Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry and are widely used in advanced optics applications. Due to the geometrical complexity of optical freeform surfaces, there is, as yet, a lack of generalized surface characterization methods which measure various types of ultra-precision freeform surfaces with sub-micrometer form accuracy and surface finish in the nanometer range. To make good this deficiency, a generalized approach for the measurement and characterization of ultra-precision freeform surfaces, named the intrinsic surface feature-based method (ISFM), is presented in this paper. The ISFM makes use of intrinsic surface properties (e.g. curvatures, normal vectors, torsion and intrinsic frames) to conduct data matching or uses some algorithms to search for correspondences such as correlation functions. The method is experimentally verified through a series of measurement experiments. The results show that the proposed ISFM is capable of addressing the deficiencies and limitations of traditional freeform surface characterization methods which are susceptible to outliers and to uncertainty due to the geometry of the freeform surfaces. ISFM is a generalized methodology which is not dependent on the type of freeform surface being characterized.