Coarray synthesis with circular and elliptical boundary arrays

An elliptical boundary aperture is a collection of points lying on an ellipse from which energy is transmitted and/or received. An important special case is the circular boundary aperture. When these apertures are used with beamforming to produce a narrowband image of a far-field source, the corresponding point spread function (PSF) is characterized by high sidelobes. The concept of the coarray of an imaging system is used here to develop techniques which synthesize the effect of a more desirable PSF with an elliptical boundary aperture. Techniques are given for use in active imaging of spatially coherent sources, as well as passive imaging of spatially incoherent sources. Discrete arrays and continuous apertures are considered separately. The approach shows that the PSF synthesis problem can be solved in many more ways than previously recognized, and this fact is exploited to develop procedures which have a least-squares optimality property