针对超精密运动台的二维亚微米级精度同步测量需求，提出并建立了平面反射式二维光栅测量系统，研究了平面反射式二维光栅的平面位移同步测量方法，分析了平面反射式二维光栅测量系统的误差传递模型。通过Vold-Kalman滤波算法，对光栅信号中存在的高次谐波误差、幅值/相位误差进行实时修正和滤除。采用反正切细分算法和周期测量法对光栅正交脉冲的频率进行测量，实现对被测目标的高分辨率测量和实时运动速度测量。同时，构建了亚微米级测量精度的平面反射式二维光栅测量系统，测量范围为500 mm×500 mm，x、y方向的定位精度为±0.3 μm，测量分辨率为0.005 μm。

Aiming at the requirement of two-dimensional sub-micron precision synchronous measurement for ultra-precision motion stage, a reflective two-dimensional grating measurement system is proposed and established. The synchronous measurement method of plane displacement of reflective two-dimensional grating is investigated, and an error transfer model of reflective two-dimensional grating measurement system is established. Through Vold-Kalman filtering algorithm, the high-order harmonic error and amplitude/phase error in the grating signal are corrected and filtered in real time. An arc-tangent subdivision algorithm and period measurement method are used to measure the frequency of the orthogonal pulse of the grating to realize the high-resolution measurement and real-time speed measurement. A reflective two-dimensional grating measurement system with sub-micron measurement accuracy is constructed, in the measurement range of 500 mm×500 mm, the positioning accuracy of the x-direction and y-direction is ±0.3 μm and the resolution is 0.005 μm.