Synthesis of Array Radiation Pattern Footprints Using Radial Stretching, Fourier Analysis, and Hankel Transformation

For the synthesis of radiation patterns using antenna arrays with thousands of elements, the combination of direct methods with non-stochastic optimization can be more efficient than stochastic optimization. Here we describe an efficient method for the synthesis of footprint patterns that combines Hankel transformation with Fourier analysis following angle-dependent homothesis (i.e., radial stretching and/or shrinking) of an axisymmetric Elliott-Stern pattern for a circular aperture. The new method can in principle be applied to arrays of radiating elements with arbitrary locations and element patterns.