Effects of finite stylus width in surface contact profilometry.

A study of the effects of stylus width in the profilometry of a randomly rough surface is presented. An approximate solution for the path of a flat-tipped stylus on an arbitrary surface is expressed as a nonlinear function of the local surface height and its first two derivatives. This solution is then averaged to find the first two moments of the measured profile when the surface and its derivatives are jointly Gaussian variates. The measured surface variance is found to decrease with increasing stylus size in a manner consistent with computer simulations.