Objective The large- scale off-axis three-mirror anastigmatic ( TMA) space- borne telescope enables the space optical remote sensing camera to meet the requirements of light weight, long focal length, large field of view, and high resolution. Meanwhile, it has a compact structure and many optimizable variables without dispersion and center blocking, which has become a research hotspot. The rectangular space mirror with a large size and high aspect ratio is an important part of the TMA, and the size of its structural rigidity, stability, the advantages and disadvantages of surface figure error, and thermal stability will directly affect the imaging quality of the whole camera. However, due to its structure asymmetry, the flexible mount design for the mirror of the TMA space camera, and the mounting and positioning of the mirror assembly are current technical difficulties. A reasonable support scheme design can eliminate the deformation of the mirror and its support assembly in processing and assembly to ensure the smaller surface figure error of the mirror. For a mirror where the gravity direction is perpendicular to the direction of the optical axis, there exists in the mirror body such a plane of action: If the actual support point of the flexible mount is on or near this surface, the gravitational moments of the various parts of the mirror body are balanced and the bending deformation of the mirror body is minimal due to its weight. This plane of action is known as the neutral plane of the mirror. For a circular mirror, the neutral surface is a plane at some distance from the center of gravity and perpendicular to the optical axis. However, as the rectangular space mirrors employed in TMA lose rotational symmetry compared to traditional circular mirrors, the supporting theories and empirical formulas in circular mirrors are difficult to extend to rectangular space mirrors. Methods We introduce a method to calculate the neutral plane position and optimal mounting position for a rectangular space mirror. First, we conduct structural design for the main reflective mirror assembly with the dimension of 1820 mmx 520 mm. Meanwhile, we adopt reaction-bonded silicon carbide ( RB-SiC) as the material for the mirror and implement a partially closed-back support structure and a triangular lightweight form at the back. Then, by evaluating the flexibility matrix of the flexible mount, we build the mechanical model of the mirror component. Subsequently, a new formula for determining the neutral surface position of a rectangular mirror is derived from this theoretical model. The validity of this theoretical derivation is confirmed by comparisons with results obtained from finite element analysis ( FEA) and optical inspection experiments. Results and Discussions By calculation, we derive the mathematical formula [ Eq. (4)] for determining the neutral surface position in the rectangular mirror. It is worth noting that, unlike circular mirrors, rectangular space mirrors lack symmetry, leading to an optimal support position consisting of curved surfaces rather than a single vertical plane. Therefore, the design for different locations should be differentiated during determining the installation depth of the flexible mounts. Based on these calculations, we determine the optimal support positions along the mirror axis and apply them to the XX-1 camera design. Conclusions We investigate the optimal mounting position of the flexible mount for rectangular space mirror assemblies with large dimensions and aspect ratios. Additionally, we build a mechanical model and according to this model, the surface figure error can be minimized under the axial force Fz = 2.24 N. By considering a support depth of 2 epsilon(2) + epsilon(1) = 20.59 mm, we calculate the neutral surface position and the optimal support position. Afterwards, we fabricate and assemble the mirror assembly based on the optimized design, and perform optical inspection and dynamic tests on the mirror assembly. In the optical inspection test, the root mean square (RMS) value of the surface figure of the mirror assembly under various gravity directions is less than 0.03.. The minimum resonance frequencies in three directions obtained from the swept-frequency vibration test are 106.30, 151.55, and 104.00 Hz, meeting the requirements of surface figure accuracy, structural rigidity, and stability of the mirror assembly.
