Multi-technique based coarse to fine form registration for ultra-precision diamond milling of freeform optics

Abstract Due to its excellent optical performance, freeform optics has found extensive applications into sophisticated optical systems. Ultra-precision diamond milling (UPDM) offers an advanced solution for manufacturing high-quality freeform optics with sub-micrometric form error. However, its varying curvature characteristics would lead to uneven residual and inconsistent surface quality. Therefore, to improve the registration process accuracy, this study proposes a multi-technique based coarse to fine form registration for UPDM of freeform optics and it provides a benchmark for evaluating the form error of machined surfaces. Firstly, two-dimensional Fourier transform and Pearson correlation coefficient were used for area coarse registration. Next, singular value decomposition was utilized to transform the coordinate systems for fine registration. Then, simulations were performed to construct two representative freeform optics-light emitting diode lens and virtual reality lens-and their forms were registered. Finally, the form error between the designed and measured surfaces was discussed in UPDM experiments. The results revealed that the proposed form registration method demonstrated strong robustness and accuracy under various errors. After registering simulation, the peak to valley and root mean square deviations between the designed surface and the measured surface of the two types of freeform optics were both less than 10 −7 μm. Significantly, this study applies advanced mathematical tools in the form registration and thus improves the precision and efficiency of form registration in freeform optics.