TRANSIENT ANALYSIS OF THE TRANSMITTING PROPERTIES OF A FOCUSED ACOUSTIC TRANSDUCER WITH AN ARBITRARY RIM

Closed-form analytic expressions are derived for the efficient calculation of the transient acoustic wave field emitted by a focused transducer with a spherical surface. The radiated transient acoustic wave field is evaluated by applying the Maggi-Rubinowicz transformation to the Kirchhoff-Huygens representation of the wave field. This transformation results in a line integral representation along the rim of the radiating aperture that holds for a rim of arbitrary shape, and for both planar and nonplanar radiators. The line integral is 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. This is shown through numerical results for a spherical-cap transducer and a spherically curved rectangular-strip transducer. The computation time needed to evaluate the (one-dimensional) integrals is in the order of seconds on a standard workstation. (C) 1995 Acoustical Society of America.