The discussion in the previous section has focused on the polarization performance of the receivers. However, the polarization performance of the antennas is equally important. In Heiles' formalism, the Mueller matrix of the antenna must be determined to sufficient accuracy. Moreover, this must be done over the entire primary beam of each antenna, and over sidelobe responses (which are usually highly polarized). Thus, there will be a different antenna Mueller matrix at each pixel in the antenna beam pattern. Determination of these Mueller matrices at every pixel can only be done by careful mapping of the polarized beam pattern of each antenna - hence, it will require astronomical calibration. Such a procedure is very time consuming. If these matrices depend on time, temperature, antenna pointing, etc., the situation is hopeless. The only hope is for the polarized beam of the antennas to be sufficiently stable that the antenna Mueller matrix map over the beam can be derived once (or infrequently) and applied over extended periods of time. Hence, any antenna design considerations that might result in changes in the polarization response of the antennas should be avoided at all costs.