Acoustic field of a wedge-shaped section of a spherical cap transducer

The acoustic pressure field at an arbitrary point in space is derived for a wedge-shaped section of a spherical cap transducer using the spatial impulse response (SIR) method. For a spherical surface centered at the origin, a wedge shape is created by taking cuts in the X-Y and X-Z planes and removing the smallest surface component. Analytic expressions are derived for the SIR based on spatial location. The expressions utilize the SIR solutions for a spherical cap transducer [Arditi et al., Ultrason. Imaging 3, 37-61 (1981)] with additional terms added to account for the reduced surface area of the wedge. Results from the numerical model are compared to experimental measurements from a wedge transducer with an 8-cm outer diameter and 9-cm geometric focus. The experimental and theoretical -3-dB beamwidths agreed to within 10% +/- 5%. The SIR model for a wedge-shaped transducer is easily extended to other spherically curved transducer geometries that consist of combinations of wedge sections and spherical caps.