The relationship between the impulse response and angular spectrum methods to evaluate acoustic transient fields

Abstract

Impulse response time domain and angular spectrum or wave vector time-domain methods can be used to investigate the spatial temporal characteristics of acoustic fields from planar ultrasonic transducers which are subjected to pulsed wideband excitations. Both methods are developed here from the time-dependent Green’s function solution of the initial-boundary value problem. The close relationship of the methods is made apparent by the use of spatial-temporal Fourier transform techniques of analysis. Axisymmetric fields are then addressed as a special case via the use of Hankel and Fourier transform techniques. Finally, classical solutions to the associated harmonic boundary value problems are then shown to result from temporal Fourier transforms of the time-dependent field solutions.