Optimal design of variable cross-section compression-bending ellipsoidal cylindrical mirror

To meet the needs of the synchrotron radiation beamline station project under construction, a design scheme of variable cross-section bending ellipsoidal cylindrical mirror is proposed. In this scheme, the calculation formula of the slope error of the variable-section (with sagittal focus) mirror is deduced based on the design theory of variable-width bending elliptical cylindrical focusing mirrors, and the design is optimized. This project is designed based on the optical parameters of the focusing lens (object distance p, image distance q and grazing incidence angle.), and the design error of mirror is calculated by finite element analysis software. The results show that within the given requirements, the optimal widths at both ends of the mirror are 49.5 mm and 90.5 mm. After calculating, simulating and optimizing, the slope error RMS value of the bending moments at both ends of the mirror is reduced from similar to 5.136 8 mu rad to similar to 0.063 6 mu rad (at 1 m of length), close to the system error similar to 0.040 7 mu rad, meeting the design requirements.