Guang Hui, Wang Yajun, Zhang Lianxin, Li Lulu, Li Ming, Ji Linhong
Appl Opt. 2017 Mar 10;56(8):2060-2067. doi: 10.1364/AO.56.002060.
Accurate wavefront integration based on gradient fields is crucial for various indirect measurement techniques, such as Shack-Hartmann sensing, shearography, and the fringe reflection technique. In this paper, a higher-order iterative compensation algorithm is proposed to enhance the reconstruction accuracy for the finite-difference-based least-squares integration (FLI) method. In this method, higher-order gradient fields are reconstructed and the calculated residual gradient fields compensate the truncation error with the traditional FLI by iterations. A comparison of different FLI methods, including traditional FLI, iterative FLI, higher-order FLI, and the proposed FLI method, is conducted. The result shows that the reconstructed wavefront with the proposed method is more accurate than those with other FLI methods. In addition, the impact of the gradient measurement noise is also discussed.
基于梯度场的精确波前积分对于各种间接测量技术至关重要，如夏克-哈特曼传感、剪切散斑干涉术和条纹反射技术。本文提出了一种高阶迭代补偿算法，以提高基于有限差分的最小二乘积分（FLI）方法的重建精度。在该方法中，重建高阶梯度场，计算得到的残余梯度场通过迭代补偿传统FLI方法的截断误差。对不同的FLI方法进行了比较，包括传统FLI、迭代FLI、高阶FLI和本文提出的FLI方法。结果表明，本文提出的方法重建的波前比其他FLI方法更精确。此外，还讨论了梯度测量噪声的影响。
