Large format focal plane arrays (FPAs) of dielectric lenses are promising candidates for wide field-of-view submillimeter imagers. In this work, we optimize the scanning gain of such imagers via shaping lens surfaces. We develop an optimization procedure using a field correlation technique between the fields generated by a reflector on the top of the lenses and those generated by the lens feeds. Based on this procedure, an FPA of quartz lens antennas combined with leaky-wave feeds is designed to efficiently illuminate the reflector, achieving a directivity of 50.5 dBi up to scanning 20.3°. The obtained scanning gain loss of 2.6 dB is much lower than that associated with the direct fields coming from the reflector (about 6 dB). The proposed FPA is validated by full-wave simulations with excellent agreement. We have fabricated and measured an example shaped quartz lens optimized for the scanning angle of 20.3° at 180 GHz. The comparison between the simulations and the measurements also shows excellent agreement.
