Calculation of wideband ultrasonic fields radiated by immersed transducers into solids

In ultrasonic nondestructive testing (NDT), configurations of immersion techniques where transducers radiate through non-planar interfaces are often encountered, e.g., pipe inspection where the probe can be scanned either inside or outside the pipe. When local radii of curvature are far larger that typical wave paths in the coupling fluid and into the piece, field predictions can often be made assuming a plane interface. For smaller radii, such an approximation is not valid. The model developed at the French Atomic ENergy Commission (CEA) to predict ultrasonic fields radiated by wideband transducers through liquid-interfaces (called Champ-Sons) is based on a modification of the Rayleigh integral to take account of refraction. It is derived under the geometrical optics approximation (GO) which introduces two factors: the transmission coefficient between the two media of elementary contributions from source-points to field-points and the so-called 'divergence factor' of the transmitted rays (denoted by DF), accounting for the principal radii of curvature of the retransmitted rays (denoted by DF), accounting for the principal radii of curvature of the refracted wave fronts (initially spherical in the coupling medium). (authors)