Transient fields radiated by curved surfaces—Application to focusing

Abstract

A theoretical model is presented for computing the transient radiated field (potential or pressure) resulting from a curved surface having an arbitrary velocity distribution. The method is a generalization of the angular spectrum theory giving the time impulse response for a given shaped surface. The technique leads to a systems theory interpretation of the radiation and diffraction effects. General expressions for arbitrary surfaces are given but important simplifications occur for radially symmetric geometries. For this case, simple expressions for the wave location may be obtained without requiring solution of the wave. Numerical simulations for common focused waves are given using computationally efficient FFT algorithms.