Fractal surface for calibration of an optical profiler

The surface profiler has become a basic metrology tool for the characterization of high-quality optical surfaces. The unknown effective resolution of the surface profiler is problematic in using the instrument, as it distorts the measured surface profile. In this paper, we suggest and describe the use of a fractal surface as a standard test surface with which to calibrate the effective resolution of a surface profiler. Fractal surfaces have the characteristics of irregularity, self-similarity and low correlation, with the correlation length being approximately equal to the length of the profile; therefore, a log-log plot of the power spectral density curve is a straight line. The power spectral density curves of fractal surfaces, which can be acquired through surface characterization techniques such as atomic force microscopy, are fitted to a straight line to act as a standard with which to calibrate an optical profiler in different ranges. Through calibration, we can obtain the effective resolution of the optical profiler, and the surface profiler is found to have good transmission capacity within the effective spatial frequency range.