Some aspects of surface roughness measurement

Abstract The connection between the profile and surface Power Spectral Densities of a rough surface is investigated, and explicit functional relations between the two are obtained for isotropic surfaces. These relations allow the surface Power Spectral Density (PSD) to be obtained from the PSD of a single profile, for isotropic surfaces. For anisotropic surfaces, it is shown how the surface PSD may be obtained from the cross-spectra of several parallel profiles. Techniques for obtaining these cross-spectra are briefly mentioned. A simple example of an isotropic surface is used to show that the profile PSD may seriously distort the spectral content of the surface roughness by giving undue weight to long wavelengths at the expense of short wavelengths. Questions of filtering of the surface and profile PSDs are discussed for isotropic surfaces, and it is shown that removal of all wavelengths smaller than λ0 on the surface requires their removal on the profile, but in addition requires some attenuation of all wavelengths on the profile greater than λ0. The question of which profile filters are admissible in the sense that they give rise to physically realizable surface filters (with 0 ⩽ attenuation ⩽ 1) is also examined, and it is shown that all profile filters involving an infinitely sharp cut-off at some wavelength are inadmissible. Based on an examination of the connection between the surface PSD and various surface statistics of interest, four indices of anisotropy involving the moments of this PSD are developed. It is shown how these indices may be evaluated by means of measurements on five nonparallel profiles.