Spectral analysis for the effect of stylus tip curvature on measuring rough profiles

Spectral analysis and computer simulation are adopted to investigate the tracing of a random profile with a mechanical profiler with a spherical tipped stylus. It is shown that the measuring error strongly depends on the ratio of the radius of stylus tip r to the rms roughness σ and the ratio of the 1/e correlation distance b to the rms roughness σ. By using the concept of critical wave number, spectral density of measured profile can be estimated. Also, formulas are developed to estimate the rms error and the critical sampling interval.