Optimizing the radiation pattern of sparse periodic linear arrays

We have developed a method for designing sparse periodic arrays. Grating lobes in the two-way radiation pattern are avoided by using different element spacings on transmission and reception. The transmit and receive aperture functions are selected such that the convolution of the aperture functions produces a desired effective aperture. A desired effective aperture is simply an aperture with an appropriate width, element spacing, and shape such that the Fourier transform of this function gives the desired two-way radiation pattern. If a synthetic aperture approach is used, an exact solution to the problem is possible. However, for conventional imaging, often only an approximation of the desired effective aperture can be found. Different strategies for obtaining these approximate solutions are described. The radiation pattern of a sparse array designed using the effective aperture concept is compared experimentally with the radiation patterns of a dense array, and sparse arrays with periodic and random element spacing. We show that the number of elements in a 128-element linear array can be reduced by at least four times with little degradation of the beam forming properties of the array.