# Interferometric DEM-Assisted High Precision Imaging Method for ArcSAR
## 6 Experiment
### The Simulation Experiment of Interferometric ArcSAR Extraction DEM  
Based on the geometric model and working mode of the ArcSAR system, we uses the existing RCS scenes and DEM data to simulate the ArcSAR image on the slant range. To facilitate subsequent experiment, the simulated ArcSAR image is shown in the polar coordinate system in Figure 18. The necessary parameters are given in Table 2.  
Figure 18: The RCS scenes for simulation, the DEM data for simulation and the simulated ArcSAR image in polar coordinate system. \(R_{\rm max}\) represents the maximum slant range from the imaging scenes to the ArcSAR system and \(R_{\rm min}\) represents the minimum slant range from the imaging scenes to the ArcSAR system. They are marked in Figure 18b. The point o in Figure 18b is the rotation center. We defined the height of rotation plane to be 0 m. In Figure 18c, the horizontal axis represents the rotation angle of the ArcSAR system, and the vertical axis is the interval from \(R_{\rm min}\) to \(R_{\rm max}\). The ArcSAR imaging result in Figure 18c was considered to be the main complex image for interference. The height baseline \(\Delta z\) was 0.2 m. We simulated the sub SAR complex image for interference. The interferometric phase can be obtained by interference with the main SAR complex image and the sub SAR complex image. The interferometric phase image is shown in Figure 19.  
The measured interferometric phase value shown in Figure 19 was modulated by \(2\pi\), ranging from \(-\pi\) to \(\pi\), and there was an ambiguity of many cycles in the interferometric phase value. Thus, it was necessary to perform phase unwrapping on the interferometric phase image. The branch cut method was applied to interferometric phase unwrapping [25; 26]. In addition, to reduce the complexity of phase unwrapping, we also removed the flat phase of the interferometric phase. After the flat phase removal and phase unwrapping operations, the interferometric phase image could be used for DEM inversion. The DEM image obtained by the interferometric phase inversion is the slant range image, as shown in Figure 20a. We utilized the proposed polar coordinate transformation method to transform it to the ground range. The DEM image on the ground range is shown in Figure 20b. We also calculated the mean square error (MSE) of the DEM image in Figure 20b with the existing DEM data. The result of the MSE was only 1.69. It can be seen that the interferometric ArcSAR could acquire high-precision DEM image of the scenes. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(r\) (m) & \(\theta_{\rm bw}\) (rad) & \(\theta\) (rad) & \(\lambda\) (mm) & \(Br\) (MHz) & \(R_{\rm max}\) (m) & \(R_{\rm min}\) (m) \\ \hline \(1\) & \(\pi\)/\(3\) & \(2\pi\) & \(17.50\) & \(150\) & \(400\) & \(200\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experiment parameters. Figure 19: Interferometric phase image of phase wrapping. Distributed Scenes Imaging Simulation Experiment Verification the DEM-Assisted High Precision Imaging Method for ArcSAR  
We used the distributed scenes imaging simulation experiment to image the scenes given in Experiment 1. The necessary parameters are shown in Table 2. The DEM image acquired in Experiment 1 was applied to assist ArcSAR imaging. In addition, we also used the traditional imaging method of ArcSAR to image the distributed scenes on the reference plane as the comparison. The height of the reference plane was 0 m. Based on Equations (17)-(19) in Section 3.2, we found the defocused area and focused area of the distributed scenes imaging results on the reference plane, as shown in Figure 21.  
The imaging results by the two imaging methods in Cartesian coordinate system are shown in Figure 22.  
It can be seen that the ArcSAR imaging result of the scenes on the reference plane showed severe defocusing, and the ArcSAR image obtained by the proposed imaging method was not defocused.