## 2 THz Imaging Character of Parabolic Antennas
Since one of the parabola's properties is that \(\beta=2\varphi\), the equation of the parabola can be formulated in this polar coordinate manner:\[\rho=\frac{2K}{1+\cos(2\varphi)}. \tag{19}\]  
Figure 3 illustrates that the location of the point of specular reflection moves along the parabola as the incident wave continuously varies angle, and the range of angle \(\varphi\) can be computed as follows:  
\[\varphi\in\left[-\frac{1}{2}\arctan\left(\frac{8 DF}{16K^{2}-D^{2}}\right),\frac {1}{2}\arctan\left(\frac{8 DF}{16K^{2}-D^{2}}\right)\right]. \tag{20}\]  
Owing to this distinctive feature, the paraboloid is classified as a sliding scattering center [28]. The point of specular reflection significantly impacts the Radar Cross Section (RCS). Additionally, the rim of the paraboloid contributes to the RCS [29]. Nonetheless, when the specular reflected point is present, this smaller part is often negligible. Therefore, the mirror-like scattering point is a characteristic of the paraboloidal imaging, in this case. According to the analysis of the sliding scattering center of the parabolic antenna, the imaging characteristics of a parabolic antenna can be categorized into specular scattering points and non-specular scattering points. Furthermore, through observations from multiple simulation experiments, we have found that the non-specular scattering points can be divided into two main categories: edge pair-points and ellipse arc. To illustrate the imaging characteristic of parabolic antenna, we give an example of EM. The parameters of the parabolic antenna are as follows: radius = 25 cm, focal depth = 25 cm, edge width = 1 cm, and relative elevation angle \(\psi=10^{\circ}\). Three typical observation apertures, AB, CD, and EF, are selected, and their imaging results are shown in Figure 4c-e, respectively. The images are presented in dB magnitude scale. The imaging result under the aperture AB has the one specular reflection point, whereas those of the apertures EF and CD have the scattered points about the edge of a paraboloid, which is consistent with the above theoretical analysis. Furthermore, it is observed that in Figure 4a,b, the amplitude discrepancies at the edge points are subject to substantial changes when the observation aperture is no longer aligned with the specular direction. This implies that the amplitude of the less intense scattered point could potentially exceed the dynamic range, resulting in it being obscured. \[N=P\cdot R_{W}\cdot R_{V}\cdot R_{U}\cdot M=P^{{}^{\prime}}\cdot M \tag{12}\]0 Geometry projection diagram of ISAR imaging. Therefore, the imaging properties of the satellite are analyzed by forward modeling and electromagnetic computations. In the case of the forward modeling, the satellite's Computer-Aided Design (CAD) model and its geometry and size are depicted in \[N=P\cdot R_{W}\cdot R_{V}\cdot R_{U}\cdot M=P^{{}^{\prime}}\cdot M \tag{12}\]1 In particular, the satellite model adopted in this paper has a total length of 8.6 m, with each side of the sail panel measuring 3.3 m in length and 0.8 m in width and the diameter of the parabolic antenna being 1.1 m, as illustrated in \[N=P\cdot R_{W}\cdot R_{V}\cdot R_{U}\cdot M=P^{{}^{\prime}}\cdot M \tag{12}\]2 Dependent on the corporeal composition and shell curvatures listed in Table 1, five primary scattering elements are identified. Among these five elements, the parabolic antenna, solar panels, main body, propeller, and lens are clearly discernible in the imaging outputs. In addition, through analysis, we believe that the parabolic antenna, solar panels, and main body are the primary components of the satellite and are mainly characterized by single reflections, with multiple scattering occurring in a few cases. Additionally, although the lens and propellers are cavity structures that lead to multiple scattering, their component sizes are relatively small, they occupy a minor proportion within the satellite, and they do not interfere with the targets we aim to detect.