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An Areal Isotropic Spline Filter for Surface Metrology



Hao H. Zhang, D Ott, Wei Chu


This paper deals with the application of the spline filter as an areal filter for surface metrology. A profile (2D) filter is often applied in orthogonal directions to yield an areal filter for a three-dimensional (3D) measurement. Unlike the Gaussian filter, the spline filter presents an anisotropic characteristic when used as an areal filter. This disadvantage hampers the wide application of the spline filters for evaluation and analysis of areal surface topography. An approximation method is proposed in this paper to overcome the problem. In this method, a profile high-order spline filter serial is constructed to approximate the filtering characteristic of the Gaussian filter. Then an areal filter with isotropic characteristic is composed by implementing the profile spline filter in the orthogonal directions. It is demonstrated that the constructed areal filter has two important features for surface metrology: the isotropic amplitude characteristic and no end effects. Some examples of applying this method on simulated and practical surfaces are analyzed.
Journal of Research (NIST JRES) - 120.006
Report Number


Gaussian filter, High-order spline filter, Areal filter, Isotropic characteristic


Zhang, H. , Ott, D. and Chu, W. (2015), An Areal Isotropic Spline Filter for Surface Metrology, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed February 29, 2024)
Created April 1, 2015, Updated November 10, 2018