# Imaging Characteristics of Disturbance Flow Field Surrounding a Hypersonic Target
## 1 Introduction  
Hypersonic targets in near space are characterized with high flight speed, excellent maneuverability, and great stealth; the importance of their efficient detection has been emphasized; and numerous studies on infrared [1, 2] and radar [3, 4] technologies for space-based and ground-based detection have been conducted. When an aircraft flies in near space at hypersonic speed, the surrounding air is violently compressed, generating a high-temperature, high-pressure, and high-density flow field [5]. The surface layers of the aircraft are ablated into gas under the effect of the high-temperature and high-pressure flow field and ionized with the surrounding air, forming a plasma sheath around the aircraft. This plasma sheath refracts and absorbs electromagnetic waves, creating challenges for radar detection [6, 7]. Furthermore, the low flight trajectory of the target in near space and the curvature of the Earth also impose difficulties on radar detection. In some cases, infrared detection proves ineffective due to the aircraft's use of gliding without powered propulsion, as well as the advancements in infrared stealth materials. However, throughout the flight of the aircraft, the disturbance flow field inevitably arises, offering an opportunity for measurement and detection. The non-uniform refractive index distribution and variation of the flow field affect the transmission of target light,resulting in the blurring and deviation of the background image [8; 9]. Current mechanism analysis or experimental exploration focuses on the impact of the flow field near the optical dome of hypersonic guided missiles on the transmission of target light [10; 11; 12], which is incompatible with the optical transmission through the entire disturbance flow field. For studying the optical transmission through the entire disturbance flow field, an effective approach is to visualize it. In April 2011, October 2014, February 2015, and December 2018, NASA [13] conducted a series of flight tests against the desert flora below 10 km and visualized the disturbance flow field of single and dual transonic aircraft through Background-Oriented Schlieren, respectively. The Background-Oriented Schlieren (BOS) technique is a flow visualization method based on the deflection of light after passing through the flow field, and measures the variation of the flow field density by computer image processing, with the advantages of the simple optical system, ensuring easy and fast measurement. Currently, the BOS technique is mainly applied to the parameter measurement of flow fields [14; 15], flow visualization [16], and the optical system transfer function measurement [17]. NASA has indeed visualized the flow field, but its flight tests were conducted for transonic aircraft at altitudes below 10 km and at Mach number approximately 1.0 Ma, where the atmospheric components and conditions are quite different from those of hypersonic aircraft in near space [18]. Additionally, NASA has not disclosed specific details about their experiments, and it is also difficult to perform BOS experiments in near space. Therefore, it is essential to investigate the imaging characteristics of the disturbance flow field surrounding hypersonic targets. This paper presents a comprehensive investigation into the imaging characteristics of the disturbance flow field. The disturbance flow field of a hypersonic target under diverse flight conditions was simulated using the computational fluid dynamics software ANSYS Fluent. Ray tracing was performed utilizing the fourth-order Runge-Kutta algorithm, enabling the calculation of essential optical parameters, such as refractive index gradients, phase differences, and deflection angles. Moreover, the imaging blurring and imaging deviation were analyzed against three representative backgrounds (desert, ocean, and city) using Fourier Optics and Background-Oriented Schlieren techniques.