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

Abstract

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.