# Three-Band Spectral Camera Structure Design Based on the Topology Optimization Method
## 4 Performance Analysis
### Optical Analysis  
An optical analysis is conducted on the structural components of the three-band camera. The applied displacement constraints restrict the six degrees of freedom at the mounting holes where the camera is attached to the device base plate. A gravitational load of 1 g (where g represent the acceleration due to gravity) is applied in the \(z\)-axis direction, vertically downward. The results for each lens are fitted into Zernike polynomials [35; 36] and imported into optical design software to evaluate the changes in the image quality of the optical system. A simulation is conducted to analyze the degradation of the system performance caused by the deformation of the optical surfaces under gravitational conditions. The primary focus is on comparing the spot diagrams and modulation transfer functions (MTFs) of the optical system before and after optimization under the gravitational influence. The MTF results under these conditions are shown in Figures 13 and 14, and the corresponding spot diagrams are also presented in Figures 13 and 14.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Direction** & **X** & **Y** & **Z** \\ \hline Result/RMS & 3.64 & 0.512 & 3.97 \\ Magnification & 1.3 & 0.18 & 1.42 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Random vibration response results of the three-band camera’s structural components.  
Figure 12: Random vibration test experiment data in X-, Y-, and \(Z\)-directions (total RMS 2.8 g).  
Figure 13: Spot diagrams of initial structure of optical system subjected to gravity: (**a**) MTF for visible light system; (**b**) spot diagram for visible light system; (**c**) MTF for mid-wave infrared system; (**d**) spot diagram for mid-wave infrared system; (**e**) MTF for long-wave infrared system; (**f**) spot diagram for long-wave infrared system.  
Using ANSYS, a finite element method (FEM) analysis is performed on the entire system. The deformation results are then imported into the optical design software Zemax  
Figure 14: Spot diagrams of optimized structure of optical system subjected to gravity: (**a**) MTF for visible light system; (**b**) spot diagram for visible light system; (**c**) MTF for mid-wave infrared system; (**d**) spot diagram for mid-wave infrared system; (**e**) MTF for long-wave infrared system; (**f**) spot diagram for long-wave infrared system.  
2024 and applied to the corresponding lens surfaces to compare the changes in image quality. A comparative evaluation of the overall system performance reveals that, under the gravitational influence, the optimized system experiences a slight performance degradation. However, the changes in the optical system's spot size remain minimal and within acceptable limits. The spot size's maximum root mean square (RMS) increased from 3.172 \(\upmu\)m to 3.214 \(\upmu\)m for the visible light system and from 13.867 \(\upmu\)m to 14.043 \(\upmu\)m for the mid-wave infrared system, and it decreased from 8.397 \(\upmu\)m to 8.272 \(\upmu\)m for the long-wave infrared system after optimization. All values meet the RMS requirements of less than 4 \(\upmu\)m, 10 \(\upmu\)m, and 15 \(\upmu\)m, respectively, for each system. The MTFs at 112 lp/mm increase from 0.2789 to 0.2791 for the visible light system, those at 34 lp/mm remain the same at 0.2513 for the mid-wave infrared system, and those at 30 lp/mm increase from 0.3329 to 0.3356 for the long-wave infrared system after optimization. All values meet the MTF requirements of greater than 0.25, 0.25, and 0.3 for the respective systems.