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Remote sensing of sea surface salinity can be performed by means of microwave radiometry at L-band, but it requires high radiometric accuracy (e.g., on the order of 0.1 K). Since the variability of salinity in the open ocean exhibits large spatial scales and long temporal scales, it is possible to use antennas with large footprints and averaging to meet this goal. However, antennas with large footprints introduce other problems such as variations of the incidence angle and direction of the polarization vectors over the footprint. Examples of these effects are computed here using antennas that are representative of those that will be flown on the Aquarius/SAC-D mission being developed for remote sensing of salinity from space. It is shown that the antenna temperature (i.e., integrated over the antenna pattern) is biased relative to the value at boresight. In part, this is due to change in incidence angles across the field of view. Polarization mixing, because of the variations of the local plane of incidence across the footprint, also induces bias (peculiarly for the third Stokes parameter). Finally, large antenna footprints limit how close to land measurements can be made.