1. A method for designing an antenna system to comply with a plurality of specified secondary pattern characteristics, the antenna system including an RF feed element and a reflector, the RF feed element characterized by a first geometric feature, and configured to exhibit a plurality of primary pattern characteristics, the method comprising: computing a plurality of partial secondary pattern complex field values for the reflector, each partial secondary pattern characteristic being associated with an individual RF feed element mode; storing the computed plurality of partial secondary pattern characteristics; optimizing a value of at least a second, to-be-optimized, feature of the RF feed element, other than the selected first geometric feature, by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising: (i) determining a cost for a current value of the to-be-optimized feature, said cost resulting at least in part from a variance between a plurality of computed secondary pattern characteristics and the plurality of specified secondary pattern characteristics; and (ii) determining, when the cost is not greater than a specified value, that the second feature is sufficiently optimized, and, when the cost is greater than the specified value, adjusting the current value of the to-be-optimized feature and repeating steps (i) and (ii); wherein the computed secondary pattern characteristics are computed by performing a linear superposition on the stored computed plurality of partial secondary pattern complex field values, the linear superposition being performed using a set of complex modal coefficients of the RF feed element determined, for a selected number of radiating modes, taking into account the current value of the to-be-optimized feature.