基于经验模态分解-Wigner分布的光学元件中频误差识别

Mid-spatial frequency error identification of precision optical surface based on empirical mode decomposition-Wigner-Ville distribution

对于大尺寸高精密光学元件,不仅要对光学元件表面低频面形精度和高频粗糙度进行控制,还需要严格限制中频误差,以保证其使用性能和稳定性.为了确定光学元件的不合格区域并指导其返修,引入经验模态分解（EMD）和Wigner分布（WVD）函数方法,通过理论分析确定该方法与功率谱密度函数间的关系,实现对光学元件表面中频误差的辨识与定位.实验结果表明：EMDWVD方法不仅可以识别分布在实验光学元件表面15～27 mm空间频率为0.1mm-1的中频误差,还可以减小多分量信号所引起的空间频率为1.0～1.5 mm-1的交叉项干扰,提高中频误差辨识的准确率.

The mid-spatial frequency error of high precision optical surface is crucial to the performance of high-energy laser system.To assure the performance and stability of the system,the low frequency error and high frequency error of the optical lens surface must be strictly controlled,the mid-spatial frequency error must also be strictly limited.In this paper,the relationship between empirical mode decomposition-Wigner-Ville distribution(EMD-WVD)method and power spectrum density is analyzed,and EMD-WVD diagnosis method is applied to identifying and locating the mid-spatial frequency error of the precision optical surface. The experimental results show that,with EMD-WVD method,the mid-spatial frequency error distribution of optical surface can be located in 15-27mm and the spatial frequency is 0.1mm-1,the interference of cross-term caused by multi-component signal whose spatial frequency is about 1.0-1.5mm-1 can also be reduced,which enhances the identification accuracy of mid-spatial frequency error.