基于角锥棱镜的激光干涉位移测量误差分析

Error analysis of laser interferometric displacement measurement based on cube-corner prism

摘要:

基于光线矢量方法和角锥棱镜光学特性，推导角锥棱镜姿态角、直线运动自由度、余弦误差以及阿贝误差对激光干涉位移测量影响的数学表达式，并使用RENISHAW XL80激光干涉仪搭建测量光路，开展相关测量实验。结果表明：姿态角对干涉位移测量的影响通常不超过0.1um；当角锥存在直线自由度误差时，返回测量光束的光斑中心会产生与水平或垂直直线度方向一致的平移，但不会引入几何位移测量误差；推导给出角锥棱镜测量光束的回光偏移量与余弦误差之间的关系，阿贝误差与阿贝臂值和角锥棱镜偏摆角之间的关系。干涉位移测量实验表明，通过修正阿贝误差，可以有效提高位移测量精度。研究结果建立了基于角锥棱镜进行干涉位移测量的误差分析方法，为干涉位移测量的误差补偿提供依据。

Abstract:

Based on ray vector and optical characteristics of the cube-corner prism, mathematical expressions of the laser interferential displacement measurement affected by attitude angle of cube-corner, straightness, cosine error and Abbe error are derived. RENISHAW XL80 laser interferometer is used to build the optical measurement path and corresponding verification experiments are carried out. The results show that the error of interferential displacement measurement produced by the attitude angle normally does not exceed 0.1um; When straightness freedom error of the cube-corner occurs, the central positon of the returned measurement beam will produce a translation which corresponds with the horizontal or vertical straightness direction, but geometric displacement measurement error will not be introduced. The relevance between the offset of returned measurement beam of the cube-corner prism and the cosine error is derived, the relevance between the Abbe error and the Abbe arm value as well as yaw of the cube-corner prism is also presented. The experiment of interferential displacement measurement indicates that the displacement measurement accuracy can be effectively enhanced through correcting the Abbe error. Results of the research establish an analytical error method based on the cube-corner for interferential displacement measurement, which also provide a basis for the error compensation of interferential displacement measurement.