首页 > 论文 > 光学学报 > 38卷 > 12期(pp:1212001--1)

基于最小二乘法的自校准位姿方案

Scheme for Position Self-Calibration Based on Least Square Method

  • 摘要
  • 论文信息
  • 参考文献
  • 被引情况
  • PDF全文
分享:

摘要

基于辅助测量装置中栅格板的不同位姿,构建了有关工作台误差和栅格板误差的数学模型。根据最小二乘原理将误差方程转化为正规方程。通过研究位姿方案对关系矩阵的秩的影响,归纳总结了位姿与自校准模型之间的规律。依据方程具备最小二乘解的条件,自校准过程中栅格板必须在初始位姿的基础上经过旋转90°及平移的位姿变换,并进行了仿真。研究结果表明,只有包含三种基本位姿的位姿方案才能使仿真计算值接近真实值,此基本三位姿是实现最小二乘法自校准的充分必要条件。

Abstract

A mathematical model related to stage errors and grid plate errors is constructed according to the different positions of grid plate in the auxiliary measuring device. Based on the least square principle, the error equation is converted into a regular equation. The influence of position scheme on the rank of a relation matrix is investigated to summarize the law between the position and the self-calibration model. With the the conditions that the equation need for the least square solution, in the self-calibration process, the grid plate must be rotated by 90° and simultaneously translated from its initial position, and this position transformation is also simulated. The research results show that it is only the position scheme containing three basic positions that makes the simulation result closer to the true value. These three basic positions are the necessary and sufficient conditions for the achievement of self-calibration by the least-squares method.

Newport宣传-MKS新实验室计划
补充资料

中图分类号:TH161.5

DOI:10.3788/aos201838.1212001

所属栏目:仪器,测量与计量

基金项目:国家重大科学仪器设备开发专项(2014YQ090709)、上海市科委基础研究重大科技项目(17JC1400804)

收稿日期:2018-06-13

修改稿日期:2018-07-07

网络出版日期:2018-07-25

作者单位    点击查看

乔潇悦:上海交通大学电子信息与电气工程学院仪器科学与工程系, 上海 200240
陈欣:上海交通大学电子信息与电气工程学院仪器科学与工程系, 上海 200240
丁国清:上海交通大学电子信息与电气工程学院仪器科学与工程系, 上海 200240
蔡潇雨:上海市计量测试技术研究院, 上海 201203
魏佳斯:上海市计量测试技术研究院, 上海 201203
李源:上海市计量测试技术研究院, 上海 201203

联系人作者:陈欣(xchen.ie@sjtu.edu.cn); 乔潇悦(xy1121@sjtu.edu.cn);

【1】Sun Y W, Li S G, Ye T C, et al. Process dependency of focusing and leveling measurement system in nanoscale lithography[J]. Acta Optica Sinica, 2016, 36(8): 0812001.
孙裕文, 李世光, 叶甜春, 等. 纳米光刻中调焦调平测量系统的工艺相关性[J]. 光学学报, 2016, 36(8): 0812001.

【2】Lu S, Yang K M, Zhu Y, et al. Design and control of ultra-precision fine positioning stage for scanning beam interference lithography[J]. Acta Optica Sinica, 2017, 37(10): 1012006.
鲁森, 杨开明, 朱煜, 等. 用于扫描干涉场曝光的超精密微动台设计与控制[J]. 光学学报, 2017, 37(10): 1012006.

【3】Kong W Q, Liu J N, Da F P, et al. Calibration method based on general imaging model for micro-object measurement system[J]. Acta Optica Sinica, 2016, 36(9): 0912003.
孔玮琦, 刘京南, 达飞鹏, 等. 基于一般成像模型的微小物体测量系统标定方法[J]. 光学学报, 2016, 36(9): 0912003.

【4】Raugh M R. Absolute two-dimensional sub-micron metrology for electron beam lithography[J]. Precision Engineering, 1985, 7(1): 3-13.

【5】Takac M T, Ye J, Raugh M R, et al. Self-calibration in two dimensions: The experiment[J]. Proceedings of SPIE, 1996, 2725: 130-146.

【6】Ye J, Takac M, Berglund C N, et al. An exact algorithm for self-calibration of two-dimensional precision metrology stages[J]. Precision Engineering, 1997, 20(1): 16-32.

【7】Ekberg P, Stiblert L, Mattsson L. A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines[J]. Measurement Science and Technology, 2014, 25(5): 055001.

【8】Zhu Y, Hu C X, Hu J C, et al. A transitive algorithm for self-calibration of two-dimensional ultra-precision stages[C]. IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 2011: 594-598.

【9】Chen X, Ding G Q, Takahashi S, et al. Self-calibration for two-dimensional stage using least squares solution[C]. The 10th International Symposium of Measurement Technology and Intelligent Instruments, 2011: 1-6.

【10】Ding G Q, Chen X, Wang L H, et al. Self-calibration method of two-dimensional grid plate[J]. Proceedings of SPIE, 2011, 8321: 83210Y.

【11】Guo T T, Wang X X, Hong B, et al. Self-calibration technology in measuring error separation of imaging instrument[J]. Optics and Precision Engineering, 2015, 23(1): 197-205.
郭天太, 王晓晓, 洪博, 等. 用于影像仪测量误差分离的自校准技术[J]. 光学 精密工程, 2015, 23(1): 197-205.

【12】Cui J W, Liu X M, Tan J B. Self-calibration for 2-D ultra-precision stage[J]. Optics and Precision Engineering, 2012, 20(9): 1960-1966.
崔继文, 刘雪明, 谭久彬. 超精密级二维工作台的自标定[J]. 光学 精密工程, 2012, 20(9): 1960-1966.

【13】Fei Y T. Error theory and data processing[M]. Beijing: China Machine Press, 2010: 105-108.
费业泰. 误差理论与数据处理[M]. 北京: 机械工业出版社, 2010: 105-108.

引用该论文

Qiao Xiaoyue,Chen Xin,Ding Guoqing,Cai Xiaoyu,Wei Jiasi,Li Yuan. Scheme for Position Self-Calibration Based on Least Square Method[J]. Acta Optica Sinica, 2018, 38(12): 1212001

乔潇悦,陈欣,丁国清,蔡潇雨,魏佳斯,李源. 基于最小二乘法的自校准位姿方案[J]. 光学学报, 2018, 38(12): 1212001

您的浏览器不支持PDF插件,请使用最新的(Chrome/Fire Fox等)浏览器.或者您还可以点击此处下载该论文PDF