Transient Analysis of the Transmitting and Receiving Properties of a FocusedAcoustic Transducer with Arbitrary Rim

摘要

We derive closed-form analytic expressions for the efficient calculation of thetransient acoustic wavefield emitted by a focused transducer with a spherical surface and for the signal response due to a point-source excited transient acoustic wavefield incident on it. The radiated transient acoustic wavefield is evaluated by applying the Maggi-Rubinowicz transformation to the Kirchhoff-Huygens representation of the wavefield. With the aid of the Rayleigh and Lorentz reciprocity relation for acoustic wavefields, we express the received signal from a point source at an arbitrary location, as a line integral over the rim of the transducer. The line integrals are readily evaluated numerically and the results are used to study the shape of the beam emitted by the transducer in its dependence on the shape of the rim as well as to analyze its resolving power in ultrasonic imaging applications.