# Error Source Analysis and Correction of GF-3 Polarimetric Data
## 3 Influence Analysis of Error Source
### Error of the Antenna Array  
For the antenna, there are crosstalks (\(\delta_{1}\), \(\delta_{2}\), \(\delta_{3}\), \(\delta_{4}\)) and channel imbalances (\(f_{t}\), \(f_{r}\)) simultaneously affecting polarization observation [6]. GF-3 satellite uses dual-polarization slotted waveguide array, in which the isolation of waveguide port is more than 65 dB and the cross-polarization level within scanning range is less than \(-\)55 dB at central frequency [21]. Furthermore, before satellite launching, the ground test result shows that polarization isolation of GF-3 global antenna is better than 35 dB [22; 23], which is also proved by the follow-up quality assessment results (in Section 4.2). Hence, the GF-3 antenna is highly isolated and crosstalks have negligent influence on the PolSAR data. In addition, the amplitude imbalance of the antenna is eliminated by antenna pattern correction in the imaging process, which is proved to be quite stable. Therefore, we focus on the phase imbalance which needs to be corrected. Specific sources of the phase imbalance include three aspects: (1) No coincidence of H and V antenna center; (2) Differences of H and V waveguides; (3) Distinction of amplitude and phase weighting between H and V antenna. Here, we describe these three error components in detail. (1) No coincidence of H and V antenna center  
The slotted waveguide array of the GF-3 satellite is composed of alternately arranged H and V waveguides [21], as shown in Figure 4a, so there is a slight difference between H and V antenna center, i.e., there is a baseline (B) between the H and V antenna. The geometric relationship is shown in Figure 5, where \(x\) axis is the azimuth direction of the antenna, which is perpendicular and into the paper, \(y\) axis is the range direction of the antenna array as shown, and \(z\) axis is perpendicular to \(x\)-\(y\) plane. Here, H is the H polarization antenna center, V is the V antenna center, B is the baseline between H and V antenna, \(\beta\) is the angle between the \(y\) axis and the ground surface, and \(\alpha\) is the angle between B and the ground surface. It should be mentioned that the baseline (B) does not coincide with the \(y\) axis, which is due to the different sizes of H and V waveguides, as shown in Figure 4b. Figure 3: Sampling delay error of (a) transmit channel and (b) receive channel extracted by internal calibration. three different beams including Q7, Q17, Q25 for GF-3, look angles of which are \(29.36^{\circ},36.41^{\circ}\), and \(41.18^{\circ}\), respectively. \[\left\{ \begin{array}{l}\theta_{r,2}=C\\ \theta_{t,2}=C\end{array} \right. \tag{3}\]  
Distinction of amplitude and phase weighting between H and V antenna  
The GF-3 satellite adopts a large-scale active phased array antenna [22]. The pattern of the entire antenna array is obtained by the weighted superposition of multiple array elements [25]. However, weights of amplitude and phase are different at different polarization, which leads that the phase of antenna pattern potentially being inconsistent. The GF-3 antenna has good phase consistency over the effective beam width, so the effect of this factor can be corrected using the peak phase of antenna pattern [21]. We can obtain the peak phase of the transmit and receive antenna in different polarization (denoted as \(HT(\phi)\), \(VT(\phi)\), \(HR(\phi)\) and \(VR(\phi)\)) by the high-accuracy antenna model of GF-3 [21]. Then, phase imbalances of this part can be written as Equation (4):  
\[\left\{ \begin{array}{l}\theta_{r,3}=VR(\phi)-HR(\phi)\\ \theta_{t,3}=VT(\phi)-HT(\phi)\end{array} \right. \tag{4}\]  
Based on the above analysis of three factors, the phase imbalance (\(\theta_{t},\theta_{r}\)) caused by antenna array is expressed as Equation (5). \[\left( \begin{array}{l}\theta_{r}=\frac{2\pi B\sin(\alpha-\phi)}{\lambda}+C+ VR(\phi)-HR(\phi)\\ \theta_{t}=\frac{2\pi B\sin(\alpha-\phi)}{\lambda}+C+VT(\phi)-HT(\phi)\end{array} \right.