由于在环境扰动下具有比激光干涉仪更好的测量稳定性，光栅干涉仪成为浸没式光刻机中硅片台六自由度位移测量传感器的最佳选择。为了实现亚纳米精度的位移实时测量，位移解算及几何校准是硅片台光栅干涉仪系统亟需解决的重大问题。本文以浸没式光刻机硅片台的六自由度位移测量光栅干涉仪系统为研究对象，针对其位移解算的三大技术难题：位移解算模型的建立、模型几何参数的校准及模型的超精密实时求解算法展开系统深入的研究。针对六自由度位移时光栅干涉仪相移的转动平移耦合问题，提出了一种基于仿射变换逐点实现光束追迹的解析建模方法。基于该方法建立了干涉信号相移与读数头六自由度位移之间的精确函数关系，并结合泰勒级数展开将复杂的相移模型简化为多项式。基于刚体运动学建立了读数头平动位移的解析模型，并通过多项式拟合统一了光栅干涉仪相移模型和读数头位移模型中的转动位移描述，建立了硅片台光栅干涉仪系统的位移解算模型。针对光栅干涉仪系统的几何参数校准问题，通过分析硅片台光栅干涉仪系统理想位移解算模型中含有的几何参数及其潜在的误差来源，建立了考虑制造装配误差的位移解算模型。在保证校准精度的前提下对模型进行了简化，减少了待校准参数的数量。提出了基于冗余系统自洽性的模型参数自校准方法，结合光刻机中的外部参考进行分步自校准，提高计算效率的同时实现了光栅干涉仪系统向外部测量基准的对齐。分析了非理想情况下的自校准误差，建立了校准后位移解算模型精度与校准过程中非几何误差的关系，可作为自校准误差预算的依据。针对光栅干涉仪系统的位移解算算法问题，分析了线性化位移解算算法因忽略非线性项产生的误差，阐明了利用相移拟合多项式进行误差补偿的局限性。通过分析非线性误差的频域特征，提出了基于集结变量（Aggregate Variables）拟合多项式的位移解算算法，在满足硅片台位移解算精度的前提下，大幅提升了位移解算模型的求解效率。通过仿真验证了集结变量多项式位移解算算法的解算性能，通过实验验证了集结变量多项式位移解算算法在实际测量噪声下对位移解算模型精度的复现能力。

Since it has better measurement stability than the laser interferometer under environmental disturbances, the grating interferometer is the best choice of the six-degree-of-freedom （6-DOF） displacements measurement sensor for the wafer stage of immersion photolithography scanner. To achieve sub-nanometer precision real-time displacements measurement, displacements calculation and geometric calibration are the major issues to be addressed of the grating interferometer system for the wafer stage. In this paper, the grating interferometer system for the 6-DOF displacements measurement of the wafer stage of immersion photolithography scanner is taken as the research object, three major technical problems of the displacements calculation: the establishment of displacements calculation model, the calibration of geometric parameters and the ultraprecision real-time algorithm for solving the model, are systematically studied in depth.Aiming at the rotation-translation coupling of phase shift of grating interferometer when 6-DOF displacements occur, an analytical modeling method for beam tracing point by point based on affine transformation is proposed. Using this method, the precise and complex function relationship between the phase shift of the interference signal and the 6-DOF displacements of the readhead is established and reduced to a polynomial by Taylor series expansion. An analytical model of the translational displacements of the readhead is established based on the rigid body kinematics. After the rotation displacements descriptions in the grating interferometer phase shift model and the readhead displacements model are unified by polynomial fitting, the displacements calculation model of the wafer stage grating interferometer system is established.Aiming at the calibration of geometric parameters of the grating interferometer system, the displacements calculation model considering manufacturing and assembly errors is established by analyzing the geometric parameters and their potential error sources contained in the ideal displacements calculation model of wafer stage grating interferometer system. On the premise of ensuring the precision of calibration, the model is simplified to reduce the number of parameters to be calibrated. A self-calibration method for model parameters based on the self-consistency of a redundant system is proposed. By combining this method and external reference in the photolithography scanner, A step-by-step self-calibration improves the calculation efficiency and alignments the grating interferometer system to the external measuring basis. The self-calibration errors under non-ideal conditions is analyzed, and the relation between the precision of the calibrated displacements calculation model and the non-geometric errors in calibration is established, which can be used as the basis of the self-calibration error budget.Aiming at the displacements calculation algorithm of the grating interferometer system, the error of the linearized displacements algorithm due to ignoring nonlinear terms is analyzed, and the limitation of the error compensation method using phase shift fitting polynomial is explained. By analyzing the frequency-domain characteristics of the onlinear error, a displacements calculation algorithm based on the fitting polynomial of aggregate variables is proposed, and greatly improves the solving efficiency of the displacements calculation model while satisfying the displacements calculation precision of the wafer stage. The performance of displacements calculation algorithm based on the fitting polynomial of aggregate variables is verified by simulation, and the ability of the algorithm to reproduce the precision of displacements calculation model under actual measurement noise is verified by experiments.