Modeling the Radiation of Focused and Unfocused Ultrasonic Transducers through Planar Interfaces

Characterizing the wave field produced by an ultrasonic transducer is one important part of developing a complete measurement model of an ultrasonic NDE system. Within the paraxial approximation [1], this wave field can be expressed as a quasi plane wave field modified by a diffraction correction tenn to account for the 3-D effects of having a finite beam generated by the transducer. Previously, diffraction corrections have been obtained analytically in some simple cases [1] and numerically, using a Gauss-Hermite expansion [2]. Here, we will show that the radiation of both planar and spherically focused probes through a planar interface can be treated in a unified manner using angular plane wave spectrum integrals and the method of stationary phase. In the paraxial approximation, this unified approach will also be shown to produce diffraction corrections in the fonn of boundary diffraction waves [3]. These boundary diffraction wave diffraction corrections are in terms of at most I-D integrations on the edge of the transducer, so that they can be easily evaluated numerically.