## 3 Method
### Point Target Response Energy Calculation  
In point target-based SAR radiometric calibration, the extraction of the point target impulse response energy is a crucial step in the calculation of the calibration constants, and this is often achieved using the integral or peak method [20; 21]. The integral method obtains the point target energy by integrating the impulse response over the specific region, while the peak method uses the product of the peak response of point target and area of the system resolution cell to obtain the energy.  
The implementation of the peak method requires knowledge of the resolution unit of the SAR system [20]. The utilization of the method is, therefore, related to the focusing performance and image quality of the system [10]. The peak method formula for calculating impulse response energy based on the point target is:  
\[\epsilon_{p}=DN^{2}ar\delta_{a}\delta_{r} \tag{4}\]  
where \(DN^{2}\) represents the pixel intensity value of the point target; \(a\) and \(r\) denote the antenna 3 dB impulse response width (IRW) in the azimuth and range directions, respectively, \(\delta_{a}\) and \(\delta_{r}\) are the same as in Equation (3).  
Compared to the peak method, which is sensitive to system focus and requires better image quality, the integral method is independent on the radar system focus and is not influenced by processor gain, scene, or processor partial coherence [21], and thus can be employed even if the image quality is unknown [22]. Furthermore, it has a wider range of application compared to the peak method.  
When using the integral method to obtain the response energy of a point target, it is necessary to accurately determine the center position of the point target and select a suitable integration region around the center position. The precise determination of the point target center position and the appropriate selection of the integration region to both respond to the accuracy of the energy calculation and the calibration results. To address the problem, our team members [PERSON] et al.proposed a method to determine the point target center position based on the sliding window method [23]. This method introduces image context  
Figure 7: Flow of radiometric calibration based on point targets.  
information and uses regional statistics to replace the traditional pixel-based positioning method, and the centroid of the sliding window with the largest sum is used as the centroid of the integration window [23]. Thus, the point target position and the integration window can be extracted more accurately.  
The selection of the integration window is shown in Figure 8, where P represents the size of image pixel, and the orange cross region is the point target response energy integration region, and the green region is defined as the background energy integration region. In this study, the integration window was a rectangular area with a size of 32 \(\times\) 32 pixels around the center point, obtained by the sliding window method.  
The point target response energy is equal to the point target integration region energy minus the average clutter energy of the background region [12], and the specific calculation formula is:  
\[\varepsilon_{p}=\left(\sum_{i\in A}^{N_{A}}DN_{i}^{2}-\frac{N_{A}}{N_{B}}\sum_ {i\in B}^{N_{B}}DN_{i}^{2}\right)\delta_{a}\delta_{r} \tag{5}\]  
where \(DN_{i}^{2}\) is the intensity value of the point target pixel \(i\), \(N_{A}\) is the total number of image pixels in the point target energy integration region, \(N_{B}\) is the number of image pixels in the background energy integration region, and \(\delta_{a}\) and \(\delta_{r}\) are the same as in Equation (3).