Effects of Antenna Cross-Polarization Coupling on the Brightness Temperature Retrieval at L-Band

TLDR: The formal proof of the insensitivity is presented: when the Faraday rotation correction is performed by the square sum of the two retrieved Stokes, the retrieved TB below the ionosphere and at the top of the atmosphere after thefaraday correction becomes insensitive to the additional rotation.

Abstract: Retrieval of the brightness temperature (TB) at the L-band is studied in the context of the remote sensing of ocean surface salinity. The measurement of antenna temperature and the retrieval of TB are simulated with a radiative transfer model and an observing system model of an orbiting spacecraft. Two sets of antenna gain patterns are used: 1) theoretical analysis and 2) measurements of a 1/10th-size scale model. The latter set notably shows the large cross-polarization coupling from the first Stokes transmit into the third Stokes receive. The large cross-polarization coupling causes an error of up to 4° in the estimate of the Faraday rotation angle (the size of the angle itself is mostly less than 15° in the severe ionospheric condition). By this amount of the error, an additional rotation is introduced to the retrieval of the second and third Stokes TBs in front of the feed horn before the Faraday rotation correction. The additional rotation also degrades the performance of the antenna pattern correction (APC). However, when the Faraday rotation correction is performed by the square sum of the two retrieved Stokes, the retrieved TB below the ionosphere and at the top of the atmosphere after the Faraday correction becomes insensitive to the additional rotation (i.e., being insensitive to the error in the Faraday angle estimate and the rotational error in the APC). The formal proof of the insensitivity is presented. The first and second Stokes TBs at the top of the atmosphere observed at 5.6-s intervals from space may be retrieved with an error smaller than 0.1-K rms without the accurate ancillary information of the gain pattern and the Faraday rotation angle, assuming correct calibration, 0.08 K NEΔT for the radiometer noise, and accurate correction or flagging of the solar and galaxy radiation.