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

Closed-form analytic expressions are derived for the efficient calcula tion of the transient acoustic wave field emitted by a focused transdu cer with a spherical surface. The radiated transient acoustic wave fie ld is evaluated by applying the Maggi-Rubinowicz transformation to the Kirchhoff-Huygens representation of the wave field. This transformati on results in a line integral representation along the rim of the radi ating aperture that holds for a rim of arbitrary shape, and for both p lanar and nonplanar radiators. The line integral is readily evaluated numerically and the results are used to study the shape of the beam em itted by the transducer in its dependence on the shape of the rim. Thi s is shown through numerical results for a spherical-cap transducer an d a spherically curved rectangular-strip transducer. The computation t ime needed to evaluate the (one-dimensional) integrals is in the order of seconds on a standard workstation. (C) 1995 Acoustical Society of America.