Prediction of acoustic field radiated from focusing transducer

A numerical solution of the KZK nonlinear parabolic wave equation is introduced to predict the acoustic field of a focusing transducer. Instead of assuming a uniform velocity distribution on the surface of the transducer, acoustic pressures are measured in the near Fresnel zone of the transducer, and used as the boundary condition, so that acoustic pressures of the first three harmonics can be calculated around the focal plane of the transducer. To verify the numerical solution, the profile of acoustic pressure across the focus is measured directly using a membrane hydrophone, then compared with the result from the numerical simulation. It is shown that each of the harmonics shares its distribution, with higher harmonic giving narrower beam-width and slightly larger axial distance for its peak pressure.