We present results of the design of an electrically small though physically large reflector antenna, to be employed as a radar antenna for incoherent scattering research of the ionosphere. First we summarize the geometrical optics (GO) and physical optics (PO) antenna synthesis techniques, followed by a presentation of the different results achieved depending on whether one or the other technique is employed. This demonstrates the need for applying PO shaping. Then we formulate a method for calculating the field which is reflected from the subreflector back into the feed system, and thus determining the return loss, or rather the isolation in the present case because the polarization is circular, of the feed system. We demonstrate how the PO synthesis procedure could be enhanced by incorporating a constraint on the return loss, and how this requires a different expansion of the subreflector surface compared to the usual modes used in TICRA's shaping program POD.
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