Design of sparse array imaging systems

A method for designing sparse periodic arrays is described. Grating lobes in the two-way radiation pattern are avoided by using different element spacings for 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. Here, the authors apply the effective aperture method to the design of a sparse array for a very high frame rate (1,000 images/s) imaging system. The high frame rate is achieved by using synthetic aperture beam-forming utilizing only a few transmit pulses for each image. To compensate for the resulting loss in signal, the power delivered to each transmit element is increased and multiple transmit elements are used for each transmit burst. By mechanically rocking the array, in a way similar to what is done with an annular array, a three-dimensional set of images can be collected in the time normally required for a single image