Convex boundary arrays for coherent and incoherent imaging

The beam pattern of an aperture of sensor elements determines the quality of the image of far-field sources produced by it. Resolution is limited by the physical size of the aperture in linear beamforming, and sidelobe characteristics are determined by the aperture weighting function or aperture apodization. For a given number of elements the largest two-dimensional physical apertures are formed if elements are distributed only around their boundaries. Results developed recently are extended to show that in general, for any convex boundary aperture in a plane, it is possible to synthesize any beam pattern which is obtainable from a filled aperture with the same boundary. Specific results for elliptical and rectangular boundaries are briefly reviewed, and a general synthesis theorem which provides the basis of the two-dimensional pattern synthesis scheme is established. This is applicable for both incoherent and coherent imaging, the latter implemented using a transmit-receive scheme.<>