In order to show the effectiveness of the method described in the previous section, we have conducted two separated tests using PALSAR data. The first is a case study, i.e.
5. The sweep velocity of the PALSAR footprint on the ground is about 10% lower that the actual satellite velocity in ALOS. The coefficient can be calculated from geometrical considerations, yielding
kg= Re/(Hs+ Re), wherein Reis the mean Earth’s radius.
6. An alternative strategy that would lead to co-registered polarimetric raw channels, is the back- ward focusing. In practice, the user can perform a simple and linear forward focusing, co-register the SLC pairs, and perform a backward focusing.
estimation of Faraday rotation and the presence of interference with ground radars can severely corrupt the data.
In the same figure, the two maps of Faraday rotation estimated from SLC data and raw data are shown. They are obtained directly by averaging (5.1) over7 ×7 pixels and 15 ×15 pixels, on raw and SLC data respectively. A preprocessing of raw data has been performed for gain/offset compensation and interference removal. The first operation is a linear shift and scaling of the pixel values for co-polar and cross-polar data. The second processing aimed at removing the in-band and out-band interferences that occur at L-band. Comparing the two maps, there is evidence that the method for estimating the Faraday rotation angle depends on the focused target on the Earth’s surface. In particular, the terrain slope in the top-left corner of the image seems to represent an important source of distortion for the estimated Faraday rotation angle. Nevertheless, the mean value of FR angle from SLC data results about 8.3 deg and from raw data results about 8.4 deg (cf. Fig. 5.4a). A qualitative inspection of the histograms in Fig. 5.4a also suggests that a Gaussian distribution is more appropriate for modeling Ω estimated from raw data. The standard deviation of the estimates is 0.93 deg from SLC and0.85 deg from raw data.
The accordance of the two values in this case study confirms that the PALSAR SAR processor does not corrupt the mean estimation of Faraday rotation. However, the local variations of FR angle estimation are also of interest. Fig. 5.4b and Fig. 5.4c show the averaged range and azimuth profiles respectively. Range profiles are almost preserved in the focusing process and FR estimation. Azimuth profiles have also a mean value around8 deg, but show local deviations. They may be due to pixels corrupted by in- terferences that have not been interpolated (as done in the focuser). One example of such variation is centered on the row 200 in Fig. 5.4c. Another reason may be the rapid spatial variation of TEC in the ionosphere, but we disregard this possibility since in Fig. 5.3c the transitions appears net and clear along the range direction.
(a) Pauli decomposition
(b) Faraday rotation angle estimated from SLC data
(c) Faraday rotation angle estimated from raw data
Figure 5.3: Full polarimetric image acquired by ALOS/PALSAR over South Italy. Note the features in the Faraday rotation angle estimated from SLC data.
(a) total histograms
(b) range profiles (c) azimuth profiles
Figure 5.4: Comparison of Faraday rotation angle estimated from SLC data and raw data using the PALSAR product of Fig. 5.3. Histograms and profiles averaged along range and azimuth directions are shown.
The same procedure described above has been applied to an extensive analysis over more than 30 PALSAR products. Fig. 5.5a illustrates the comparison between the FR angle estimated from SLC and raw data. The linear trend confirms that the mean estimate of FR from raw data is in good agreement with the mean value of the FR angle estimated from SLC data. In the analysis above, the system has been consid- ered calibrated, i.e. the polarimetric distortion matrices on receive and transmit has been neglected. Fig. 5.5b shows the Faraday rotation estimates from calibrated and un-calibrated SLC data and confirms that the PALSAR system distortions can be ne- glected for the purpose of FR estimation. This is a further proof of the good conditions
(a) impact of the SAR processor
(b) impact of the calibration matrices
Figure 5.5: Extensive analysis over several PALSAR products for the assessment of the effects of the SAR processor (a) and the effects of the polarimetric calibration matrices (b).
3. Some operations in the SAR processor can be nonlinear with respect to the po- larimetric channels and this might corrupt the estimation of FR angles from SLC data.
4. The spatial distribution of TEC in the ionosphere corresponds more closely to the raw data than SLC data and hence the generation of TEC map is more realistic. 5. Faraday rotation can be estimated and corrected before any operation in the ground segment, without need to generate necessarily SLC data. This, for in- stance, would save time when detected products are requested.
6. The simplicity of the method makes it fast to implement and to run. Programming code already designed for SLC can be easily reused for raw data.
Although the encouraging results, we recognize some weak points of the proposed method.
1. For a faster implementation, we have disregarded the delay between H- and V- transmission. In order to co-register raw data, specific algorithm should be de- signed for the purpose.
2. The effects of the calibration matrix may be not negligible. Polarimetric system distortions are usually calculated on SLC data. Even if they can be removed easily from raw data, it is not ensured that the calculated values agree.
3. Selecting appropriate targets in the scene, such as those respecting reflection symmetry or high SNR, it may be difficult on raw data, which indeed is an average of all these targets.
Further investigations over test sites with known Faraday rotation are in progress. In particular, some acquisitions over Alaska have been used for crosschecking the results in
the SAR community and would be serve to test out approach. Finally, we remark that future missions such as TerraSAR-L, BIOMASS, DesdynI and SAOCOM that operates at lower frequency may benefit of the estimation and correction of Faraday rotation from raw data.