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It is becoming widely accepted that radar polarimetry provides accurate and informative weather measurements, while phased-array technology can shorten data updating time. In this paper, a theory of phased array radar (PAR) polarimetry is developed to establish the relation between electric fields at the antenna of the PAR and the fields in a resolution volume filled with hydrometeors. It is shown that polarimetric measurements with an electronically steered beam can cause measurement biases that are comparable to or even larger than the intrinsic polarimetric characteristics of hydrometeors. However, these biases are correctable if the transmitted electric fields are known. A correction to the measured scattering matrix that removes biases in meteorological variables is derived. The challenges and opportunities for weather sensing with a polarimetric PAR are discussed.