Characterization and filtering of profile and areal surface topography by combining the discrete Legendre and cosine transforms

Abstract

Abstract In the standardized processing of surface topography data, the form removal and filtering operations are clearly separated. This is reflected in the current ISO standards concerning profile surface texture and areal surface texture, the ISO 21920 and the ISO 25178 series respectively. When the scale-limited surface texture is significant compared to the form to be removed, for example with additive manufactured surfaces, the dependence of the surface Fourier spectrum on the removed form and orientation may become significant. This may lead to interaction between the form removal and filtering operations. To counter this interaction, in this paper, the lower-order discrete Legendre polynomials that describe the form are combined with cosine functions that describe the surface texture. This set of base functions is orthonormalized using a Gram-Schmidt procedure. This results in a set of orthonormal functions that allow an independent parameterization of both form and texture. The concept and the related theory are given and illustrated using examples of filtering profiles and areal topographies, description of cylinders and treatment of missing data. The examples show that the concept as presented in this paper is useful for filtering surfaces with a dominant form and can be used in the parametrization of surfaces and cylindrical geometries. Also, the methods presented here can be used for filtering and parametrization in the case of missing points in the data, actual holes in the profile or non-rectangular surfaces.