## 4 Image Quality Assessment Results
\[X_{N}(k_{1},k_{2})=\sum_{n_{1}=0}^{N-1}\sum_{n_{2}=0}^{N-1}x(n_{1},n_{2})exp \bigg{\{}-j2\pi\bigg{(}\frac{k_{1}n_{1}}{N}+\frac{k_{2}n_{2}}{N}\bigg{)} \bigg{\}}\hskip 14.226378 ptk_{1},\ k_{2},\ n_{1},n_{2}\in[0,N-1] \tag{15}\]\[X_{M}(k_{1},k_{2})=\left\{ \begin{array}{ll}L^{2}\times X_{N}(k_{1},k_{2})&k_{1} \in\left[0,\frac{N-1}{2}\right],k_{2}\in\left[0,\frac{N-1}{2}\right]\\ 0&k_{1}\in\left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1\right],k_{2}\in\left[0,\frac {N-1}{2}\right]\\ L^{2}\times X_{N}(k_{1}-M+N,k_{2})&k_{1}\in\left[\frac{N-1}{2}+1,M-1\right],k_{2 }\in\left[0,\frac{N-1}{2}\right]\\ 0&k_{1}\in\left[0,M-1\right],k_{2}\in\left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1 \right]\\ L^{2}\times X_{N}(k_{1},k_{2})&k_{1}\in\left[0,\frac{N-1}{2}\right],k_{2}\in \left[\frac{N-1}{2}+1,M-1\right]\\ 0&k_{1}\in\left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1\right],k_{2}\in\left[\frac{N -1}{2}+1,M-1\right]\\ L^{2}\times X_{N}(k_{1}-M+N,k_{2})&k_{1}\in\left[\frac{N-1}{2}+1,M-1\right],k_{ 2}\in\left[\frac{N-1}{2}+1,M-1\right]\\ \end{array} \right. \tag{16}\]  
\[\hat{x}(m_{1},m_{2})=\frac{1}{MM}\sum_{i_{1}=0}^{M-1}\sum_{k_{2}=0}^{M-1}X_{M} (k_{1},k_{2})exp\left\{+j2\pi\left(\frac{k_{1}m_{1}}{M}+\frac{k_{2}m_{2}}{M} \right)\right\}\ k_{1},\ k_{2},\ m_{1},m_{2}\in[0,M-1] \tag{17}\]  
Here, \(L\) is the interpolation multiplier. Figure 10 shows the one-dimensional IRF contours of the 3 rd CR (CR-3) in range and azimuth directions for UFS and FSI mode data, where (a) and (b) correspond to the UFS mode and (c) and (d) correspond to the FSI mode. It can be seen that IRFs all show a shape similar to sinc function [28], which is consistent with the general rule of point target echo signal during SAR imaging. Figure 10: CR-3 one-dimensional contours of IRF in the range and azimuth directions: (**a**) range direction interpolation of UFS mode data on 12 May; (**b**) azimuth direction interpolation of UFS mode data on 12 May; (**c**) range direction interpolation of FSI mode data on 15 May; (**d**) azimuth direction interpolation of FSI mode data on 15 May. According to the point target IRFs, the spatial resolution, PSLR, and ISLR of each point target on the two modes data were calculated, and the results are presented in Tables 3 and 4, respectively. As shown in Table 3, for UFS mode data, the evaluated resolutions in range and azimuth directions are \(1.365\) and \(2.876\) m, respectively, which are better than that of the nominal resolution of \(3\) m. The evaluated PSLR in range and azimuth directions are \(-22.832\) and \(-23.881\) dB, respectively, which are better than that of the design index of C-SAR/01 of \(-22\) dB. Lastly, the evaluated ISLR are \(-21.853\) and \(-20.587\) dB, which are better than that of the design index of \(-15\) dB. As shown in Table 4, for FSI mode data, the calculated resolutions in range and azimuth directions are \(1.634\) and \(4.807\) m, respectively, which are better than that of the nominal resolution of \(5\) m. The evaluated PSLR in range and azimuth directions are \(-23.685\) and \(-23.844\) dB, respectively, which are better than that of the design index of \(-22\) dB. The calculated PSLR in range and azimuth directions are \(-20.975\) and \(-19.150\) dB, respectively, which are better than that of the design index of \(-15\) dB.