Towards using a focussed phased array of millimetre length scale elements for ultrasound imaging

Sparse phased array ultrasound transducers with millimetre length scale elements have previously been proposed for generating hyperthermia but not for imaging. Numerical simulation with a pseudospectral solver was used to investigate: (a) how the position of the maximum pressure in the focal region changed with element diameter and frequency; (b) how the size and position of the focal region changed with focal distance under steering; and (c) the imaging performance of 15 element random arrays. These analyses were performed for both piston-like and non piston-like millimetre diameter elements since previous work has shown a shift in the distance to the maximum pressure in the focal region with the latter. The results for these elements were compared with elements where the diameter was  <λ/2. The distance from the array to the position of maximum pressure in the focal region diverged from the value with element diameter  <λ/2; values for piston-like elements increased positively whilst values for non piston-like elements increased negatively. With distances expressed in λ, no difference was found for arrays at 1 MHz and 2.5 MHz. For piston-like elements, but not for non piston-like elements, two peaks were found in the focal region which were in-line with the direction of propagation for a focus on the central axis but which rotated to become parallel with the direction of propagation when steering exceeded 20°. The size and position of the focal region under steering was similar for the non piston-like elements and elements with diameter  <λ/2. Little difference was found in image quality or the size of the point spread function (PSF) between images at 2.5 MHz with piston-like and non piston-like behaviour for steering angles less than 20° when compared with a linear array of similar size. These results suggest that imaging with random arrays of millimetre length scale elements is possible.