Dong Zhichao, Cheng Haobo, Tam Hon-Yuen
Appl Opt. 2015 Apr 1;54(10):2747-56. doi: 10.1364/AO.54.002747.
The linear equation dwell time model can translate the 2D convolution process of material removal during subaperture polishing into a more intuitional expression, and may provide relatively fast and reliable results. However, the accurate solution of this ill-posed equation is not so easy, and its practicability for a large scale surface error matrix is still limited. This study first solves this ill-posed equation by Tikhonov regularization and the least square QR decomposition (LSQR) method, and automatically determines an optional interval and a typical value for the damped factor of regularization, which are dependent on the peak removal rate of tool influence functions. Then, a constrained LSQR method is presented to increase the robustness of the damped factor, which can provide more consistent dwell time maps than traditional LSQR. Finally, a matrix segmentation and stitching method is used to cope with large scale surface error matrices. Using these proposed methods, the linear equation model becomes more reliable and efficient in practical engineering.
线性方程驻留时间模型可以将子孔径抛光过程中材料去除的二维卷积过程转化为更直观的表达式，并可能提供相对快速和可靠的结果。然而，这个不适定方程的精确解并非易事，其对于大规模表面误差矩阵的实用性仍然有限。本研究首先通过蒂霍诺夫正则化和最小二乘QR分解（LSQR）方法求解这个不适定方程，并自动确定正则化阻尼因子的可选区间和典型值，它们取决于刀具影响函数的峰值去除率。然后，提出了一种约束LSQR方法来提高阻尼因子的鲁棒性，与传统LSQR相比，它可以提供更一致的驻留时间图。最后，采用矩阵分割和拼接方法来处理大规模表面误差矩阵。使用这些提出的方法，线性方程模型在实际工程中变得更加可靠和高效。
