# Analysis and Correction of Antenna Pattern Effects in AMAO Spaceborne SAR Images
## 1 Introduction  
Synthetic aperture radar (SAR) provides high-resolution observation under most weather conditions during day and night. Conventionally, spaceborne SARs observe in cross-track directions. In recent years, based on the continuously improved beam-steering capability, a novel azimuthal multi-angle observation (AMAO) spaceborne SAR technique was put forward in [1] and relevant researches have been conducted in [2; 3; 4; 5; 6; 7; 8]. With highly flexible antenna beams, AMAO spaceborne SAR can achieve efficient observation of multi-azimuth information, such as the target scattering information, geometric information, and motion information.  
SAR images (sequences) require accurate calibration to achieve comparability and quantitative application. The antenna pattern is a primary source of errors in SAR radiometric calibration. From the point of view of SAR radiometric calibration in [9], the two antenna patterns play separate roles: the elevation antenna pattern (EAP) determines the spatial radiation gain over the swath, and the azimuth antenna pattern (AAP) is generally negligible except for in ScanSAR correction. Current spaceborne SARs have achieved high radiometric accuracy with the EAP correction. For example, the radiometric accuracy of PALSAR on ALOS is 0.22 dB (1\(\sigma\)) from the Amazon forest data [9], and that of TerraSAR-X is better than 0.3 dB (1\(\sigma\)) during the commissioning phase [10]. However, for the novel AMAO SAR, the antenna beam is steered to a squint angle of up to several tens of degrees [7; 8] and rotated to extend the target exposure time for high resolution. In an on-ground point target view, the antenna pattern becomes broadened, nonideal, and varies in space. Commoncorrection methods do not apply to the spatial-variant antenna pattern, so radiometric variations appear in the image. Therefore, it is necessary to analyze the antenna pattern effects in the AMAO SAR imaging context, and then propose the corresponding innovative correction method to deal with the radiometric variations in AMAO SAR images.  
This paper firstly gives the geometric properties of AMAO SAR imaging, establishes an antenna pattern model accounting for squint beam-steering, and then analyzes the antenna pattern characteristics in the AMAO SAR imaging context. Subsequently, a practical and analytical model of the antenna pattern effect on SAR image intensities is presented by introducing two factors derived from the two-dimensional (2D) antenna pattern. After that, the improved method of the antenna pattern correction is given to normalize the 2D radiometric effects. Finally, experiments are conducted to quantify the antenna pattern effects and verify the precision of the proposed correction method.  
The rest of this paper is organized as follows: the antenna pattern characteristics are presented in Section 2. The antenna pattern effects in images are investigated in Section 3, and the improved correction method is given in Section 4. Experiments are performed in Section 5. The proposed approach and the results are discussed in Section 6, and the conclusions are summarized in Section 7.