六自由度(6-DOF)超精密位移测量技术是实现光刻机工件台运动精度的关键技术之一，对光刻机性能的实现具有重要作用。本文以光刻机硅片台为应用对象，从硅片台运动系统对位移测量系统的需求出发，提出一种基于光栅干涉仪的6-DOF位移测量方法，在光栅干涉仪测量模型、测量布局、位移解算算法、读数头切换误差等几个方面开展了深入的研究。 在光栅干涉仪位移测量模型方面，本文详细分析运动台的6-DOF位移对光栅干涉仪中衍射光束干涉信号产生的影响，在此基础上提出了改进的测量表达式。基于光栅测量原理及运动学建模方法，建立了两轴光栅干涉仪的位移测量模型，为后续的测量方案设计、位移解算提供基础，该模型适用于大多数采用一次衍射方案的光栅干涉仪。结合实验室现有条件，通过仿真和3-DOF运动台实验验证了测量模型的合理性。 本文从硅片台的测量需求出发并考虑运动台结构以及平面光栅尺寸方面的限制，设计了一种典型的6-DOF光栅测量系统的布局方案。针对该方案，从提高位移解算精度及解算速度的角度出发，提出了一种将近似封闭解和数值迭代法相结合的6-DOF位移解算算法。该算法选择由近似封闭算法得到的粗解作为迭代初值代入方程组中进行求解，有效地结合了近似封闭算法的快速性以及迭代运算的高精度的特点，可以实现快速收敛并得到高精度的位移解。仿真结果显示，当设定收敛精度为10-9时，转动位移的解算误差在10-15 rad量级以下，平动位移的解算误差为10-16m量级以下；对于大多数位姿状态，该算法只需要一步迭代即可达到所设定的精度要求。 读数头切换误差是光栅测量系统中的一个重要的理论与应用问题。本文分别针对单自由度和多自由度位移测量系统详细地分析了传感器的切换过程及切换误差产生的原因，在此基础上，提出了一种利用冗余测量数据减小切换误差的方法。具体而言，即充分利用两个读数头同时测量过程中的大量的测量数据，对待切换的读数头进行初始化，降低切换误差对测量精度的影响。理论推导及仿真结果表明，相较于传统的方法，该初始化方法大大降低了传感器的初始化常数中的误差，即使存在多次切换操作时，各传感器的初始化常数中的误差也远小于传感器自身的测量误差。

Six-degree-of-freedom (6-DOF) ultra-precision displacement measurement technology is one of the key technologies to ensure dynamic positioning accuracy of wafer stage, and it plays an important role to realize the performance of lithographic equipment. Taking wafer stage as the application background and from the perspective of wafer stage’s requirements, this thesis focused on the grating-based 6-DOF displacements measurement method and carried out in-depth research in the measurement model of grating interferometer, layout of measurement system, computational algorithm and switching error of sensor head. In terms of the measurement model of the grating interferometer, the influence of wafer stage’s 6-DOF movement on the measurement of the grating interferometer was analyzed in this thesis. A modified measurement expression was proposed by considering these influence on the interference signals of the diffraction beams. Based on the modified measurement expression and the kinematic modeling theory, the measurement model of the two-axis grating interferometer was established, which was the basis for design of the measurement layout and displacement computation. The established model was suitable for most grating interferometers that had one-time diffraction structure. Considering the restriction of equipments in the laboratory, a 3-DOF motion stage was developed, and the results validated the availability of the proposed measurement model. By considering the measurement requirement of the wafer stage and the constraints of the structure of wafer stage and the size of planar grating, a typical layout of 6-DOF grating-based measurement system was designed. From the perspective of improving the computational accuracy and computational speed, a algorithm combining of the approximate closed solution and the Newton iterative method was proposed. To improve the convergence rate of the iteration, the approximate closed solution derived from the approximate closed algorithm, which was close to the optimal value, was set as the initial value of the iteration. This solving strategy combined with the advantages of the high solving rate of the approximate closed algorithm and the high accuracy of the iterative method. The simulation result showed that, when the convergence precision was set as 10-9, the computational errors of the rotational displacements and the translational displacements were reduced to 10-15 rad and 10-16 m and below, respectively. In addition, for most position and posture of the stage, the required precision could be achieved by one step of iterative computation. Switching problem in grating-based measurement systems was an important theoretical and practical problem. The switching procedure of the sensor and the causes of the switching error in single-DOF and multi-DOF displacement measurement systems were analyzed respectively. On this basis, a method utilizing redundant measurement data to reduce the switching error was proposed. Specifically, the initialization constant of each sensor to be used is derived by analyzing the numerous measurement data of the adjacent sensors over an extended period and was used for the switching operations. Theoretical analysis and simulation results showed that, Compared with the conventional method, the proposed method could effectively reduce the accumulative errors in the initialization constants of each sensor. In addition, even if there were large numbers of switching operations, the error in the initialization constant of each sensor was much less than its measurement error.