Density-tapered spiral arrays for ultrasound 3-D imaging

The current high interest in 3-D ultrasound imaging is pushing the development of 2-D probes with a challenging number of active elements. The most popular approach to limit this number is the sparse array technique, which designs the array layout by means of complex optimization algorithms. These algorithms are typically constrained by a few steering conditions, and, as such, cannot guarantee uniform side-lobe performance at all angles. The performance may be improved by the ungridded extensions of the sparse array technique, but this result is achieved at the expense of a further complication of the optimization process. In this paper, a method to design the layout of large circular arrays with a limited number of elements according to Fermat's spiral seeds and spatial density modulation is proposed and shown to be suitable for application to 3-D ultrasound imaging. This deterministic, aperiodic, and balanced positioning procedure attempts to guarantee uniform performance over a wide range of steering angles. The capabilities of the method are demonstrated by simulating and comparing the performance of spiral and dense arrays. A good trade-off for small vessel imaging is found, e.g., in the 60λ spiral array with 1.0λ elements and Blackman density tapering window. Here, the grating lobe level is -16 dB, the lateral resolution is lower than 6λ the depth of field is 120λ and, the average contrast is 10.3 dB, while the sensitivity remains in a 5 dB range for a wide selection of steering angles. The simulation results may represent a reference guide to the design of spiral sparse array probes for different application fields.