A study of extrapolation of freeform surfaces to improve the edge effect in surface filtering

Surface filtering is a hot research topic especially in the field of freeform surface metrology, since filtering is an important data processing technique before further characterization of the measured surfaces. There is a large number of surface filtering algorithms developed by researchers to improve the robustness and accuracy of the filtering results. However, the filtering result is still far from complete which is particularly true in the edge area where is always found to have large distortion. This is so-called the edge effect which is mainly caused by a lack of data when performing convolution in the edge area in the filtering algorithms. In this paper, a Gaussian process machine learning-based surface extrapolation method of the measurement data is presented to extend the measured surface before conducting surface filtering. A Gaussian process data modelling method is utilized for the surface extrapolation and hence a Gaussian filtering method is used for the surface filtering. A series of simulation and practical measurement experiments have been conducted to evaluate the performance of the proposed method. The accuracy and efficiency of the new filtering method are demonstrated and analyzed in the experiments. The results show that the edge effect can be significantly improved and the efficiency can also be improved by introducing the extrapolation method. The proposed method provides a new way for surface filtering and thus surface characterization for the complex freeform surfaces.