## 3 RFI Detection and Mitigation Algorithm in Synthetic Aperture Microwave Radiometry Imagery
### Full-Polarimetric Mode Algorithm  
At the end of the SMOS commissioning phase it was decided that the instrument should operate in full-polarimetric mode only. In this mode of operation the four Stokes parameters images (T\({}_{\mathrm{XX}}\), T\({}_{\mathrm{YY}}\), Real\(\{\)T\({}_{\mathrm{XY}}\}\) and Im\(\{\)T\({}_{\mathrm{XY}}\}\) are obtained after four switching intervals, as sketched in Figure 11. In many cases, pulsed RFI sources happen in one or several of the intervals, but not in all with the same amplitude, which distorts the side lobes and tails of the impulse response, preventing the use of the Sun cancellation algorithm described in Section 3.1. Also, since they affect only a subset of the whole visibility samples, fictitious third and fourth Stokes parameters may appear. In order to better understand the differences of the problem in the full-polarimetric case, as compared to the dual-polarization one (section 3.1), Figure 15 illustrates these effects with an SMOS image acquired on September 3, 2010 over the Aegean Sea (Cyprus island appears in the bottom part of the image). As can be appreciated in the \(\mathrm{T_{XX}}\) image (Figure 15a,b), there is an intense RFI source around (\(-\)0.25, \(+\)0.35) whose \"tails\" (impulse response) are not even symmetrical: the tails at \(+\)30\({}^{\circ}\) and at \(-\)90\({}^{\circ}\) with respect to the \(\xi\) axis are mostly negative (dark blue color), instead of positive, indicating that this RFI source has occurred only during some intervals of the switching sequence. The other RFI sources, being even stronger (e.g., (\(-\)0.35, \(-\)0.02) and (0.19, \(-\)0.35)) appear more \"round\" and symmetric, indicating that the RFI was most probably present during the four switching periods. Figures 15c and 15d show the \(\mathrm{T_{YY}}\) image. Compared to Figure 15a, the strongest sources are now in different positions, new ones can also be seen, while others have nearly disappeared, particularly the one at (\(-\)0.25, \(+\)0.35). Figures 15e and 15f show the real and imaginary parts of \(\mathrm{T_{XY}}\) (Re[\(\mathrm{T_{XY}}\)] and Im[\(\mathrm{T_{XY}}\)]) in the alias-free FOV, which should be close to zero in the Earth horizontal-vertical reference frame (Re[\(\mathrm{T_{HV}}\)] and Im[\(\mathrm{T_{HV}}\)]), but actually are not. This reveals the presence of new RFI sources that have passed inadvertently in the \(\mathrm{T_{XX}}\) and \(\mathrm{T_{YY}}\) images. The fact that Re[\(\mathrm{T_{XY}}\)] and Im[\(\mathrm{T_{XY}}\)] should be close to zero is based on two factors:  
(1) the low cross-polar antenna pattern in the alias-free FOV, and  
(2) the fact that the third and fourth Stokes parameters in the Earth's reference frame are negligible (if not zero for most surface covers). Outside the alias-free FOV, the values of Re[\(\mathrm{T_{XY}}\)] and Im[\(\mathrm{T_{XY}}\)] increase due to the overlapping of regions far away from the antenna boresight, where the co- to cross-polar ratio is much lower. Figures 16a and 16b show the mean values of Re[\(\mathrm{T_{XY}}\)] and Im[\(\mathrm{T_{XY}}\)] computed over the ocean to minimize the risk of undetected RFI. Note also that, within the alias-free field of view, the \(\mathrm{T_{XX}}\)(\(\xi\), \(\eta\)) and \(\mathrm{T_{YY}}\)(\(\xi\), \(\eta\)) images (Figure 16a,b) capture the angular dependence of the brightness temperatures at X- and Y-polarizations in the antenna reference frame, which allows easily distinguishing RFI contaminated pixels. Over land, the problem is more complex due to the large range of BTs that can be encountered. Figure 15: _Cont._  
At this moment, two strategies can be followed:  
1. to use only the YY- and XX-polarization BT images obtained during the time intervals 0-\(\tau\) and 2-\(\tau\)-3-\(\tau\), respectively (marked as 1 and 1' in Figure 11), and use the dual-polarization RFI detection and mitigation algorithm (Section 3.1).