Measuring optical freeform surfaces using a coupled reference data method

Flat optical freeform surfaces usually possess non-rotational symmetry with a small curvature and lack of strong features for surface alignment. Due to the lack of strong features and small curvature, it is difficult to align the design and measured surfaces for characterizing the surface quality of flat optical freeform surfaces with sub-micrometre form accuracy. The traditional least squares method (LSM) generally produces large errors as there is a lack of strong features as reference for the alignment of the design and measured surfaces. This paper proposes a novel and practical method named the coupled reference data method (CRDM) to evaluate flat optical freeform surfaces with high efficiency and precision in the nanometre scale. The method couples reference data to the workpiece of the freeform surface designed model and the concerning reference features are machined together with the workpiece. By aligning the reference data, the proposed CRDM carries out fast surface matching. This makes good preparation for the next matching optimization which is conducted by the least-squares and minimax zone method. After the precise surface matching, the flat optical freeform surface can be evaluated by 3D form error topography and parameters. As compared with a traditional freeform measurement method such as LSM, it is interesting to note that the accuracy and the stability of the measurement can be significantly enhanced by the CRDM.