基于经验模态分解的精密光学表面中频误差识别方法

Mid-spatial Frequency Error Identification of Precision Optical Surface Based on Empirical Mode Decomposition

对于高端光学元件,除限制低频面形误差和高频表面粗糙度之外,需要严格控制中频误差,以确保其使用性能。目前国际上广泛采用功率谱密度(Power spectral density,PSD)曲线评价中频误差,该方法以Fourier变换为基础,在全局水平上给出中频误差的综合评价。但是,光学元件磨削与抛光工艺过程中,局部波动和变周期波动是常见的中频误差存在形式。为更加准确地评价中频误差,指导补偿加工,需要识别中频误差频率及位置信息。鉴于此,从光学表面属于非平稳空间信号的角度出发,提出基于经验模态分解的精密光学表面中频误差提取和识别方法,对光学表面拟合残差进行经验模态分解,得到一系列固有模态函数,根据各阶固有模态函数特征,识别不同空间位置存在的表面误差和波动频率,并将其合成得到光学表面的中频和高频误差。仿真与实际检测结果分析证实该方法可以有效识别中频误差特征及其方位。

Mid-spatial frequency surface error of optical lens is crucial to the performance of high-energy laser systems and high-resolution optical systems. Power spectrum density （PSD） is generally employed to evaluate mid-spatial frequency error of optical surface. PSD is based on Fourier transform which averages local characters to the whole space. And it gives a whole evaluation of mid-spatial frequency error of optical surface. It not only weakens characters but also loses location information of surface error. Abrasive processing, such as grinding and polishing, always introduces local waviness with time-varying frequency on optical lens surface, PSD fails for this situation. A new error separation method, which is based on empirical mode decomposition, is introduced in this paper in order to more accurately evaluate mid-spatial frequency error and guide compensation machining. Curve of optical surface is preliminary fitted and the difference between the origin data and the fitting curve is decomposed to a series of intrinsic mode functions （IMFs）. Local waviness characters of optical lens surface and its frequency can be recognized from each IMF and the corresponding instantaneous frequency plot. All IMFs are divided into high-frequency group and mid-spatial frequency group by average of instantaneous frequency of each IMF considering with IMF characters. IMFs in the same group are added to acquire high-frequency error or mid-spatial frequency error of optical surface. The simulation and experimental results of optical surface with different machining methods are employed to validate the effectiveness and correctness of the method.