Abstract: A filter with the transmission characteristic described by the Gaussian curve is the most common filter used in surface metrology to separate roughness, waviness, and form. The most natural way to implement the Gaussian filter is to convolve the registered profile with the filter impulse response. An important drawback of this approach, however, is that it is difficult to correctly determine the mean line for the profile end parts, this being referred to as the edge effect. Since a registered profile is frequently too short, it is undesirable to reject any of its fragments. In the paper, we propose a method for determining the mean line for a whole profile. This requires extrapolating the profile at both its ends by fragments being some polynomial functions of the spatial variable. The coefficients of the polynomials are selected so that the mean square difference between the profile and the mean line reaches a minimum. Experimental results show that the proposed method eliminates the edge effect even if the amplitude of the form component significantly exceeds the roughness component.
B I B L I O G R A F I A1. ISO 11562:1996. Geometrical product specifications (GPS) - surface texture: profile method - metrological characteristics of phase correct filters.
2. Krystek, M., "Form filtering by splines", Measurement, vol. 18, 1996, p.9-15
3. Krystek, M., "Discrete L-spline filtering in roughness measurements", Measurement, vol. 18, 1996, p.129-138
4. Goto, T.& Miyakurab, J.& Umedaa, K.& Kadowakib, S.& Yanagic, K., "A Robust Spline Filter on the basis of L2-norm", Precision Engineering, vol. 29, 2005, p.157-161
5. Numada, M.& Nomura, T.& Yanagi, K.& Kamiya, K.& Tashiro, H., "High-order spline filter and ideal low-pass filter at the limit of its order", Precision Engineering, vol. 31, 2007, p.234-242
6. Janecki, D., "A generalized L2-spline filter", Measurement, vol. 42, 2009, p.937-943
7. Goto, T.& Yanagi, K., "An optimal discrete operator for the two-dimensional spline filter", Measurement Science and Technology, vol. 20, 2009, p.125105, (4 pp.)
8. Brinkmam, S.& Bodschwinna, H.& Lemke, H.W., "Accessing roughness in three-dimensions using Gaussian regression filtering", International Journal of Tools Manufacture, vol. 41, 2001, p.2153-2161
9. ISO/TS 16610-22:2006. Geometrical product specifications (GPS) - filtration. Part 22. Linear profile filters: spline filters.
10. ISO/TS 16610-31:2010. Geometrical product specifications (GPS) - filtration. Part 31. Robust profile filters: Gaussian regression filters.
11. Dobrzanski, P.& Pawlus, P., "Digital filtering of surface topography. Part I. Separation of one-process surface roughness and waviness by Gaussian convolution, Gaussian regression and spline filters", Precision Engineering, vol. 34, 2010, p.647-650
12. Hanada, H.& Saito, T.& Hasegawa, M.& Yanagi, K., "Sophisticated filtration technique for 3D surface topography data of rectangular area", Wear, vol. 264, 2008, p.422-427
13. Zhang, H.& Yuan, Y.& Piao, W., "A universal spline filter for surface metrology", Measurement, vol. 43, 2010, p.1575-1582 
Pełny tekst 
DOI 
Web of Science 
YADDA/CEON