| The application of super-smooth optical element has been throughout all aspects of life. Whether in the civil or military equipment, super-smooth optical elements play a very important role. Whether characterize correctly super-smooth optical surface quality, it will affect the scope of application of the super-smooth optical elements. The current research focus of optical field at home and abroad is how to characterize super-smooth optical surface. The complete framework of characterization includes: to preprocess measuring image of super-smooth optical surfaces; to measure the correct separation of the frequency surface error of optical elements’super-smooth surfaces; to determine the evaluation of super-smooth optical component surface characterization parameters; to establish the relationship between characterized parameters and super-smooth optical surface optical properties.This paper comparative analyzes the current various measurement methods of the ultra-smooth optical element, points out its advantages and disadvantages and the noise error in measurement, and studies how to pretreat the measured image, puts forward to measurement image applying wavelet preprocessing, which can effectively remove image noise caused by the external factors.In this paper, method of extracting surface error has disadvantages at home and abroad, which leads to advantages of the dual-tree complex wavelet that applies in optical 3D surface error drew, establishing a mathematical model of the surface error of intermediate frequency in the dual-tree complex wavelet separation. Through the actual simulative spheroid-surface optical surface, comparing changes extracted-surface error of dual-tree complex wavelet with the discrete-wavelet, it can confirm that the dual-tree complex wavelet having the advantages of approximate shift invariance in practice. And it has obvious advantages in extracting the accuracy error and maximum reconstruction error of the datum. In conclude, dual-tree complex wavelet have irreplaceable advantages that is very suitable for the extraction of 3D optical surface error compared with discrete-wavelet. In order to solve the difficult problem of determining traditional wavelet the number of decomposition, it puts forward application of compositive characterized parameters to make sure the number of wavelet decomposition by mean of square wavelength. Experimental results show that: the dual-tree complex wavelet can extract practical optical 3D Surface error very successfully, which can lay the foundation for subsequent characterized parameters.This paper is based on basic theory of metrology, putting forward employing the standard basic parts about the surface of super-smooth optical elements of 3D characterizing parameter from ISO 25178-2 in 2012, and find out the corresponding surface optical properties. Finally by the simulation, it maybe exist in relations by discussing and analyzing the parts of 3D characterization parameters and super-smooth optical surface properties for the improvement and development of studied method in super- smooth optical element surface characterization. |