A Comparison of Least-Squares Methods Applied on Form Removal in Metrology with Application Guidelines

Form removal, aiming to remove nominal form components from the primary profile, is a fundamental step prior to further surface metrological operations. ISO 3274 (1996) suggests that the association approaches can be used to separate form and form error. However, the ISO standards do not elaborate on specific methods or define the application scope. Furthermore, there is an absence of guidance regarding the selection of methods and parameter adjustment based on different types of surfaces. The most commonly employed set of association methods is least-squares (LS) methods, which use polynomial regression to fit the reference form. This study compares three typical least-squares models: ordinary least-square, total least-square and robust least-square across a variety of surface measurements and examines their characteristics, which inform the establishment of application guidelines. Additionally, a parametric analysis for RLS is provided as it involves different weight functions. These guidelines could be beneficial for the practical implementation of surface characterization, particularly for users and engineers who do not possess a full understanding of the mathematics of these models.