# Interferometric DEM-Assisted High Precision Imaging Method for ArcSAR
## 4 The Principle of Interferometric DEM-Assisted High Precision Imaging Method for ArcSAR
### DEM Image Transforming from Slant Range to Ground Range  
In this paper, the ArcSAR images used for extracting DEM are the slant range images. Therefore, on the range direction, the pixel units of the ArcSAR image are equally spaced according to the slant range. The DEM image obtained by the interference with the ArcSAR images is also the slant range image (each pixel unit on the DEM image represents DEM data). However, assisted ArcSAR imaging requires the use of DEM image on the ground range. Thus, it is necessary to transform the DEM image from slant range to ground range.  
The process of DEM image from slant range to ground range in linear scanning GBSAR is generally achieved in Cartesian coordinate system. This is because the range direction and azimuth direction of  
Figure 7: The model of interferometric ArcSAR.  
the linear scanning GBSAR are along the coordinate axes of the Cartesian coordinate. Thus, in the Cartesian coordinate system, the linear scanning of GBSAR only requires operating in one dimension to complete the transformation of the DEM image.  
However, if we realize the transformation of ArcSAR DEM image in Cartesian coordinate system, we have to operate in two dimensions. Because the azimuth direction of the ArcSAR system is the rotation direction of the antenna, and the range distance of the ArcSAR is the radial direction of the antenna motion track. To simplify the transformation process of ArcSAR DEM image, we propose a transformation method in polar coordinate system.  
The DEM image in polar coordinate system is shown in Figure 8. The \(\theta\)-axis of the coordinate system represents the azimuth direction. The pixel units in azimuth direction are equally spaced according to the rotation angle (\(\theta\)) of the ArcSAR system, and there are N pixel units in this direction. The \(R\)s-axis of the coordinate system represents  
Since \(R_{\rm ge}(j)\) is numerically close to \(R_{\rm ne}\), the position of their corresponding DEM data on the DEM image will be very close. Therefore, we assume that the DEM data of \(R_{\rm ge}(j)\) are also \(H_{\rm ne}\).
7. According to \(R_{\rm ge}(j)\) and \(H_{\rm ne}\), the slant range corresponding to \(R_{\rm ge}(j)\) can be calculated: \[R_{\rm new} = \sqrt{R_{\rm ge}^{2}(j)+H_{\rm ne}^{2}}\] (30)
8. Let \(R_{\rm new}\) interpolate on the sequence \(R_{\rm n}\) (the purpose of this operation is to find the position of \(R_{\rm new}\) on the sequence \(R_{\rm n}\)). According to the position of \(R_{\rm new}\) on the sequence \(R_{\rm n}\), we can find the DEM data corresponding to \(R_{\rm new}\) on the sequence \(DEMs\), which we define as \(H_{\rm new}\).
9. Since \(R_{\rm ge}(j)\) is the ground range corresponding to \(R_{\rm new}\), the DEM data of \(R_{\rm ge}(j)\) are also \(H_{\rm new}\).  
Through the above steps, the DEM data with coordinate (\(\theta_{i}\), \(R_{\rm g}\)) on the slant range are transformed to the ground range. The coordinate of these DEM data on the ground range is (\(\theta_{i}\), \(R_{\rm ge}(j)\)). The above steps only describe the process of transforming one DEM datum in the DEM image from the slant range to ground range. The complete transformation process is shown in Figure 10.  
Figure 10: The polar coordinate transformation method proposed in this paper.  
Figure 9: Flow chart of calculating the sequence \(R_{\rm g}\).