# Imaging Characteristics of Disturbance Flow Field Surrounding a Hypersonic Target
## 3 Results and Discussion
### The Results of Imaging Deviation  
According to Table 2 and Figure 3, the distance from the background to the center of the disturbance flow field, denoted as \(Z_{O}\), corresponds to the flight altitude and is set at 20 km, 30 km, and 50 km, respectively. The length of disturbance flow field \(W\) is 6 m. The distance from the background to the camera lens \(Z_{B}\) is the orbit height and is set to 400 km. The pixel size of the CCD camera is 5 \(\upmu\)m and the focal length of the camera lens is 1.0 m.  
Figures 8 and 9 show the results of the \(x\) direction and \(y\) direction deflection angles under different flight conditions calculated by Equations (24)-(28), where the positive value represents the positive deflection towards \(x\) or \(y\) direction, while the negative value represents the opposite direction. Apparently, as flight altitude increases, the deflection angle decreases, and as the Mach number increases, the deflection angle increases, which follows the same pattern as the phase difference. In addition, the \(y\) direction deflection angle is an order of magnitude greater than the \(x\) direction, indicating that the former has a more pronounced influence on the imaging deviation. The deflection angle is also affected by the density or refractive index distribution of the disturbance flow field. The greater the fluctuation in the refractive index distribution along the path of propagation, the larger the deflection angle of light. The larger values of the deflection angle are similarly symmetrical in the downstream of the disturbance flow field. When specifying the Mach number or flight altitude, the disturbance flow field attains its highest density at 20 km or 12 Ma, resulting in the greatest imaging deviation. \begin{table}
\begin{tabular}{l c c c c c} \hline \multirow{2}{*}{**PSNR/dB**} & **20 km** & \multicolumn{3}{c}{**30 km**} & **50 km** \\ \cline{2-6}  & **10 Ma** & **8 Ma** & **10 Ma** & **12 Ma** & **10 Ma** \\ \hline Desert & 9.23251 & 9.93444 & 9.98668 & 10.12562 & 10.81715 \\ Ocean & 13.35157 & 14.90093 & 15.34042 & 15.72033 & 16.66509 \\ City & 14.61291 & 16.59343 & 17.15776 & 17.67577 & 19.56554 \\ \hline \end{tabular}
\end{table} 
Table 3: PSNR of imaging blurring varies with flight altitude and Mach number. Figure 7: The results of imaging blurring over city. The pixel shift is calculated by dividing the displacement by the CCD pixel size. The displacement results indicate that the majority of the pixel shifts are at the sub-pixel level. Figures 10-12 illustrate the imaging deviation results, based on the pixel shift, for the desert, ocean, and city backgrounds, respectively. For comparison with the natural background, Figure 13 demonstrates imaging deviation with a speckle pattern as the background. Although no significant visual difference is observed between the deviated image and the original image, the profile of the disturbance flow field can be extracted through background subtraction. The profiles of the disturbance flow field, shown in the last row of Figures 10-13, are found to be consistent with the existing experimental studies. These profiles can provide insights into the presence of a hypersonic target in flight, serving as an alternative method for hypersonic target detection. It is evident that the imaging deviation is influenced by the background image, with a more speckled background image retaining more information about the extracted disturbance flow field. In addition, according to the Gladstone-Dale relationship, the refractive index proves to be insensitive to wavelength variation, allowing for the utilization of the infrared band for nighttime imaging. Table 4 presents the Peak Signal-to-Noise Ratio (PSNR) of imaging deviation, which varies with flight altitude and Mach number. In contrast to imaging blurring, PSNR of imaging deviation demonstrates an increasing trend with flight altitude, yet slightly decreases with Mach number, and is several magnitudes larger.