Radon transform: A different perspective on planar array synthesis

In this paper the Radon transform is used to study planar arrays. It is shown that the Radon transform (in its discrete version) and the associated projection-slice theorem define interesting relations between the array factor and the amplitude coefficients of a planar array. These relations are used to develop a synthesis procedure for 2D arrays that have a pencil beam shaped array factor with the same shape (apart an angular scaling factor) on any plane through the boresight direction. With respect to previously known methods the Radon transform thus provides a different perspective, to the aforementioned planar array synthesis. The various steps of such a procedure are reported. The output of the synthesis procedure is the set of real amplitude coefficients for the array. The limitations on the applicability of the synthesis procedure are explained, and finally two examples are reported to show its application.