Keywords: ultrasonic transducer, sparse array, genetic algorithms.

Using sparse array transducers is one of the efficient ways to reduce system complexity and cost for medical imaging systems, especially for real time 3-D ultrasound systems, in which 2D arrays are necessary. 2D dense arrays are far from practical nowadays due to their large amount of elements and supporting electric channels. Simply reducing active elements from dense arrays may lead to the well-known grating lobes and side lobes in their radiation field [1], which will deteriorate the imaging quality. However, to design and optimize sparse arrays is computationally demanding because of a large number of parameters to be considered. For broadband arrays, the time consuming procedure to calculate radiation field, which works as optimization criteria is another problem.

In this paper, an efficient approximate algorithm to calculate the radiation field has been developed first, based on spatial impulse response method [2]. The algorithm abandons the exact calculation procedure for the whole array to improve efficiency. On the other hand, by extracting information from a single array element, the accuracy is ensured. The method is validated by comparing the results with the exact method. This algorithm works as the fitness evaluation operator for genetic algorithms (GAs), which makes it possible to optimize both 1D and 2D broadband sparse arrays.

Software has been developed using modified GAs to optimize sparse arrays under various design strategies. A few GAs operators, such as crossover, mutation are developed or modified to be suitable for the given applications. The parameters of GAs including population size, mutation rate, generation number are tested and selected. Some new GAs strategies reported in the literature are adopted to improve performance. They include tournament selection [3], steady-state GAs, duplicate check [4], etc. Several design cases are studied using the software. The radiation field can be optimized for given sparse order, or the number of elements can be minimized for given field performance. This software provides the ability to design sparse arrays with trade-off among number of elements, maximum side lobe level, and beam width, etc.

1 10.1109/58.165560

B.D. Steinberg, Principles of Aperture and Array System Design, New York, A Wiley-Interscience Publication, 1976.

2

L.G. Ullate, and J.L.S., Emeterio, "A New Algorithm to Calculate the Transient Near-field of Ultrasonic Phased Arrays", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47(6), 745-753, 1992. doi:10.1109/58.165560

3

B.L. Miller, D.E. Goldberg, "Genetic Algorithms, Tournament Selection, and the Effects of Noise", Univ. Illinois, Urbana-Champaign, IlliGAL Tech. Rep. 95006, 1995.

4

J.M. Johnson, Y.R-Samii, "Genetic Algorithms in Engineering Electromagnetics", IEEE Antennas Propagation Magazine 39. 7-21, 1997. doi:10.1109/74.632992

5

L.J. Eshelman, J.D. Schaffer, "Real-Coded Genetic Algorithms and Interval- Schemata", Foundations of Genetic Algorithms 2, San Mateo, Morgan Kaufmann, 1993.

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