“Improving the Robustness of Curve Fitting in Figure and Finish Metrology”

Abstract

Curve fitting has many applications in topographic characterization including areas such as datum definition, modelling, and filtering e.g. the use of Zernike polynomials in figure metrology and the removal of tilt and curvature in finish measurement. However, topography measurement data does not represent a purely theoretical manufacturing process and contains events which are part of the "true" surface such as scratches and digs (also referred to as pits and troughs or cosmetics), and include erroneous data which are not part of the "true" surface resulting from measurement errors (e.g. signal noise). These events and measurement errors may result in outliers in the measured surface data. The general treatment of outliers is subject to functional considerations but essential to a comprehensive characterization system is the ability to identify outliers and determine their significance on subsequent characterization. Specifically, the presence of outliers within surface data limits the robustness of conventional curve fitting algorithms and thus limits subsequent characterization fidelity.