基于修正Levenberg-Marquardt算法的非球面面形误差校正

Aspheric Surface Shape Error Correction Based on Modified Levenberg-Marquardt Algorithm

随着光学非球面行业的快速发展,生产面形精度优于0.1μm的非球面镜片产品已成为趋势。在非球面镜片的面形检测中,由于存在机械系统误差,被检测工件的坐标存在6个自由度的偏差,这将直接影响非球面的面形测量精度。因此,针对检测系统,需要开发不确定度只有几十纳米的误差校正算法,以保证测量结果更贴近实际。通过数据仿真,在理想非球面的基础上叠加位置误差和面形误差以获得非球面原始三维数据,进而利用修正后的Levenberg-Marquardt全局优化算法,将所获原始三维数据与非球面标准方程作对比,并利用均方根(RMS)误差最小原理,成功分离和校正了非球面的位置误差。针对4种不同规格型号的玻璃非球面镜片,通过将实验结果与商用非球面轮廓仪UA3P的测量结果作对比,得出高匹配的结果,二者的峰谷值之差小于5 nm,均方根相差约为0.1 nm,结果验证了算法的准确性和稳健性。

With the rapid development of the optical aspheric surface industry, it has become a trend to produce aspheric lens products with a surface shape accuracy better than 0.1 μm. In the surface shape detection of the aspheric lens, due to the existence of mechanical system error, the coordinates of the detected workpiece have a deviation of 6 degrees of freedom, which will directly affect the measurement accuracy of the aspheric surface. Therefore, we need to develop an error correction algorithm with an uncertainty of only tens of nanometers for the detection system to ensure that the measurement results are closer to reality. In view of this, this paper uses data simulation to superimpose the position error and the surface shape error on the ideal aspheric surface to obtain the original three-dimensional(3 D) data of the aspheric surface, and then use the revised Levenberg-Marquardt global optimization algorithm to compare the obtained original 3 D data with the standard equation of aspheric surface. The principle of minimum root mean square error is used to successfully separate and correct the position error of the aspheric surface. Finally, for four glass aspheric lenses of different specifications and models, through comparing the experimental results and measurement results of the commercial aspheric profiler UA3 P, a high matching result is obtained. The difference in peak-valley values is less than 5 nm, and the difference in RMS is about 0.1 nm, which verify the accuracy and robustness of the algorithm.