Unequally Spaced Arrays Based on the Poisson Sum Formula

It has been recognized that unequally spaced arrays can offer some advantages over equally spaced arrays, mainly in the following areas: 1) thinned array by reducing the number of elements to achieve the high resolution without producing grating lobes; 2) broadbanding or wide scanning without grating lobes; 3) reducing sidelobes for the array of uniform amplitude; and 4) unequally spaced arrays on a curved surface. Historical accounts and a basic theory of unequally spaced arrays based on Poisson Sum Formula are given. Most of the analytical approach can be obtained by numerical computation. Analytical methods may show additional physical mechanisms and offer alternative approaches. This paper also discusses some additional applications on circular arrays, active impedance and arrays on a curved surface.