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

机译：使用基于固有表面特征的方法测量和表征超精密自由曲面

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摘要

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.
机译：超精密自由曲面是具有非旋转对称性的复杂曲面，已广泛用于高级光学应用中。由于光学自由曲面的几何复杂性，目前尚缺乏通用的表面表征方法，该方法可测量亚微米级的形状精度和纳米范围内的表面光洁度的各种类型的超精密自由曲面。为了弥补这一缺陷，本文提出了一种用于测量和表征超精密自由曲面的通用方法，即基于固有表面特征的方法（ISFM）。 ISFM利用固有的表面特性（例如曲率，法向矢量，扭转和固有框架）进行数据匹配，或使用一些算法来搜索对应关系（例如相关函数）。通过一系列测量实验对方法进行了实验验证。结果表明，提出的ISFM能够解决传统自由曲面表征方法的不足和局限性，这些方法易受离群值和由于自由曲面的几何形状导致的不确定性的影响。 ISFM是一种通用方法，不依赖于要表征的自由曲面的类型。

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