## 5 Results and Discussion
### Calibration of Under-Sampled SAR Data  
As the proposed calibration technique does not require azimuth compression, it does not require the azimuth sampling to fulfill the Nyquist criterion. As argued in Section 2, the latter point is of practical relevance in the context of DBF techniques, where independent channels are under-sampled but need to be interferometrically calibrated. Relevant examples of future spaceborne systems include HRWS systems with multiple azimuth apertures [31; 32] but also multiple beam systems operating the SCORE concept to cover a larger swath [19]. Figure 16 illustrates, qualitatively, why sub-sampling is not an issue in the proposed approach. It compares the results of target analysis obtained for a single target at the full channel Pulse Repetition Frequency (PRF) and after the sampling rate has been artificially reduced by dropping two out of every three pulses of raw data. While the phase and frequency content of the raw data are, of course, severely affected by the sub-sampling, the inputs to the actual calibration process (the residual errors shown in \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Baselines [cm]**} \\ \cline{2-4}  & \(\delta x\) & \(\delta y\) & \(\delta z\) \\ \hline X1h & \(0.121\) & \(0.065\) & \(0.051\) \\ \hline X1v & \(0.014\) & \(-0.023\) & \(0.000\) \\ \hline X2h & \(-0.041\) & \(-0.042\) & \(-0.050\) \\ \hline X2v & \(-0.093\) & \(0.000\) & \(-0.001\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The position refinements estimated for the four phase centers of the X-band polarimetric across track interferometer of F-SAR using the baseline optimization of Section 4.4. The changes are given in cm and correspond to those in the phase evaluation of Figure 14.  
Figure 15: A comparison of the consistency of digital surface models (DSMs) extracted from F-SAR single pass interferometry over the Rhone glacier in Switzerland. **Top**: Polarimetric RGB color composites showing the backscatter amplitude in the lexicographic basis (HH, HV, VV) for two consecutive acquisitions with opposite look directions onto the glacier. **Middle**: The single-pass interferometric phase in the HH polarization, relative to the SRTM elevation model used for motion compensation, and the DSM derived therefrom. **Bottom**: The difference of the DSMs obtained, one for each look direction, assuming the nominal baseline (left) and using the refined baseline after calibration (right). the bottom two rows) remain largely unaffected due to the compensation of the model phase (5) in the response correction of (8). Table 2 quantifies the impact of sub-sampling on the calibration of the four X-band phase centers of the F-SAR across track interferometer. To derive these results, the sub-sampling of Figure 16 is applied to all raw data channels. The first three columns show the difference in the absolute phase center position. These differences amount to an offset of around 1 cm that has no measurable impact on the geometric accuracy of the data: constant range delays are absorbed by calibration constants, while the variation across the swath is negligible. The relative position changes, obtained by subtracting the mean from each of the first three columns. These are given in the middle columns and are on the order of 1 mm. The pointing changes, given in the last three columns, are significantly smaller than \(0.1^{\circ}\). As illustrated in Figure 17, these baseline and pointing changes do not have a measurable impact on the observable calibration quality. Figure 16: The impact of azimuth under-sampling on the residual errors obtained in the analysis of a trihedral reflector response at X-band. The left column summarizes the analysis of the original target response at the full azimuth sampling frequency. The right column shows the results obtained when only every third pulse of the raw data is used (the other pulses are discarded in pre-processing).