An Isotropic Areal Filter Based on High-Order Thin-Plate Spline for Surface Metrology

Isotropy, end effect suppression, calculation efficiency and robustness are basic requirements of areal filters for surface metrology. However, current areal filters cause problems in different aspects, which cripples the operation of surface metrology like roughness evaluation. In this paper, a high-order thin-plate spline (TPS) filter is proposed to construct a real isotropic areal spline filter with minimum end effects and high efficiency, aiming to provide a more universal and efficient topography filtration method. The new filter is structured by approximating Gaussian filter to ensure uniform transmission characteristics. The robust algorithm is derived to process surface data with outliers and defects. A fast implementation is also provided in this paper. Performances of various areal metrology filters are illustrated by processing both simulated and practical surfaces, through which the proposed high-order TPS filter herein manifests real isotropy, higher calculation efficiency, slighter end effect as well as robustness comparing to current areal surface metrology filters. Comparing with the ISO 16610–61, the new areal filter can obtain more ideal results, therefore it can take the place of ISO 16610–61 on most occasions.