Angular spectrum method and ray algorithm for the acoustic field of a focusing transducer in an anisotropic solid

The angular spectrum method is applied to calculating the acoustic field of a liquid-coupled focusing transducer in an anisotropic slab-shaped solid with surfaces normal to the axis of the transducer. The stationary phase approximation (SPA) is used to determine the dominant contributions to this field and calculate the echo signals produced by waves that have been reflected off the rear surface of the solid. The dominant features of this field and of the echoes are reproduced well by a hybrid ray method devised to simulate the finite point-spread function of the lens. Both approaches in the paraxial approximation yield a split focus for each wave polarization branch for a general direction of the surface normal. Echo arrival times and amplitudes calculated by the two methods are in good agreement. The hybrid ray method is shown to be particularly suited to handling multiple stationary phase points within the angular spectrum of the incident field and stationary phase points not associated with the normally incident ray, and should be useful for dealing with scattering from cracks and other defects. Pulse echo calculations for different crystallographic directions in a nickel-based superalloy are shown to be in good agreement with measurements carried out on single crystal specimens of the alloy.