The TPS soft x-ray bendable mirror clip design and slope error analysis

The TPS Phase III soft x-ray beamlines, designated as 33, 35, and 43, employ bendable mirrors to achieve the required optical performance across a broad energy range. All mirrors, except for the grating mirrors, are designed with adjustable height and position to optimize alignment. The mirrors are secured to the bending mechanism using specially designed clips and bolt joints. During bending, the mirror surface deformation can be approximated by second- and third-order polynomial terms, which must be removed to minimize optical aberrations. After applying these corrections, the residual slope error in the useful optical area must remain below ±1.5 × 10-6 rad to meet performance criteria. Therefore, the design of the mirror clip and the precise application of bolt joint forces are critical to achieving high-accuracy figure control. This study systematically investigates how varying bolt joint forces at the mirror clip can compensate for high-order residual deformations. Finite element method simulations were conducted to determine optimal force distributions, providing guidance for experimental setup and safe mounting conditions. In experiments, the bolt joint forces were adjusted using a calibrated torque wrench, while the long trace profiler continuously measured the slope error to identify the configuration yielding the widest functional optical area with minimal residual error.