Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than lambda/30 (lambda=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 lambda (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Automated summary

A non-null testing method utilizing Shack-Hartmann wavefront sensor is proposed to measure freeform surfaces, which improves measurement accuracy and dynamic range. A mathematical model and algorithm are developed to calculate the corresponding relationship between sampling points and spots, and experimental results demonstrate the feasibility and measurement capabilities of the method.