Spectral analysis for the effects of stylus tip curvature on measuring fractal profiles

Spectral analysis and computer simulation are adopted to investigate the tracing of a two-dimensional fractal profile with a mechanical profiler with a spherical tipped stylus. It is shown that the critical wavenumber strongly depends on the fractal dimension D and the ratio of the non-scale parameter G to the tip radius r. By using the concept of the critical wavenumber, the spectral density of a measured profile can be estimated. Also, formulae for estimating the critical wavenumber and the error of the mean square height are developed.