二维光栅尺可同时测量平面内两个维度的位移，结构紧凑。与激光干涉仪相比，抗干扰性好，成本较低；与用两个一维光栅尺测量平面位移相比，能够减小因入射点不一致引起的阿贝误差，消除两维度安装不垂直的影响。随着平面电动机的出现，用二维光栅尺测量平面位移在精密加工、纳米测量等领域显现出较强的应用前景。二维光栅的制造误差是二维光栅尺的主要系统误差来源之一，通过标定二维光栅可以补偿二维光栅尺的测量误差，提高测量精度。本论文针对二维光栅的两个主要参数，栅线垂直度和栅距均匀性的标定方法进行了研究。 二维光栅垂直度误差将使两维度位移测量互相不独立，引起测量误差。本论文提出的垂直度标定方法利用光栅不同级次衍射光形成的干涉条纹来对准光栅绕其法线旋转的角位置。该方法通过绕法线旋转光栅，两次对准光栅周期方向，用自准直仪测量两次角位置间的小角度夹角，直接测得二维光栅垂直度偏离角。实验测量了栅距1 m的二维光栅垂直度，结果标准不确定度优于0.28″（k = 1），测量结果与用光学衍射法测量的结果一致。 二维光栅栅距均匀性将造成位移测量结果中的非线性累积误差。本论文提出的方法结合激光干涉仪比对和衍射波面分析，利用两者优点，分离光栅尺的一些系统误差，达到快速、有效标定二维光栅尺测量误差的目的。本论文的研究内容包括：设计和制作对角度变化不敏感的外差型二维光栅尺读数系统，减小光栅尺读数头误差，提高用激光干涉仪比对光栅尺的精度；提出衡量激光干涉仪比对结果的自洽性评价标准，通过绕法线旋转光栅180°，比较旋转前后测量结果的一致性，判断系统是否存在除光栅制造误差外其它幅值较大的误差来源；设计和搭建满足自洽性评价标准的双轴激光干涉仪比对系统，并在实验中结合激光干涉仪比对结果和衍射波面信息，尝试分离光栅制造误差和移动台相关误差，有效提高二维光栅尺测量精度。 本论文提出的二维光栅尺标定方法可帮助光栅制造者得到位移测量用衍射光栅的制造容差，指导光栅尺安装者尽可能消除安装误差，让光栅尺使用者可以快速、低成本地对不同使用情况下的光栅尺进行再标定。

A planar grating encoder is able to measure two-dimensional displacements simultaneously. Compared to a laser interferometer, a planar grating encoder is more stable to environment turbulence and less expensive. Compared with using two linear encoders to measure planar displacements, using a planar grating encoder can reduce the Abbe error caused by multiple measuring points and remove the non-orthogonality error caused by installation of two linear encoders. With the development of planar motors, planar grating encoders have many applications in the fields of precision machining, nano-measurement, etc. The two-dimensional grating’s fabrication error is one of the main systematic error sources in planar encoder’s measurement results. The planar encoder’s accuracy can be improved by calibrating the two-dimensional grating and compensating the measurement errors. This dissertation focuses on the research of calibration method of two-dimensional grating’s orthogonality and pitch uniformity, which are two key parameters of two-dimensional gratings. Two-dimensional grating’s orthogonality error makes cross-talk errors since the two-dimensional displacement measurements are not independent with each other anymore. This dissertation proposes an orthogonality calibration method, which utilizes the interference fringes generated by diffracted beams of different orders to align the grating’s angular position around its normal. In the method, the grating is rotated around its normal, whose periodic directions are aligned twice. The small angle between these two angular positions is measured with an auto-collimator, and the non-orthogonality angle of the two-dimensional grating is measured directly. Orthogonalities of 1m-pitch two-dimensional gratings are measured, and the standard uncertainty is better than 0.28″ (k = 1). The results agree well with the measurement results of optical diffractometry. Two-dimensional grating’s pitch uniformity causes non-linear errors in the planar encoder’s measurement results. The calibration method presented in this dissertation combines two calibration approaches, one of which is comparing the grating encoder’s measurement results with those of a two-axis laser interferometer, and another one is analyzing the grating’s diffracted wavefront data to get the pitch deviations. With the advantages of these two approaches, this method can separate some systematic errors and calibrate the planar encoder effectively and efficiently. In this dissertation, we design and assemble a heterodyne planar grating encoder with insensitivity to grating tilts, to reduce the planar encoder’s errors and improve the accuracy of laser interferometer comparator’s results. We propose a self-consistency requirement to judge the laser interferometer comparator’s results, in which by rotating the grating around its normal for 180 degrees and checking the consistency of measurement results before and after rotation, one can tell whether the measurement system has any big error sources besides the grating fabrication errors. We design and set up a two-axis laser interferometer comparator, whose results fulfill the self-consistency requirement. The laser interferometer comparator’s results are combined with diffracted wavefront data to separate the grating fabrication errors and stage related errors. The calibration improves the planar encoder’s accuracy effectively in the experiments. The planar encoder calibration method proposed in this dissertation will help a grating maker to know the grating fabrication requirement, assist a grating encoder setter to minimize the setup errors, and provide a planar encoder user with a fast and low-cost method to re-calibrate the planar grating encoder in different conditions.