Gaussian filters with profile extrapolation

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.