## 2 Dechirp Influence on Squint Sliding-Spot Imaging Mode
### Extension of the Range-Doppler Model after Dechirp  
The classical geometric positioning model--RD equation--is as follows [23], which associates the target position vector with the position and velocity vector of the SAR satellite at a certain azimuth moment. At this moment, the observation geometry between SAR and the target is determined by the distance and the doppler frequency of the target from SAR. This model closely fits the geometric property of SAR imaging, and can perform absolute positioning toward any image pixel without control points, so it is widely used in the system-level geometric processing of spaceborne SAR. \[\left\{ \begin{array}{c}\text{Rangeequation:}\ r=\left|\overset{ \rightharpoonup}{S}-\overset{\rightharpoonup}{T}\right|\\ \text{Dopplerequation:}\ f_{d}=-\frac{2}{\lambda R}\left(\overset{ \rightharpoonup}{S}-\overset{\rightharpoonup}{T}\right)\cdot\left(\overset{ \rightharpoonup}{V_{S}}-\overset{\rightharpoonup}{V_{T}}\right)\\ \text{Earthmodelequation:}\ \frac{T_{x}^{2}+T_{y}^{2}}{(R_{x}+h)^{2}}+\frac{T_{z}^{2}}{R_{ p}^{2}}=1\end{array} \right. \tag{6}\]  
\(\overset{\rightharpoonup}{S}\) is the SAR antenna center position vector and its velocity vector is \(\overset{\rightharpoonup}{V_{S}}\). \(\overset{\rightharpoonup}{T}=\left(T_{x},T_{y},T_{z}\right)\) is the ground position vector of the target point, and its velocity vector is \(\overset{\rightharpoonup}{V_{T}}\). \(r\) represents the range between the target point and SAR, and \(\lambda\) is the echo center wavelength. \(f_{d}\) is the doppler center frequency at this azimuth moment, which is output by the imaging processing. \(R_{e}\) and \(R_{p}\) are the Earth ellipsoid parameters. The RD equations can be directly applied in the geometric processing of the side-looking strip or low squint mode. However, high-resolution or squint SAR modes must be achieved through a large range of the azimuth scanning angle, which means the azimuth aliasing phenomenon under this condition may be very complicated and the dechirp operation before the focusing imaging process is necessary. As shown in Section 2, the key step of dechirp is to multiply the range-compressed data within the azimuth time and range frequency domain by a slant range bias factor \(\widetilde{Q}(f_{\tau},\eta)\), which varies non-linearly along the azimuth direction so that the curved range history of each target becomes symmetrical and straight. As shown in Figure 6, the SAR satellite antenna rotates through an angular range around the virtual rotation point and continuously observes a certain target during sliding-spot imaging. The curved range history of the target echo data after range compression is shown in Figure 6(a). After dechirp, the range history is straightened as in Figure 6(b), and then the data are neatly cropped along the azimuth direction as in Figure 6(c). Due to the time domain offset introduced by dechirp, the near range of each azimuth line on the new one-dimensional range image (Figure 6(c)) varies along the azimuth direction. Then the imaging algorithms can be executed on this dechirped new data to generate an image. Since the original geometric relationship between the image point and the satellite has been destroyed during the dechirp process, the main purpose of this paper is to re-establish the geometric relationship between the image and the satellite so as to propose a geometric processing scheme suitable for the dechirp imaging algorithm. As validated in [20], after dechirp processing, the range history of each target is shifted to be symmetrical in the azimuth direction, and the doppler center is moved to zero. Thus, there are two characteristics of this image output in the virtual range history space after dechirp: one is that the range history of any target is symmetrical and straight relative to the satellite position at the imaging azimuth moment of the target; the other is that on the entire satellite orbit, the distance between the target and the satellite at this moment is the shortest.