Sub-aperture stitching interferometry with a dual-frequency laser interferometer

Elliptical cylindrical mirrors are essential optical components for x-ray focusing in synchrotron radiation sources. With the rapid development of synchrotron radiation sources, the surface quality requirements for x-ray mirrors have become increasingly stringent. Corresponding measurement capabilities are necessitated by the ultra-precision manufacturing of elliptical cylindrical mirrors. Consequently, the high-accuracy surface measurement technology of x-ray mirrors is considered as a significant challenge in the field of optical measurement. Currently, the Fizeau interferometer with sub-aperture stitching is utilized as one of the most effective methods for measuring large-aperture elliptical cylindrical mirrors. During sub-aperture measurement, mechanical positioning errors in each sub-aperture at the sub-pixel level cause mismatch in the overlapping regions and reduce stitching accuracy. This paper investigates the effect of sub-pixel positioning errors on stitching accuracy, proposes a method that employs a dual-frequency laser interferometer to calibrate the position of each sub-aperture, and validates the method through corresponding simulations and experiments.