Integral approximation method for calculating ultrasonic beam propagation in anisotropic materials

Plane-wave solutions to the acoustic wave equations in a generally anisotropic solid are reviewed, along with their connection to geometric ray theory. A Fourier-transform formulation of the field of a focused beam (coherent point source) passed from a liquid couplant to an anisotropic specimen through a plane surface is derived. The integral is approximated asymptotically using the stationary-phase method. The result for isotropic media is derived analytically to facilitate a direct comparison to the ray theory. The application of this method to the anisotropic case is illustrated, using the real-world example of the austenitic stainless-steel weld.