## 2 Principles of the Formation and Elimination of Stray Light Backgrounds  
Stray light is non-imaging light that radiates to the detector surface or imaging light that propagates via an abnormal path and reaches the detector. The influence of the formation mechanism and the principle of eliminating nonuniform backgrounds from surveillance images will be discussed in detail in this section. There are different sources of stray light, which are of three main types: (1) internal radiation stray light, which is the infrared heat radiation generated by high-temperature optomechanical components such as control motors and temperature-controlled optics inside the system during its normal operation; (2) non-target stray light beyond the field of view, which refers to non-target optical signals that propagate directly or indirectly on the focal plane of the image sensor, and which come from radiation sources located outside the field of view of an optical telescope; and (3) imaging target stray light in the field of view, which can be understood as light rays from targets that reach the focal plane of the detector via abnormal means. Regarding the internal radiation stray light, its wavelengths are mostly distributed on the micrometer scale, so this kind of stray light mainly influences the infrared imaging system rather than the space-based wide-field surveillance systems applied to visible light in this paper. Hence, we ignore its effect on surveillance images. Non-target stray light beyond the field of view exists widely in all kinds of optical telescopes, especially in the  
Figure 1: Flowchart of the proposed IBSGM method. large field optical telescopes used to detect faint targets. After strong stray light enters the optical system, it causes a nonuniform noise signal to reach the detector, increasing the image gray values and spreading the gray scale from one edge to the other. The main reason for this is a gradual change in the material scattering intensity. Furthermore, since stray light is beyond the field of view, the gray value is maximized at the corresponding edge of a surveillance image, as shown in Figure 2a. We name this the first type of stray light background. Imaging target stray light in the field of view also causes a nonuniform noise signal and increases the gray values of surveillance images, resulting in a relatively bright area in the surveillance image with gray scale spreading from the center to the periphery, as shown in Figure 2b. The primary cause of this is the complete reflection in the lens that occurs when light from brighter stars reaches the lens at a specific angle. We name this the second type of stray light background. Any complex image can be regarded as a combination of these two forms of background. To better comprehend the features of nonuniform backgrounds in surveillance images, we will analyze them using energy transfer equations [26]. To simplify the complex stray light transmission process, we can divide the transmission path into several parts, including several emitting and receiving surfaces where the receiving surface of each process is the emitting surface of the next. The transmission of stray light on any two surfaces conforms to the radiation transfer theory [27], the principle of which is shown in Figure 3.  
Figure 3: Radiation transfer schematic. Figure 2: Two types of simulated stray light background gray-scale images. (**a**) the first type; (**b**) the second type.