Invariant-Feature-Pattern-Based Form Characterization for the Measurement of Ultraprecision Freeform Surfaces

Ultraprecision freeform surfaces (UPFSs) are increasingly being used in advanced optical systems due to their superior optical properties. However, current research on the measurement of machined UPFSs is still hindered by lack of efficient and robust form characterization techniques which can characterize the form error of measured freeform surfaces with submicrometer accuracy. This paper presents an invariant-feature-pattern-based form characterization (IFPFC) method. IFPFC makes use of intrinsic surface features (e.g., Gaussian curvature) to map the surface into an orientation-independent feature pattern to represent the surface geometry. Surface matching and comparison are then undertaken in terms of feature pattern registration. Compared with conventional methods, the IFPFC is not only robust to the initial position of the measured surface relative to the design template but also computationally efficient since it does not involve much iteration. A series of computer simulations and actual measurement are conducted to demonstrate the performance and the validity of the IFPFC method in the measurement and characterization of UPFSs with submicrometer form accuracy.