Approximating Spline filter: New Approach for Gaussian Filtering in Surface Metrology

Abstract

Abstract-This paper presents a new spline filter named approximating spline filter for surface metrology. The purpose is to provide a new approach of Gaussian filter and evaluate the characteristics of an engineering surface more accurately and comprehensively. First, the configuration of approximating spline filter is investigated, which describes that this filter inherits all the merits of an ordinary spline filter e.g. no phase distortion and no end distortion. Then, the approximating coefficient selection is discussed, which specifies an important property of this filter-the convergence to Gaussian filter. The maximum approximation deviation between them can be controlled below , moreover, be decreased to less than 1% when cascaded. Since extended to 2 dimensional (2D) filter, the transmission deviation yields within − . It is proved that the approximating spline filter not only achieves the transmission characteristic of Gaussian filter, but also alleviates the end effect on a data sequence. The whole computational procedure is illustrated and applied to a work piece to acquire mean line whereas a simulated surface to mean surface. These experimental results indicate that this filtering algorithm for 11200 profile points and 2000 × 2000 form data, only spends 8ms and 2.3s respectively. 4.36%0.63% 1. 48% + Index Terms-surface metrology, profile filter, approximating spline filter, Gaussian filter, form filter