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Optimization of random sparse 2-D transducer arrays for 3-D electronic beam steering and focusing

Recent progress reported from different groups have shown that 3-D ultrasonic imaging is possible using electronic beam steering with 2-D matrix arrays having rare and random array patterns. In simulation studies Turnbull et al (1990) have shown that reducing the number of elements of a 2D matrix array down to order 8 keeps resolution and leads still to sufficient contrast. These random arrays are usually obtained by generating a random pattern with the desired numbers of elements. We have investigated main to side lobe levels of random sparse arrays and found substantial differences in side lobe levels in different random patterns containing the same element number. Based on this finding an optimization process has been developed which generates optimized array patterns for a given matrix array and fixed order of reduction using a genetic algorithm. Almost independent from the initial array pattern the optimized pattern is obtained after 400 iteration steps. The function to be minimized is the difference between the radiation pattern of the random array and the fully sampled λ/2 array. The radiation power irradiated outside the main lobe is approximate four times lower compared to the unoptimized array