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The third Stokes parameter will be observed from space for the first time at L-band by the Soil Moisture and Ocean Salinity and Aquarius/SAC-D satellites. The correlation between polarizations, which is the source of the third Stokes parameter, is of interest at L-band to measure Faraday rotation and also to indicate novel features of the surface. However, spurious signals (false indication of correlation) can occur in the third Stokes parameter. For example, this happens when the radiometer crosses boundaries associated with a large change in brightness temperature, such as land-water boundaries. In this paper, calculations with the Aquarius radiometer antennas will be used to show that these spurious signals are due to the cross-polarization coupling and large beamwidth associated with realistic L-band antennas in space.