超精密掩模台位置测量系统算法优化

Algorithm optimization for ultra-precision position measurement system of reticle stage

基于掩模台平面光栅尺的位置算法是多元非线性隐函数方程组,针对其解算较困难的问题,工程上常使用迭代法进行数值解算。但随着掩模台扫描速度的提高,迭代法解算会使位置算法引入较大的迭代误差。开展了掩模台位置解算算法对比实验,并设计了位置模型补偿算法。实验结果表明:在10 kHz的采样频率和2.8 m/s的扫描速度条件下,X,Y和Rz的解算误差分别减少到5.877E-11m,8.617E-11m和5.316E-11rad及以下。

The position algorithm based on the reticle plane grating scale is a multivariate nonlinear implicit func-tion equation group.For the problem that its solution is difficult,the iterative method is often used for numerical solu-tion in engineering.However,as the scanning speed of the reticle stage increases,the iterative method solves the posi-tion algorithm and introduces a large iteration error.The comparison experiment of the reticle stage solving algorithm is carried out,and the position model compensation algorithm is designed.The experimental results show that the solution errors of X,Y and Rz are reduced to 5.877E-11 m,8.617 E-11m and 5.316 E-11rad and below,respectively,under the sampling frequency of 10 KHz and the scanning speed of 2.8 m/s.