Generalized Form Characterization of Ultra-precision Freeform Surfaces Using an Invariant Feature-based Pattern Analysis

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry and are widely used in many industries, such as advanced optics and biomedical implants, due to their superior optical and mechanical properties. In view of the geometrical complexity of freeform surfaces, there is no international standard for the traceable measurement and characterization of machined ultra-precision freeform surfaces with sub-micrometre form accuracy and nanomatric surface finishing.;Motivated by the need for such a standard, this thesis presents an Invariant Feature-based Pattern Analysis Method (IFPAM) for the generalized form characterization of ultra-precision freeform surfaces. The IFPAM makes use of intrinsic surface properties to map the surface into a special image to form an orientation invariant feature pattern (IFP) for the representation of the surface geometry. The digital image processing techniques are then employed to conduct the IFP registration and correspondence searching for the form characterization of the surface. A bidirectional curve network based sampling strategy combined with a robust surface fitting and reconstruction algorithm are developed for ensuring the accurate extraction of the intrinsic surface features from a machined freeform surfaces. To access the reliability and accuracy of the IFPAM, a task specific uncertainty analysis model is developed based on Monte Carlo method to evaluate the uncertainty in the form characterization of ultra-precision freeform surfaces. Three uncertainty contributors are considered in the model, including the instrument error, the surface form error, and the sampling strategy. The developed uncertainty analysis model is helpful for control and optimization of the IFPAM so as to provide more reliable form characterization results.;The IFPAM substantially addresses the deficiencies and limitations of traditional freeform surface characterization methods which are susceptible to embedded coordinate systems and possess uncertainty due to the geometrical complicity and form variety of freeform surfaces. It has better robustness and is not only free to the types of the surface being characterized but also independent from the coordinate frames. The outcome of this study not only significantly contributes to the state-of-the-art of measurement science and technology but also provides approaches that can be used in the standardization of measurement and characterization of freeform surfaces.