Radio waves moving through the ionosphere can experience a rotation of polarization vector known as Faradayâ€™s rotation. Ionospheric effects in L-band strongly exceed those observed in C-band. Rotations exceeding 45 degrees are likely to happen which will significantly reduce the accuracy of geophysical parameter recovery from SAR, if uncorrected. Therefore, the estimation and correction of Faraday rotation effects is necessary to assure high and consistent data quality in mission such as ALOS-2, SAOCOM, and soon NISAR and TanDEM-L.Correction is done following [R-6][R-16] by estimating the rotation angle at each pixel, and then applying the correction using a smoothed rotation angle, or the average of all the rotation angles. The correction relies on cross channel correlation. The complex SAR data are averaged over an area large enough to reduce speckle noise but small enough to retain possible low-frequency Faraday rotation variations within the image (e.g. 10x10);Next, Faraday rotation angle is estimated using:the scattering matrix M' of a calibrated image transform M' to a circular basis Z as then the Faraday rotation angle Î© can be estimated as Once the Faraday rotation is estimated, a correction of the full-pol SAR data for the Faraday rotation can be performed by inversing the system above resulting in .Faraday rotation correction will be a general operator for multi-pol products of wavelengths longer than C-band thereby in addition to L-band missions it should work for future S-band (NISAR) and P-band (Biomass) missions.

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