Singularities in wave fields and their application to materials characterization

Applications of two kinds of wave field singularities, namely, dislocations and caustics, were investigated. Dislocations are singularities in the phase of a wave and were applied to the characterization, using pulse-echo ultrasound, of surface roughness, metallic microstructure and pitting corrosion. Caustics exist in the short wavelength limit where the wave field can accurately be described by bundles of rays. Caustics are singular planes in such sets of rays. The application of caustics to ultrasonic imaging, three dimensional microscopy and the measurement of small displacements was investigated. The ultrasonic experiments were performed in water immersion at a frequency of 20 MHz.