## Case Study: Data Analysis and Results
### Power Estimation for Point Targets from SAR Images  
The imaged point targets appear as bright crosses in the processed image. Two methods are distinguished when deriving the point target power: the peak and the integral method. With the peak method, the target power is described by the pixel with the peak power (complex pixel amplitude squared) whereas with the integral method, the target power results as the sum of pixel powers over a relevant region around the target. It was shown that the integral method is advantageous as it leads to accurate results even if the image is not perfectly focused [21]. Thus the integral method was chosen for this analysis.  
The goal of this analysis step is to derive a table of relative point target intensities for all point targets in all images. Although an absolute scale is not necessary (and the RADARSAT-2 absolute calibration factor is ignored here), it is crucial that the point target intensities derived from different images are all calibrated with respect to each other. This is achieved by applying the (range-independent) _beta naught_ look-up table delivered together with the images [22]. It was confirmed that no obvious incidence-angle dependence remained in the data.  
The following steps were performed to derive a targets' integrated impulse response intensity:  
1. Define a search window around the point target in the georeferenced, processed image.
2. Find and record the brightest pixel location.
3. Define an analysis window, centered on the brightest pixel of the previous step.
4. Estimate the clutter power from four non-overlapping areas surrounding the peak.
5. Integrate the target power over a cross area (see Figure 4 and Table 3), capturing all pixels with significant point target power.
6. Subtract the estimated clutter power from the integrated target power to get a clutter-compensated target power.  
This procedure is in line with the one described in [3].  
Figure 4: Integration area for the _integral method_.  
An exemplary transponder impulse response is shown in Figure 5. The peak power lies more than 60 dB above the clutter level. This large separation is already an indication that clutter power compensation, in practice, is not necessary. Nevertheless, it was performed for all 126 analyzed point targets.  
Exemplary impulse responses for 3.0 m and 1.5 m corners are show in Figures 6 and 7, respectively. Although the impulse response is clearly visible in the range and azimuth cuts, both corners are comparatively hard to spot in the image patches themselves. This is due to the way the intensities in the image patches have been clipped for visualization. All digital values above a threshold (2.7 times the mean absolute amplitude within the patch) are set to the threshold value.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Pixels** \\ \hline Cross length & 21 \\ Cross width & 3 \\ Square width & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cross parameters according to Figure 4 used during analysis.  
Figure 5: Transponder impulse response for the first overpass on 7 April 2013. A large target-to-clutter ratio is apparent. The four red squares indicate the areas from which the clutter power was estimated.  
Figure 6: 3.0 corner impulse response at site D24 for the first overpass on 7 April 2013. Also see caption of Figure 5.  
Figure 7: 1.5 corner impulse response at site D26 for the first overpass on 7 April 2013. Also see caption of Figure 5.