Realizable feed-element patterns for multibeam reflector antenna analysis

The radiation pattern of a feed element is approximately described by a simple function
(\cos \theta)^{q}
. For a given element spacing of the feed array, we give simple formulas for estimating the practical value of
q
when the element is an open-ended rectangular waveguide, an open-ended circular waveguide, a pyramidal horn, or a cigar antenna.