Acoustic field of a spherically curved wedge transducer

Abstract

High-intensity focused ultrasound (HIFU) applications typically utilize spherically curved transducers, often with modifications to the surface electrode. These modifications, such as rectangular cut-outs, can normally be modeled as a collection of annular rings and wedges. The acoustic field of an annular ring has been well characterized, but a wedge shape has not. We present a model of the acoustic field of a wedge transducer based on the spatial impulse response (SIR) method. A wedge transducer is created by making a cut normal to a spherical cap and keeping the section with the smaller surface area. Analytic expressions for the SIR are derived for an arbitrary point P in space. To find the time domain pressure at P, the SIR is convolved with the time derivative of the wedge surface velocity. Numerical examples of SIRs and the acoustic pressure field are given for a wedge formed from a spherical cap with a geometric focus of 9 cm and an outer diameter of 8 cm. For a single frequency drive of 4.7 MHz, calculations of pressure are compared to hydrophone measurements of a HIFU transducer with equivalent geometry. The results show an excellent agreement between theory and experiment.