Improving the surface metrology accuracy of optical profilers by using multiple measurements

Abstract

The performance of high-resolution optical systems is affected by small angle scattering at the mid-spatial-frequency irregularities of the optical surface. Characterizing these irregularities is, therefore, important. However, surface measurements obtained with optical profilers are influenced by additive white noise, as indicated by the heavy-tail effect observable on their power spectral density (PSD). A multiple-measurement method is used to reduce the effects of white noise by averaging individual measurements. The intensity of white noise is determined using a model based on the theoretical PSD of fractal surface measurements with additive white noise. The intensity of white noise decreases as the number of times of multiple measurements increases. Using multiple measurements also increases the highest observed spatial frequency; this increase is derived and calculated. Additionally, the accuracy obtained using multiple measurements is carefully studied, with the analysis of both the residual reference error after calibration, and the random errors appearing in the range of measured spatial frequencies. The resulting insights on the effects of white noise in optical profiler measurements and the methods to mitigate them may prove invaluable to improve the quality of surface metrology with optical profilers.