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Spectral analysis for the effects of stylus tip curvature on measuring isotropic rough surfaces

Spectral analysis and computer simulation are adopted to investigate the tracing of three-dimensional isotropic rough surfaces with a spherical tipped stylus. It is shown that the measuring error strongly depends on the ratio of the radius r of the stylus tip to the root-mean-square (rms) roughness σ and on the ratio of the 1/e correlation distance b to the rms roughness σ. By using the concept of critical wavenumber, the profile and surface spectral densities of a measured surface can be estimated. Also, a formula is developed to estimate the error of the rms height.