# Imaging Characteristics of Disturbance Flow Field Surrounding a Hypersonic Target
## 4 Summary  
In this study, we have thoroughly examined the remote sensing imaging of the disturbance flow field surrounding a hypersonic target under five different flight conditions. Utilizing Fourier Optics and Background-Oriented Schlieren techniques, we have presented imaging blurring and deviation against three typical backgrounds. The imaging quality has been evaluated using the Peak Signal-to-Noise Ratio (PSNR). We have quantitatively analyzed the influences of flight conditions and imaging system parameters on the imaging characteristics. The key findings of our investigation are as follows: The disturbance flow field significantly impacts the background images, resulting in varied degrees of blurring and deviation. The extracted profiles of the disturbance flow field from the deviated images are in accordance with current experimental studies. As the flight altitude increases, the phase difference and deflection angle decrease, leading to a reduced blurring of the images and higher PSNR, owing to the lower atmospheric density at higher altitudes. Conversely, as the Mach number increases, the phase difference and deflection angle increase due to the greater compression of the atmosphere surrounding the hypersonic target. However, the degree of image blurring decreases due to the larger flow field area. The majority of pixel shifts in imaging deviation are at the sub-pixel level, making them indistinguishable to the naked eye. Nevertheless, the profile of the flow field can be extracted from the deviated images. The imaging deviation is closely related to the focal length, pixel size, and orbit height of the space-based imaging system. Our quantitative analysis highlights the importance of a space-based imaging system with a large focal length and a small pixel size, while a low orbit or sun-synchronous orbit is preferred. The imaging results confirm the feasibility of detecting hypersonic targets through disturbance flow field imaging, providing an alternative detection approach when  
Figure 14: The influence of pixel size and focal length on \(y\) direction pixel deviation: (**a**) the influence of pixel size under different flight altitudes where the focal length is 1.0 m; (**b**) the influence of pixel size under different Mach numbers where the focal length is 1.0 m; (**c**) the influence of focal length under different flight altitudes where the pixel size is 5 \(\upmu\)m; (**d**) the influence of focal length under different Mach numbers where the pixel size is 5 \(\upmu\)m.  
traditional infrared and radar systems lose effectiveness. Moreover, the remote sensing detection of the flow field profile around hypersonic targets not only contributes to the field of high-speed target detection but also enables an in-depth analysis and optimization of the performance and flight characteristics of hypersonic targets. This research also offers theoretical support for experimental studies in this area. Conceptualization, C.Z. and S.G.; methodology, S.G.; software, N.C. and S.G.; formal analysis, N.C., S.G., C.Z., Y.W. and F.T. ; investigation, F.T. ; data curation, N.C.; writing--original draft preparation, N.C.; writing--review and editing, N.C., S.G. and C.Z. ; supervision, C.Z. ; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the Major International (Regional) Joint Research Project of National Natural Science Foundation of China (42020104008); The Key Program of National Natural Science Foundation of China (41530422); Shaanxi Fundamental Science Research Project for Mathematics and Physics (22 JSZ007); National High Technology Research and Development Program of China (863 Program) (2012 AA121101); The General Program of National Natural Science Foundation of China (617/5176); Shaanxi Province Key Research and Development Program of China (2021 GXLH-Z-058); National Natural Science Foundation of China (62005221); Open Foundation of the State Key Laboratory of applied optics (SKLAO2021001A04). Not applicable.