Wideband 2-D Array Design Optimization With Fabrication Constraints for 3-D US Imaging

Ultrasound (US) 2-D arrays are of increasing interest due to their electronic steering capability to investigate 3-D regions without requiring any probe movement. These arrays are typically populated by thousands of elements that, ideally, should be individually driven by the companion scanner. Since this is not convenient, the so-called microbeamforming methods, yielding a prebeamforming stage performed in the probe handle by suitable custom integrated circuits, have so far been implemented in a few commercial high-end scanners. A possible approach to implement relatively cheap and efficient 3-D US imaging systems is using 2-D sparse arrays in which a limited number of elements can be coupled to an equal number of independent transmit/receive channels. In order to obtain US beams with adequate characteristics all over the investigated volume, the layout of such arrays must be carefully designed. This paper provides guidelines to design, by using simulated annealing optimization, 2-D sparse arrays capable of fitting specific applications or fabrication/implementation constraints. In particular, an original energy function based on multidepth 3-D analysis of the beam pattern is also exploited. A tutorial example is given, addressed to find the $N_{\mathrm{ e}}$ elements that should be activated in a 2-D fully populated array to yield efficient acoustic radiating performance over the entire volume. The proposed method is applied to a $32 \times 32$ array centered at 3 MHz to select the 128, 192, and 256 elements that provide the best acoustic performance. It is shown that the 256-element optimized array yields sidelobe levels even lower (by 5.7 dB) than that of the reference 716-element circular and (by 10.3 dB) than that of the reference 1024-element array.