# Imaging Characteristics of Disturbance Flow Field Surrounding a Hypersonic Target
## 3 Results and Discussion
### The Results of Imaging Deviation
Figure 8: The \(x\) direction deflection angle distribution: Refer to Table 1 for flight conditions from (a–f). Figure 9: The \(y\) direction deflection angle distribution: Refer to Table 1 for flight conditions from (a–f). Figure 11: The results of imaging deviation over ocean: The last row is the difference between the deviated image and the original image; the red dashed box indicates the location of the disturbance flow field. Figure 12: The results of imaging deviation over city: The last row is the difference between the deviated image and the original image; the red dashed box indicates the location of the disturbance flow field. Figure 10: The results of imaging deviation over desert: The last row is the difference between the deviated image and the original image; the red dashed box indicates the location of the disturbance flow field. As stated in Equation (28) and mentioned previously, the imaging deviation is influenced by several factors, including the deflection angles \(\varepsilon\), focal length \(f\), orbit height \(Z_{B}\), flight altitude \(Z_{O}\) and pixel size \(a\). However, the influence of deflection angles and flight altitude on imaging deviation is mutually constrained. As the flight altitude increases, the atmospheric density becomes sparser, leading to a significant reduction in the deflection angles. Moreover, the magnitude of the decrease in deflection angles far surpasses that of the increase in flight altitude. Additionally, flight altitude is often uncontrollable; thus, our primary focus is on exploring the impact of other parameters on imaging deviation. It is observed that a lower orbit height leads to a larger pixel shift; however, it also reduces the detection range. Therefore, selecting a low orbit or sun-synchronous orbit for detection is deemed appropriate. Figure 14 shows the effect of pixel size and focal length on \(y\) direction pixel shift under different flight conditions. When the focal length is specified, the pixel shift in the \(y\) direction increases as the pixel size decreases, whereas when the pixel size is specified, the pixel shift in the \(y\) direction increase as the focal length increases. Meanwhile, the influence of flight altitude and Mach number on the pixel shift remains consistent with the previously discussed trends. To achieve an image that preserves more deviation characteristics, the camera necessitates a large focal length and a small pixel size. However, it is crucial to acknowledge that both focal length and pixel size cannot be adjusted indefinitely. Increasing the focal length leads to a larger camera system volume, which may pose challenges for the satellite and escalate research and development costs. Conversely, decreasing the pixel size results in a reduction of luminous flux, and there exists a trade-off between these two parameters. Hence, a comprehensive consideration of the system requirements and constraints is essential when determining the optimal focal length and pixel size for the camera. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **20 km** & \multicolumn{3}{c}{**30 km**} & \multicolumn{1}{c}{**50 km**} \\ \cline{2-6}
**PSNR/dB** & **10 Ma** & **8 Ma** & **10 Ma** & **12 Ma** & **10 Ma** \\ \hline Desert & 46.42771 & 57.55659 & 56.69947 & 55.65402 & 83.28530 \\ Ocean & 46.82656 & 58.70044 & 56.70328 & 56.40288 & 78.51409 \\ City & 42.09763 & 53.03142 & 52.52691 & 51.28720 & 73.28530 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PSNR of imaging deviation varies with flight altitude and Mach number. Figure 13: The results of imaging deviation over speckle: The last row is the difference between the deviated image and the original image; the red dashed box indicates the location of the disturbance flow field.