coefficients. Based on both simulated and real data, numerical experiments show that our method outperforms other conventional methods, and provides an estimate of Zernike coefficients with a low mean square error.

Zernike扩展是光学领域中像差检索的重要工具。扩展中的Zernike系数可以在线性系统中从那些焦点区域强度图像中求解，可以通过扩展的Nijboer-Zernike方法建模。在这里，我们指出，这些系数通常来自不同的先验分布，尤其是它们的方差可能会大大不同。为了合并现有信息，我们进一步对这些Zernike系数引入了定制的惩罚，并采用全局自适应生成调整算法来估计系数。基于模拟和实际数据，数值实验表明我们的方法优于其他常规方法，并提供了均方误差低的Zernike系数估计。