Subaperture moving strategy and related systematic errors in stitching interferometry of X-ray mirrors

Abstract

For high-precision metrology of X-ray mirrors, the subaperture moving strategy significantly impacts the accuracy of stitching interferometry. In this work, we investigated the systematic errors associated with various subaperture moving strategies of rotational stitching (RS), rotational displacement stitching (RDS), and displacement stitching (DS) in measuring X-ray mirrors. The effects of stitching strategies on a flat mirror and a spherical mirror with a radius of curvature (RoC) of 180 m and 60 m were compared. For the mirror with RoC of 60 m, the DS strategy showed the smallest height error of 3.3 nm (RMS) between algorithm-based stitching and the Nanometer Optical component Measuring machine (NOM), while RS showed a large error of 37.4 nm (RMS). The different regions of the interferometer aperture have different amplitudes of retrace errors, defocusing errors, and lateral distortion, which can lead to accumulations of systematic errors using the RS strategy. By reducing the pixel size from 0.268 mm/pixel to 0.089 mm/pixel, the measurement accuracy using the same RDS strategy improved from 7.4 nm (RMS) to 4.4 nm (RMS). Based on the optimal stitching strategy, the measurement accuracy of residual figure error of the X-ray mirror with a radius of curvature of 30 m reaches 0.2 nm (RMS).