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Spaceborne polarimetric microwave correlation radiometer is a new type of instrument for the passive microwave remote sensing from space, which can provide an important way for remote sensing of sea surface wind vector and other ocean atmosphere environmental parameters. Antenna cross-polarization correction is an important part of the data pre-processing algorithm. In this paper, for the demand of antenna cross-polarization correction in spaceborne polarimetric microwave correlation radiometer, we have independently derived the full polarization antenna temperature equation based on the polarization coherent detection theory and the definition of Stokes parameters. The equation for the four parameters of Stokes antenna temperature introduced the cross polarization amplitude and phase between the Stokes parameters. Besides, the influence of the polarization rotation angle on the antenna pattern computation was considered. Finally, we established a geometric correspondence between the antenna scanning beam and the earth scene. The principle for determining the parameters of the antenna temperature equation was also discussed. Stokes antenna temperature equation laid the foundation for antenna cross-polarization correction for spaceborne polarimetric microwave correlation radiometer in the future.