Aberrated foci in the time and frequency domains and experiments with acoustical diffraction catastrophes.

Abstract

Properties of wave fields at and near foci are considered for situations in which the amplitude is limited by the shape of an initial wave front rather than its aperture or initial dimensions. Such aberrated foci are relevant to high-frequency scattering from curved surfaces and to understanding the response of source and receiver arrays. Caustics classified by generic catastrophes are considered such as produced by random phase perturbations or by aberrations of imaging systems [M. V. Berry and C. Upstill, Prog. Opt. 18, 258 (1980)]. Experiments were carried out in which ultrasonic transients and tone bursts were reflected from a curved metal sheet in water such that the resulting caustic surface was a cusp which opens up generally transverse to the propagation direction of the reflected wave front [C. K. Frederickson, Ph.D. dissertation, Washington State University (1991)]. The results illustrate several more general properties of transient responses and diffraction patterns near weak foci. For example, the singular part of the travel time surface describing the merging of echoes has a shape like that of the next higher cuspoid catastrophe: a swallowtail catastrophe. Conditions for neglecting the effects of apertures on catastrophe diffraction patterns are examined. [Work supported by ONR.]