Time-domain pressure of a spherically curve wedge transducer

The electrode patterns of a spherical cap transducer are often created from combinations of annular rings and wedges, where a wedge is formed by making a cut in the spherical cap parallel to its diameter when viewed along the axial direction. We present a technique calculate the time-domain pressure of a wedge transducer using the spatial impulse response (SIR) method. Analytic expressions are derived to find the SIR at any point P in the sound field. Convolving the SIR at P with the acceleration of the transducer surface yields the time-domain pressure waveform at experimental hydrophone measurements of a wedge transducer operated at 4.7 MHz having a geometric focus of 9 cm and an outer diameter of 8 cm. Good agreements was observed between the experimental and theoretical 3-dB beamwidths. The utility of the wedge SIR model is that it can be used in a modular fashion with well-known spherical cap SIR model to expedite beam computations of novel transducer designs.