# A High-Resolution SAR Focusing Experiment Based on GF-3 Staring Data
## 2 Focusing Experiment Based on GF-3 Staring Data
### Antenna Pattern Modulation  
GF-3 uses an active phased array antenna to achieve azimuth beam steering. However, the active phased array antenna has three drawbacks in practical application.  
At first, the scanning range is limited by the distance between the two adjacent elements \(D\), which is equivalent to the ratio of antenna aperture \(D_{zz}\), and the number of element \(N_{zz}\) in azimuth. If \(D\) is not small enough, grating lobes will appear and constrain the steering range. The position of the grating lobes \(\theta_{g}\) can be described by Equation (24):  
\[\theta_{g}=\arcsin\left[\sin(\theta_{s})\pm n\frac{\lambda}{D}\right] \tag{24}\]  
where \(\theta_{s}\) is the steering angle, \(\lambda\) is the carrier wavelength, and \(n\) is an arbitrary non-zero integer. Figure 3b shows the main lobe and the grating lobes between \([-15^{\circ},\,15^{\circ}]\) when \(\theta_{s}=1.9^{\circ}\). There are six peaks in Figure 3b, and obviously, the highest peak is the main lobe and the others are the grating lobes. The interval between the two adjacent peaks is about \(5.1^{\circ}\), which means that the maximum steering range is \(5.1^{\circ}\). In operational SL or ST mode, GF-3 could steer from \(-1.9^{\circ}\) to \(1.9^{\circ}\) in azimuth.  
In addition, the antenna's maximum power gain changes with the steering angle. Equation (25) shows the active phased array antenna pattern  
\[G=\sqrt{G_{0}}\cdot sinc\bigg{(}\frac{D}{\lambda}\pi\sin(\theta)\bigg{)}\cdot \sqrt{\frac{N_{el}}{N_{az}}}\cdot\bigg{|}\frac{N_{az}}{n}\exp\bigg{\{}j\frac{2\pi }{\lambda}nD[\sin(\theta)-\sin(\theta_{s})]\bigg{\}}\bigg{|} \tag{25}\]  
where \(G\) is the power gain of the array antenna, \(G_{0}\) is the power gain of a single element, \(N_{el}=64\) is the number of elements in elevation, \(\theta\) is the look direction or azimuth antenna pattern angle, and \(\theta_{s}\) is the steering angle. The envelop of array gain is modulated by a \(sinc(\cdot)\) function and Figure 3a,b shows relationship between the steering angle and the antenna pattern. The influence of the element pattern is more obvious in TOPSAR [26]. In this experiment, 32,130 frames of data in azimuth were acquired, and the normalized modulation factor of every frame can be found in Figure 3c.  
Finally, the antenna always illuminates the same scene on the ground in ST mode; therefore, the magnitude of images would be modulated by the antenna pattern. An intuitive phenomenon when the middle part of an image is brighter than the edges in azimuth Take the data acquired in this experiment as an example, we can get the antenna pattern in both transmit and receive mode with the help of auxiliary data, as shown in Figure 4a,b. According to the width of the imaged scene and distance of each pixel in azimuth, the beam width of the whole scene can be calculated. In this experiment, the beam width of the imaged scene is about 0.287\({}^{\circ}\) and the number of the azimuth samples in the final image is 38,588. In order to demodulate the antenna pattern, an interpolation operation is carried out on the round-trip antenna pattern, and the interpolated result can be found in Figure 4c. Then, the inverse of the curve shown in Figure 4c can demodulate the brightness of the focused image by every pixel at the image level.  
Figure 4: GF-3 azimuth antenna pattern of the data acquired in this experiment. (**a**) The antenna pattern within \([-18^{\circ},18^{\circ}]\) in transmit mode; (**b**) The antenna pattern within \([-18^{\circ},18^{\circ}]\) in receive mode; (**c**) The interpolated round-trip antenna pattern.  
Figure 3: Antenna pattern of GF-3. (**a**) The antenna pattern when \(\theta_{s}=0^{\circ}\); (**b**) The antenna pattern when \(\theta_{s}=1.9^{\circ}\); (**c**) The normalized modulation factor of GF-3 antenna gain in azimuth in this experiment.