1. A method, pattern comprising: computing, for an antenna system, the antenna system including an RF feed element and a reflector, 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, wherein the RF feed element exhibits a plurality of primary pattern characteristics and is characterized by a first design feature, the first design feature being a geometric feature; storing the computed plurality of partial secondary pattern characteristics; optimizing a value of at least a second, to-be-optimized, design feature of the RF feed element, other than the first design feature, by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising: (i) a determination of a cost for a current value of the second design feature, said cost resulting at least in part from a variance between a plurality of computed secondary pattern characteristics and a plurality of specified secondary pattern characteristics; and (ii) a decision block wherein, when the cost is not greater than a specified value, a first decision of the decision block is that the second design feature is sufficiently optimized, and, when the cost is greater than the specified value, a second decision of the decision block is to enter a step of adjusting the current value of the second design feature and repeat 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 second design feature.