A universal spline filter for surface metrology

In this study, a novel fractional spline filter is proposed for surface metrology. The filter combines arbitrary order fractional spline function with variational principle, and is endowed with an adjustability of transition characteristic. If the order is high enough, the fractional spline filter can obtain more step-edge-like cut-off characteristic of the low-pass filter, and it can also realize the transmission characteristic of the Gaussian filter with high accuracy if the order equals to two. In addition, if the approximation parameter is set to zero, this filter will be simplified to a form of ordinary spline filter. Therefore, this fractional spline filter is called the universal spline filter. In order to reduce the computation time, the universal spline filter is calculated by a fast Fourier transform (FFT) algorithm. Furthermore, for practical use, an improved method prior to the FFT algorithm is proposed to suppress the end effect. Finally, the efficiency of the whole algorithm in comparison with the ordinary spline filter is demonstrated by the experiments, and it is also shown that the universal spline filter is able to alleviate the end effect significantly.