Zhang Yongfeng, Wang Shengqian, Xian Hao, Rao Changhui
Opt Lett. 2022 Mar 15;47(6):1466-1469. doi: 10.1364/OL.452352.
The Shack-Hartmann wavefront sensor (SH-WFS) is widely used as a slope-based wavefront sensing device. The modal method is favored for wavefront reconstruction from SH-WFS output because of its excellent performance. In this case, the calibration of modal (commonly Zernike modes) slope is required in advance. Traditional numerical or symbolic integral-based methods are not satisfactory because of their low accuracy or efficiency, particularly when an extremely large number of microlenses are involved. In this Letter, a novel method based on matrix product is proposed in which two key matrix operators are utilized. The first, namely the derivative matrix operator, is used to obtain the derivative of the Zernike modes; the second, that is, the transformation matrix operator, is then used to map the Zernike derivative defined in the original, whole circular pupil into modes defined in a scaled, translated circle pupil enveloping a specific microlens. With these two operators, the evaluation of slope response of Zernike modes could be unified into a matrix-product framework, which contributes its high efficiency. Numerical simulations show the superior advantages of the proposed method in accuracy and efficiency over traditional ones.
夏克-哈特曼波前传感器（SH-WFS）作为一种基于斜率的波前传感装置被广泛应用。模态法因其出色的性能而在从SH-WFS输出进行波前重构时受到青睐。在这种情况下，需要预先对模态（通常是泽尼克模态）斜率进行校准。传统的基于数值或符号积分的方法由于其精度低或效率低而不尽人意，特别是当涉及极大量微透镜时。在本信函中，提出了一种基于矩阵乘积的新方法，其中利用了两个关键矩阵算子。第一个，即导数矩阵算子，用于获得泽尼克模态的导数；第二个，即变换矩阵算子，随后用于将在原始的整个圆形光瞳中定义的泽尼克导数映射到包围特定微透镜的缩放、平移圆形光瞳中定义的模态。通过这两个算子，泽尼克模态斜率响应的评估可以统一到一个矩阵乘积框架中，这使其具有高效率。数值模拟表明，所提出的方法在精度和效率方面优于传统方法。
