# Near-Space Wide-Area and High-Resolution Imaging System Design and Implementation
## 2 Wide-Area and High-Resolution System Design
### High-Resolution Camera Design
#### 2.1.2 Optic System Design  
For the purpose of high-resolution imaging, the long focal length of the optical system is relatively large. Considering the limitations of the photoelectric sphere platform on load size in this project, the design process needs to compress the lens structure size as much as possible. Through the complex design of the initial structure, a three-fold zoom optical system with a long focal length of 320 mm, a short focal length of 106.7 mm, and F/# 4.3 was ultimately obtained. The optical path structure is shown in Figure 3, including two moving components. The movement of the zoom moving component from the short to long focal length is 33.1 mm, and the compensation moving component from the short to long focal length is 27.5 mm. The total length of the optical path is 310 mm, with a maximum aperture of 90 mm. There are 20 optical lenses, with a total weight of less than 1.8 kg. The evaluation of the imaging quality of an optical system mainly considers the modulation transfer function (MTF), point plot, and distortion curve. According to the task requirements, the imaging quality of the optical system on the five preset focal segments are examined separately. 1. f = 320 mm  
From the data of the telephoto endpoint of the optical system, the maximum RMS radius of the diffuse spot within the field of view is about 1.8 \(\upmu\)m, as shown in Figure 4, which is less than a pixel size. From the MTF curve, the system has ideal image quality. At a Nessler frequency of 156 lp/mm, the full field MTF is close to 0.4, corresponding to an optical angular resolution of:  
\[\sigma=\frac{1}{N_{d}f}=20\ \upmu\text{rad} \tag{1}\]  
When the resolution requirement of 20 \(\upmu\)rad is met, the relative distortion curve of the system is as follows--with a maximum relative distortion of less than 0.4% in the full field of view. Figure 3: Optical path structure of the lens. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Data** \\ \hline long focal length & \(f_{L}^{\prime}=20000\ \text{m}\frac{32.\upmu\text{mm}}{0.2\ \upmu\text{mm}}=320\ \text{mm}\) \\ short focal length & \(f_{S}^{\prime}=\frac{320}{3}\ \text{mm}=106.7\ \text{mm}\) \\ horizontal field of long focal & \(2\omega=2\times\arctan\left(\frac{29.9\ \text{mm}}{2\times f_{L}^{\prime}}\right) \approx 5.3\ ^{\circ}\) \\ vertical field of long focal & \(2\omega=2\times\arctan\left(\frac{22.4\ \text{mm}}{2\times f_{L}^{\prime}}\right) \approx 4^{\circ}\) \\ horizontal field of short focal & \(2\omega=2\times\arctan\left(\frac{29.9\ \text{mm}}{2\times f_{S}^{\prime}}\right) \approx 16.0^{\circ}\) \\ vertical field of short focal & \(2\omega=2\times\arctan\left(\frac{22.4\ \text{mm}}{2\times f_{S}^{\prime}}\right) \approx 12^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 3: High-resolution camera optical parameters. 2. f = 260 mm From the data of the telephoto endpoint of the optical system, the maximum RMS radius of the diffuse spot within the field of view is about 2 \(\upmu\)m, as shown in Figure 5, which is less than a pixel size. From the MTF curve, the system has ideal image quality. At a Nessler frequency of 137 lp/mm, the full field MTF is close to 0.4, corresponding to an optical angular resolution of: \[\sigma=\frac{1}{N_{q}f}=28\ \upmu\text{rad}\] (2)  
When the resolution requirement of 28 \(\upmu\)rad is met, the relative distortion curve of the system is as follows--with a maximum relative distortion of less than 0.3% in the full field of view. 3. f = 213 mm From the data of the telephoto endpoint of the optical system, the maximum RMS radius of the diffuse spot within the field of view is about 2.3 \(\upmu\)m, as shown in Figure 6, which is less than a pixel size. From the MTF curve, the system has ideal image quality.