An improved algorithm for thermal compensation of synchrotron radiation optical mirrors based on Hessian matrix

Tong Li; Haipeng Zhang; Limin Jin; Wanqian Zhu; Jiahua Chen; Song Xue

doi:10.1063/5.0165525

An improved algorithm for thermal compensation of synchrotron radiation optical mirrors based on Hessian matrix

Rev Sci Instrum. 2023 Nov 1;94(11):113103. doi: 10.1063/5.0165525.

Authors

Tong Li^{1

2}, Haipeng Zhang³, Limin Jin^{1

3}, Wanqian Zhu^{1

3}, Jiahua Chen^{1

3}, Song Xue^{1

3}

Affiliations

¹ Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China.
² University of Chinese Academy of Sciences, Beijing 100049, China.
³ Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201204, China.

PMID: 37982721
DOI: 10.1063/5.0165525

Abstract

The heaters-based thermal-compensated adaptive adjustment of a reflection mirror at Shanghai high repetition rate X-ray Free-Electron Laser and extreme light facility (SHINE) is presented here based on finite element analysis. The correction performance of different control algorithms [singular value decomposition and gradient descent (GD)] is analyzed and compared. This study has demonstrated that a significant control algorithm can further improve the surface shape accuracy of the mirror. After optimizing the mirror control algorithm, the calculated slope errors and height errors of the mirror are reduced to nearly less than 50 nrad rms and 0.5 nm rms, respectively. The optimization result indicates that the GD control algorithm based on the Hessian matrix exhibits superior performance and practicality compared to the control algorithm before optimization.