Reducing Relative Gain and Noise Response Variations for Phased-Array Feed Imaging of Radio Astronomical Sources

In comparison to a single horn-feed system, single dish radio astronomical imaging with a phased-array feed (PAF) has additional noise due to variations in the responses of the various beams used in the creation of the image. This increased noise may obscure weak sources of interest and discredit the ability of a PAF to increase sky survey speed. In order to reduce the beam-to-beam variations, we introduce several new PAF beamforming strategies. A dual constraint beamformer is designed to simultaneously satisfy uniform main beam and noise response constraints, eliminating one aspect of the variation. A rim constraint beamformer that relies on calibrator sources on the rim of the reflector dish to control the spillover pattern variations among beams with eigenvector constraints is introduced and shown to reduce beam-to-beam variations. Finally, by combining the dual constraint and rim constraint beamformers, we are able to construct a beamformer that provides spillover pattern control while meeting specified gain and noise response constraints to reduce the beam-to-beam variations and improve PAF imaging.