工作空间测量定位系统是一种采用光平面交汇原理的大尺寸坐标测量系统, 测量过程中发现扫描光面并不是理想平面, 影响了测量精度。提出了一种思路: 利用二次曲面方程来描述扫描光面。运用线性最小二乘法对扫描光面上的离散点进行拟合, 得到二次曲面方程, 在正交线性变换的基础上, 分析了扫描光面的形状。对同一组测量点数据分别用二次曲面和平面进行拟合, 将拟合的效果进行比较, 结果表明: 利用抛物柱面方程能够更准确地描述扫描光面。

Workspace measuring and positioning system is a type of large-size measurement system based on intersection of optical planes. Optical surface was discovered a non-planar face while measuring, which influenced the measuring accuracy of the system. We presented a method of describing optical surface by using ternary quadratic equation. Ternary quadratic equation could be obtained by fitting the discrete points on the optical surface with the method of linear least square. Based on the ternary quadratic equation and orthogonal linearity transformation, we analyzed the shape of the optical surface. By using the method of quadric surface fitting and plane fitting, respectively, with the same group of data, then comparing the results, we draw the conclusion that it’s more accurate to describe the scanning optical surface with parabolic cylinder equation.