Radiation efficiency of dense antenna arrays forming flat-top and contour radiation patterns

Infinite 1D and 2D periodic planar arrays of densely spaced radiators that are used to form flat-top and contour patterns are analyzed. It is proposed to determine the amplitude distributions over the antenna aperture as the Fourier transforms of the window functions corresponding to the respective patterns. The proposed distributions are used to derive the explicit expressions showing that the efficiency of an array with a specified flat-top or contour pattern is equal to the mean efficiency of a uniformly excited array in the scan region covered by the specified pattern.