Generalized form characterization of ultra-precision freeform surfaces

This paper presents a generalized form characterization method named intrinsic feature-based pattern analysis method (IFPAM) for measuring ultra-precision freeform surfaces with sub-micrometer form accuracy. The IFPAM makes use of intrinsic surface properties, the Fourier–Mellin transform, and phase correlation to conduct surface registration. A bidirectional curve network based sampling strategy and a robust surface fitting method are built for accurate representation of the measured freeform surfaces. Compared with traditional least-squares-based methods, the IFPAM not only possesses better robustness and higher precision but also less susceptible to the uncertainty due to geometrical complexity and registration problems involving translation and rotation operations.