非球面光学元件在光学系统中的应用日益广泛。非球面点云数据调平坐标变换是非球面检测系统误差分析的一个重要环节。提出了一种基于Zernike多项式拟合的非球面点云数据自动调平方法, 通过计算Zernike多项式X和Y倾斜项系数确定调平旋转矩阵, 通过迭代使其最小化, 最终将点云数据回转轴调整至与坐标Z轴平行, 使得非球面三维点云测量结果可以进行后续三维比对和截面误差分析。通过理论仿真和实验数据测试验证了方法的有效性, 能够将非球面数据倾斜降低到可忽略的程度; 方法计算过程简单, 对于各类非球面和曲面点云数据的调平变换都具有较好的参考意义。

Aspherical optical components are increasingly used in optical systems. The leveling coordinate transformation of aspherical point cloud data is an important part of the error analysis of the aspheric surface profiling system. An aspheric point cloud data automatic leveling method based on Zernike polynomial fitting is proposed. The Zernike polynomial X and Y tilt term coefficients are calculated to determine the leveling rotation matrix, which is minimized by iteration. Finally, the point cloud data rotation axis is adjusted to be parallel to the coordinate Z axis, so that the aspherical 3D point cloud measurement results can be used for subsequent 3D comparison and cross-section error analysis. The effectiveness of the proposed method is verified by theoretical simulation and experimental data tests, which can reduce the aspherical data tilt to a negligible degree. The calculation method of this method is simple, and it can be of good reference for the leveling transformation of all kinds of aspheric and curved point cloud data.