On Archimedean-spiral-based Imaging

Ultrafast ultrasound imaging has been extensively studied in linear-array and phased-array configurations. However, the literature is lacking regarding convex-array geometries while ultrafast ultrasound imaging can be of great interest for several applications, e.g. shear-wave elastography of deep abdominal organs. In this work, we derive a theoretical formalism for ultrafast ultrasound imaging in such a geometry. We propose a simple linear-delay strategy similar to plane-wave imaging. We demonstrate that such a strategy propagates an Archimedean-spiral wavefront within the medium, from which we suggest an expression of the transmit time of flight. We also propose a coherent compounding strategy of Archimedean-spiral wavefronts and we derive necessary conditions in terms of the number of insonifications and steering angles required to reach the equivalence with focused imaging. We validate such theoretical considerations through simulated and phantom experiments.