Ultrasonic transducer beams model, using transient angular spectrum

A method for modeling the ultrasonic transducer field in any medium has been developed. This method can take into account the crossing of a plane interface separating two media. This model takes into account the transient side of the field, with the help of an extension of angular spectrum notion. Indeed, it has been shown that a change of variable (components of the slowness vector instead of those of the wave number vector) at the spatio-temporal spectrum level, permits, for each propagation direction, the response signal to be reconstructed. In this way, a decomposition into transient plane waves (transient angular spectrum) is obtained. The recomposition at any point of the field is then no more than a summation, with the suitable delays of all these plane waves. The advantage of this method is that the decomposition into transient plane waves, which is the longest operation, has to be performed just once, for a given transducer. The adaptation to varied geometrical configurations (interface, incident angle etc.) is only taken into account at the step of the final recomposition. The presented results have been interpreted in terms of geometrical wave and edge waves. Subsequently, it will permits the integration to be simplified, by taking into account only the waves of which the summation does contribute to the resulting signal.