Paraxial approximations for ultrasonic beam propagation in liquid and solid media with applications to nondestructive evaluation
Quantitative models can play an important role in the development and validation of ultrasonic nondestructive evaluation procedures. Successful prediction of inspection results can greatly reduce the time and monetary expense incurred by a completely experimental approach. One type of model, which is necessary in order to make such predictions, is a model for the propagation of the ultrasonic beams which are generated by the transducers used in nondestructive inspections. Two examples of this type of model have been derived in this work. The first predicts the radiation field only on the axis of a focused elliptical piston transducer radiating into an isotropic material and possibly through a bicylindrically curved interface. The solution takes the form of either a simple analytical formula for some cases or a simple numerical integration over a finite interval for other cases. The second example predicts the full off-axis radiation field produced in either an isotropic or anisotropic material and possibly transmitted through a bicylindrically curved interface. The solution takes the form of a series summation over a set of Gauss-Hermite eigenfunctions. Both models are derived from the angular spectrum of plane waves approach and have made use of the paraxial, or Fresnel, approximation. The latter, more general, Gauss-Hermite model is validated by comparison with experimentally mapped ultrasonic beam fields in a range of materials, both isotropic and anisotropic. The model agrees very well with experimental results except for a few cases for which the limits of the Fresnel approximation are reached. The results of two applications of the model, transducer design and the analysis of beam distortions due to nonsmooth interfaces, are discussed and other potential applications are indicated.