Surface profile and topography filtering by Legendre polynomials

Abstract

A surface filtering method based on Legendre polynomials is proposed that can be used to separate form and roughness of surface profiles and areal topographies. The filter has been designed in such a way that it well approaches the properties of a Gaussian filter, especially in the center of the measured region. Theoretical profiles and measurement examples show that there is little difference to the zero- and second order Gaussian regression filters, both in the obtained topography and in the calculated profile- and areal parameters. Compared to the Gaussian regression filters the filtering becomes gradually weaker outside the center of the profile/area, while for the Gaussian Regression filters the filtering is constant over the profile/area, but becomes weaker at the edge region within half of the L-nesting index distance. Especially for cases where the nesting index is equal to or not much smaller than the dimensions of the measured area, such as the default case according to ISO 25178-2:2012, the principal advantage of the polynomial filter is that the form removal is an integral part of the filtering, so it does not interact with the filter and does not need to be carried out separately. Also the reference plane is principally unchanged after application of this filter. Some applications are shown and a fast numerical implementation is given.