Finite element calculation for surface shape optimization of a polished synchrotron radiation thin mirror based on Bessel-point supporting

The X-ray optical mirror is one of the most important optical elements on the beam-line of a synchrotron radiation facility. The deformation of the working surface of the mirror greatly affects the quality of reflected beam, therefore it needs to be properly controlled. The deformation caused by gravity is one of the important sources of mirror shape error. In order to reduce the gravitational deformation and improve the surface accuracy, the mechanical responses of a Bessel-point supporting thin mirror (100 mm × 20 mm × 5 mm, length × width × height) with a downward working surface down is studied, via finite element analysis (FEA). In particular, to obtain the better surface accuracy, the top surface of the mirror is polished correspondingly to further reduce the deformation caused by gravity. Moreover, by comparing the results under a range of different polishing amounts, the recommended polishing amount is given according to the processing conditions and actual installation conditions. Finally, compared with the deformation results of the Bessel-point supporting theory, the obtained deformation (RMS) after polishing can be reduced by 30.86%, and the slope error (RMS) is reduced by 25.54%.