Improved Dual Tree Complex Wavelet for the Reference Extraction of the Step Characteristic Structure Surface

Abstract

There are a lot of discontinuous characteristics such as grooves and the steps in the device surface with the groove size. The least squares fitting method is required by ISO regulation when the datum is extracted for its quality evaluation,but its robustness is far worse than filtering method. Fluctuations which are called the pseudo Gibbs phenomenon will be generated in the discontinuous surface if the traditional filtering method(such as Gaussian filtering,wavelet filtering,etc.) is used directly. A new filtering algorithm is proposed. By gradient processing the dual tree complex wavelet transform(DT-CWT) though the total variation minimization theory(TVM),which means initializing the wavelet coefficients of each layer by using the threshold value method; combining the idea of TVM with DT-CWT with projected subgradient method; continuous iteration; and finally the robustness of the DT-CWT transform in extracting the datum which has plane geometry characteristic is enhanced. The simulation results show that compared with the traditional filtering methods,the algorithm has the optimality in the characterization of precision(maximum reconstruction error and the mean square error),and its assess height is the closest to the ideal height. Assessment carried out on a real convex sticker block,fluctuations can be well restrained at steps whether from the intuitive 3D view or side contrast figure,and the geometrical characteristics of the product are ensured as the theoretical height deviation with the actual processed standard block is only 0.0403 μm,and an effective reference extraction method is provided for practical engineering application.