基于无衍射光莫尔条纹大行程工作台运动误差测量方法研究

Precision long travel stage plays an important role in modern industry and scientific research field. However the inevitable motion errors of the stage directly determine the accuracy of the manufacture and measurement. The nondiffracting beam can keep the same form in a long rang, and Moiré fringe can improve measurement accuracy with its amplification characteristic. The aim of this project is to research a technique to measure the multi-dimension motion errors of long travel stage real-time by combining the advantages of nondiffracting beam and Moiré fringe. An axicon is used to produce long distance nondiffracting beams which are used to produce Moiré fringe after split and combined. A motion unit, composed of a half transparent and half reflecting mirror and a rectangular prism, fixed with the stage, is put into the optical path, and its pose can express the errors such as: vertical straightness, pitching angles, deflection angles and roll angles of the stage. The Mathematical models between the pose of the motion unit and optical path direction are presented with vector technique, and the theoretic relationship of between the optical path direction and the Moiré fringe is discussed as well. The error types and values are roughly identified by the center positions of nondiffracting beams captured by CCDs, and precise values of the errors are calculated by the accurate center positions of two nondiffracting beams in one of CCDs, which are deduced by counting the number of Moiré fringe. The project has the advantages of wide range, high precision, low cost and simple structure.

大行程超精密工作台在近代尖端工业生产和科学研究领域内占有极为重要的地位，其运动误差将直接决定加工和测量精度。本课题拟结合无衍射光长距离恒稳定的优点与莫尔条纹放大的特性，研究一种大行程、高精度的实时多自由度运动误差测量方法。其具体思路是以轴锥镜作为无衍射光产生元件，两束无衍射光经分光、合束后产生莫尔条纹；以半透半反镜和直角棱镜组成运动单元固定在工作台上，利用其姿态的变化感知工作台的垂直直线度、俯仰角、偏摆角和滚转角；根据矢量方法建立运动单元姿态与多自由度误差之间的数学模型，并进一步推导光路方向与莫尔条纹形状之间的理论关系；在利用双CCD中无衍射光中心点位置识别各误差和粗计算基础上，再通过对其中一个CCD中无衍射光莫尔条纹数量的变化得到中心点的精确位置，进而计算出各运动误差的实际大小。本项目研究的方法具有测量范围大、精度高、结构简单、成本低的特点。

研究大行程精密工作台的运动误差具有重要的意义，高精度多自由运动误差测量方法能有效提高加工或测量精度。本课题结合无衍射光长距离恒稳定的优点与莫尔条纹放大的特性，提出了一种大行程、高精度的实时多自由度运动误差测量方法，能够同时测量垂直直线度、俯仰角、偏摆角和滚转角四种运动误差。该方法以轴锥镜作为无衍射光产生元件，由分光棱镜产生两束无衍射光，这两束光经分光、合束后产生莫尔条纹；以半透半反镜和直角棱镜组成测量单元固定在工作台上，利用其姿态的变化感知工作台的垂直直线度、俯仰角、偏摆角和滚转角四种运动误差。根据光束传播的矢量方法建立了多自由度误差与无衍射光图像之间的数学模型，并进一步推导了无衍射光中心光斑位置与运动误差类型的对应关系。利用光学软件ZEMAX建立了多自由度测量模型，并仿真了不同运动误差对应的无衍射光莫尔条纹的图像。在分析单束无衍射光和无衍射光莫尔条纹特性的基础上，利用Hough变换、最小二乘法、傅里叶变换、坐标变换等数字图像处理方法，得到无衍射光莫尔条纹数量的变化得到中心点的精确位置，根据误差类型与无衍射光中心光斑的理论关系，实现运动误差的分解，进而计算出各运动误差的实际大小。通过对转台和直线导轨的运动误差测量，验证了该方法的应用价值。本项目研究的方法对工作台多自由运动误差的测量提供了一种新的方法，同时对无衍射光莫尔条纹的处理提供了有益的参考。