# Analysis and Correction of Antenna Pattern Effects in AMAO Spaceborne SAR Images
## 6 Discussion  
AMAO spaceborne SAR, with its powerful beam-steering capability, can acquire rich information flexibly and efficiently. On the other hand, it brings new challenges to radiometric calibration. In particular, the antenna pattern effect and correction are concerns for SAR calibration engineers. The main differences are that for conventional SARs, the AAP is not important to the radiometric accuracy, so the antenna pattern correction usually refers to the correction in the range direction (see [9]). Current spaceborne SARs have achieved high radiometric accuracy with this EAP correction approach. However, in the case of AMAO, especially with high-squint and high-resolution, targets at different positions within a scene are exposed to different antenna patterns, each a different cut of the 2D antenna pattern, resulting in complex 2D effects on image. The spatial-variant radiometric error can reach about 1.7 dB, as analysis in Section 3 and experimental results in Section 5 show. The correction error of the antenna pattern effect is a systematic error, which must be corrected accurately to achieve the consistency and accuracy of SAR radiometric measurements. In this paper, the antenna pattern characteristics are analyzed for the first time. The 2D variation is identified in the antenna pattern of a squint beam, which is mainly because the two angles--azimuth and the elevation off-axis--are both variables, especially in the high-squint, high-resolution case. Moreover, the antenna beam is often steered to a rotation center during AMAO SAR acquisition to achieve high resolution and/or wide swath. As a side effect, the shape of the antenna pattern becomes less than ideal. The spatial variation and nonideality of the antenna pattern make radiometric normalization difficult. Since the spatial variation in antenna pattern is not considered in [9], the EAP correction approach is precise only at the reference squint angle, but causes high relative variation across the high-squint image. Numerical examples of the SAR image calibrated with EAP show that the 2D variant effect of the antenna pattern does exist in the AMAO SAR image and can be very high (e.g., 1.69 dB in the example). A straightforward approach to antenna pattern correction is to numerically evaluate the integrated energy per resolution cell or coarser grid, taking the full 2D antenna pattern into account. In this way, the authors in [14; 15] carefully considered the full 2D antenna pattern in airborne F-SAR calibration. However, this method requires many integration operations. The considerations needed for airborne SAR are mainly the variations in the platform track and the sensor attitude angles, which are not the main problems of AMAO spaceborne SAR. Therefore, this paper developed a practical radiometric error model for AMAO spaceborne SAR. The model contains an elevation-dependent linear factor and a signal centroid shift factor, both of which can be derived from the antenna pattern. On \begin{table}
\begin{tabular}{c c c c c c c c} \hline Azimuth location (m) & \(-4500\) & \(-3000\) & \(-1500\) & \(0\) & \(1500\) & \(3000\) & \(4500\) \\ \hline Integrated energy (dB) & \(0.028\) & \(0.010\) & \(0.002\) & \(0.000\) & \(0.003\) & \(0.011\) & \(0.032\) \\ \hline \end{tabular}
\end{table} 
Table 4: Imaging results for targets at azimuth scene center, calibrated with reference EAP. \begin{table}
\begin{tabular}{c c c c c c c} \hline Azimuth location (m) & \(-4500\) & \(-3000\) & \(-1500\) & \(0\) & \(1500\) & \(3000\) & \(4500\) \\ \hline Integrated energy (dB) & \(0.028\) & \(0.010\) & \(0.002\) & \(0.000\) & \(0.003\) & \(0.011\) & \(0.032\) \\ \hline \end{tabular}
\end{table} 
Table 5: Imaging results for targets at azimuth scene center, calibrated by the proposed method. this basis, an improved antenna pattern correction approach is proposed.