Fig. 1. Schematic diagram of mounting structure of a rectangular mirror with large aperture

Fig. 2. Typical constraints for a mirror. (a) 2-2-2 Constraint; (b) 3-2-1 Constraint

Fig. 3. A bi-axial flexural hinge based on kinematic equivalence principle

Fig. 4. Bi-axial flexural support

Fig. 5. Schematic diagram of equivalent flexural short straight beam

Fig. 6. Relationship between k_x and height a, thickness t, width w of the short straight beam

Fig. 7. Relationship between k_θy and a, t, w

Fig. 8. Relationship between the flexural support and CG plane

Fig. 9. Finite element model of the mirror assembly

Fig. 10. Optical axis of 1.8 m rectangular mirror

Fig. 11. Effect of ε₁ (a) and ε₂ (b) on the surface figure RMS

Fig. 12. Effect of ε₁ (a) and ε₂ (b) on the first-order natural frequency of PMA

Fig. 13. Mounting angle of the flexural supports

Fig. 14. Surface deformation at different θ₁ values under 1 G gravity (removed rigid-body displacement)

Fig. 15. Effect of different θ₂ values on the RMS and first-order natural frequency

Fig. 16. Effect of different sizes of flexural support on the RMS value

Fig. 17. Effect of different sizes of flexural supports on the first-order natural frequency

Fig. 18. Schematic diagram of the flexural supports′ structure

Fig. 19. Surface deformation under 1 G gravity in x and y directions (rigid-body displacement removed)

Fig. 20. The first three modes of PMA

Fig. 21. Dynamic test scene site map

Fig. 22. Swept frequency test results in x direction

Fig. 23. Sweep sine vibration result in y direction

Fig. 24. Random vibration test in z direction

Fig. 25. Schematic diagram of mirror aspheric interferometry optical testing layout

Fig. 26. The surface figure of the mirror tested in 0° direction

Fig. 27. The surface figure of the mirror tested in 180° direction