Design and analysis of stress-free clamping of mirrors used in free-electron laser beamlines

The reflector is an important optical element in free-electron laser beamlines. Deformation error caused by gravity can seriously affect the image quality of a beamline. To reduce deformation error, a gravity compensation scheme based on the Bessel point theory is proposed and a stress-free clamping device is designed. Taking a 440 mm × 50 mm × 50 mm mirror as an example, the analysis results indicate that the deformation error in the bottom surface of a mirror clamped with the traditional support method is 1.647 μrad. Adopting the newly designed device proposed in this paper, the results of a finite element analysis showed that the deformation error reduced to 0.085 7 μrad, which is better than the engineering index of 0.1 μrad. To prevent the mirror from moving when switching modes, a small clamping force of no more than 2 N can be added to the mirror, at which point the surface error of the mirror becomes 0.093 9 μrad. Additionally, a dynamic analysis of the device is also carried out, which indicates that the device mutes the low natural frequency, which means that resonance will not occur during operation. Therefore, this scheme satisfies our requirements for the beamline.