# Three-Band Spectral Camera Structure Design Based on the Topology Optimization Method
## 3 Three-Band Optimization Results  
### Topology Optimization Results  
In this study, OptiStruct was used to optimize the structure, with the first limitation being the first-order natural frequency of 100 Hz, set as the lower limit, since the excitation power tends to be significantly higher under 100 Hz in the working platform, which could lead to resonance. The 100 Hz lower bound is selected to avoid the structural design resonance. Regarding the penalty factor, based on Equation (3), the value is computed. A minimum of 7.5 was selected to ensure stiffness while avoiding excessive material usage. Higher values will over-penalize structural elements, introducing an unnecessary stiffness reduction. In the multispectral camera, a lack of stiffness leads to structural vibrations and misalignment, causing irreversible degradations in the image accuracy. Finally, the minimum mass of the housing was set as the objective. The optimization process, as shown in Figure 4, initially exhibited a rapid decline in both the mass and first-order natural frequency, followed by gradual stabilization, and it converged after 26 iterations. The first-order natural frequency (red curve) decreased sharply from around 200 Hz to approximately 100 Hz within the first few iterations before stabilizing, while the mass (black curve) was reduced from around 7 kg to approximately 1.5 kg, demonstrating the effectiveness of the optimization in reducing the weight. The final optimization model, without surface skin treatment, achieved a first-order natural frequency close to 100 Hz and a mass of approximately 1.5 kg. However, to meet the requirements for light shielding and dust protection, a 0.5 mm skin was added to the external surface of the housing, ensuring functionality while maintaining structural integrity.  
Figure 3: Overall flowchart of optimization process.  
Structures A, B, C, D, and E were individually optimized for minimum compliance, and the objective function converged after 12, 10, 8, 9, and 12 iterations, respectively. Key components, such as the inner diameter for the mounting lenses and the areas around the screws, were designated as non-design domains. The final density distribution, as shown in Figure 5, was determined after optimization. For material elements with densities approaching zero, the deformation or response to external forces or stimuli was minimal, so these elements were removed. Conversely, elements with higher densities that contributed more significantly to the structural performance were retained.  
Figure 4: Iteration optimization curve.  
Figure 5: _Cont_.  
Optimization involves removing low-stress regions or materials that contribute little to load transfer and are not significantly relevant to key functions. These regions, for instance, do not participate in load bearing, stability, or other critical functions and have minimal contributions to the stiffness. Optimization achieves lightweighting by retaining the primary load paths, stress balance, stiffness, and functional integrity. As a result, it has a minimal impact on other performance indicators, such as strength and stiffness. The performance indicators before and after optimization are compared in Table 1. Although the first-order frequency decreased slightly, the first-order natural frequencies of both the housing and the support structure remained above the 100 Hz threshold. The optimization achieved a weight reduction of 42.5% for the housing and 30.6% for the support structure, resulting in an overall weight reduction of 41.6%. While the deformation in the Z-direction under gravity conditions increased in the static analysis, the mechanical performance remained stable overall, meeting the design requirements.