The design and analysis of high-precision x-ray mirror benders for Kirkpatrick–Baez mirror system in Hefei advanced light facility

Hefei Advanced Light Facility is a diffraction-limited synchrotron radiation light source in the soft x-ray range. The BL04 beamline needs micro-focusing spots for spatial and time-resolving experiments, and the Kirkpatrick-Baez mirror system is adopted as a post-focusing system. In this paper, a high-precision mirror bender with flexure mechanism modules has been designed to dynamically bend the flat mirror to an elliptical form. Given the required high surface accuracy, the mirror bender is optimized with the variable mirror profile. The bending moments can be applied independently on the bender ends, so the mirror can be bent to a different elliptical form, meeting the needs of focusing on different experimental stations. Based on the optomechanical design, the mirror bender can bend a 500 mm long flat mirror to an elliptical form with a small radius of curvature (∼400 m). When focused on the photo emission electron microscopy station, the residual slope error of the bent mirror surface is optimized to 7.2 nrad (rms). This work introduces the bender's optomechanical design and simulation process for verification. In addition, the machining and assembly errors' influence on the bending surface is evaluated and the influence of mirror substrate manufacturing errors on surface accuracy is systematically discussed. The tolerance requirements for mirror manufacturing are specified based on the analysis results. The optomechanical design and optimization for the bender provide a reference for subsequent engineering design.