# Thermal Stability Design of Asymmetric Support Structure for an Off-Axis Space Camera
## 4 Finite Element Analysis of the Support Structure
### The Establishment of Finite Element Model  
We established the finite element model of the camera as shown in Figure 8. In order to reduce the joint stress between different materials caused by thermal load, the optical components of the camera in this model were composed of Zerodure mirrors and Invar backplanes.  
Figure 7: Definition of ply angle in the load-bearing cylinder.  
Considering the particularity of the off-axis TMA space camera structure, when the structure is thermally deformed, the thermal deformation can be offset due to the symmetry of the structure in the X direction, so the displacement of the optical elements in the X direction is small in the macro view; however, in the Y and Z directions with significant asymmetry, the thermal displacement of the optical elements is obvious [18; 27].  
It can be seen from the thermal deformation clouds that the thermal deformation of the camera support structure is obvious when the support structure is designed with iso-tropic layers. The maximum thermal deformation occurs in the front frame. However, the thermal deformation of the whole structure tends to be uniform when the support structure-ture is designed with an asymmetric zero-expansion layer.  
Based on the actual displacement of the reflectors under the two support structures, the reflector displacement caused by the thermal load is not obvious due to the good struc-tural symmetry in the X direction. However, in the Y and Z directions, where the struc-tural asymmetry is obvious, the displacement of the mirror in the zero-expansion design is obviously smaller than that of the isotropic laminate, which proves that the zero-expan-sion design in the asymmetric direction in the off-axis remote sensing camera has an ob-vious effect on reducing the rigid body displacement of the thermal deformation of the camera reflectors.  
In order to further determine the effect of the zero-expansion support structure in improving the thermal stability of the camera, we input the displacement data of the mir-rors in Table 3 into Zmax to analyze the influence of the thermal deformation of the struc-ture on the optical transfer function. The results of this analysis are shown in Figure 10.  
Figure 10: _Cont._  
The analysis shows that when isotropic layers are used in the support structure, the MTF of the optical system decreases from 0.422 to 0.378 at a rise of 5 \({}^{\circ}\)C, and the decrease percentage is 10.43%. When the zero-expansion layers are used in the support structure, the MTF of the optical system decreases from 0.422 to 0.411 at a rise of 5 \({}^{\circ}\)C, and the de-crease percentage is 2.61%. The influence of the thermal deformation on the MTF of the optical transmission is greatly reduced. These results prove that the application of the zero-expansion design in the support structure of the off-axis remote sensing camera can improve the imaging performance stability under the conditions of periodic temperature  
Figure 10: Comparison of MTF reduction of an optical system with two kinds of structures. (**a**) Theoretical MTF of the optical system; (**b**) MTF with the thermal deformation in an isotropic structure; (**c**) MTF with the thermal deformation in a zero-expansion structure.  
changes. It has a significant effect on the thermal stability design of the support structure of a space off-axis remote sensing camera.