Achievable field of view of chequerboard phased array feed

Placing a phased array at the focus of a paraboloidal reflector increases the area of sky a radio telescope can observe. For a 9×10 chequerboard phased array on a 12 m parabolic dish the available field of view increase from 1 to 36 square degrees at 1.4 GHz. To access this field of view multiple beams are formed. It is impractical to form enough beams to recover all the energy incident on the phased array. Here a 6×6 square array of beams is analysed. The astronomical objective is to observe large areas of the sky with uniform sensitivity. The 6×6 beam array shows sensitivity variations on the scale of the beam size and the array field of view. A method of flattening the sensitivity is described.