Communication systems based on low-earth-orbit (LEO) satellites have generated a requirement for high-performance phased array antennas with exceptional gain, sidelobe levels, and axial ratio over broad scan angles and 360 degree azimuth coverage. One approach to mitigating the effects of scan dependence is to cover the planar array with a hemispherical lens, or dome, which implements passive or active phase correction of the scanned beam. The phase correction over the dome surface may be represented as the function (Delta) (Phi) ((theta) , (phi) ), with (theta) and (phi) the polar and azimuth angles in a coordinate system having z-axis normal to the array. The purpose of this study was to determine the performance improvement achievable with such an ideal lens. Three cases were considered: a conventional lens with fixed optimum phase correction, an active lens with scan-dependent phase correction a function of polar angle only, and an active lens with phase correction a function of polar and azimuthal angles. In all cases, the planar array distribution had a fixed radial Taylor amplitude distribution and a phase taper consisting of a linear beam-pointing term and a non-linear focusing term.