Linear ultrasonic array design using cantor set fractal geometry

Naturally occurring resonating systems utilize structures containing a range of length scales to produce a broad operating bandwidth. It has previously been reported that a piezoelectric composite transducer based on a fractal geometry, which thereby introduces components with varying length scales, results in a wider operational bandwidth and a higher sensitivity. In this paper, the work is now extended to an ultrasonic array device using a Cantor Set (CS) fractal geometry. The behavior of this fractal array is explored using both finite element (FE) modeling and experimentation, including comparison with a conventional 2-2 linear array. The FE simulated pulse-echo responses correlate well with the experimental data, which indicates that the CS fractal array elements possessed a wider-6 dB bandwidth (57.3 % against 49.4 0/0), and a higher sensitivity, (11.4 mV against 8.9 mV peak-to-peak voltage) compared with a conventional 2-2 design. In addition, an improved crosstalk reduction is achieved by the CS fractal array. Images of a wire-water phantom produced by the two arrays using the total focusing method (TFM) and full matrix capturing (FMC) data shows that the CS fractal array outperforms the conventional 2-2 array in terms of image resolution and signal strength. Finally, another advanced fractal geometry comprising orthogonal CS fractal geometries, known as the Cantor Tartan (CT) is investigated to further enhance the bandwidth performance of the array, where a -6 dB pulse-echo bandwidth of 68.1 % can be predicted using FE modeling.