Reflection of focused sound from curved, rigid surfaces

Abstract

Target geometry and orientation significantly affect the current accuracy of ultrasonic sensors used for gauging and proximity sensing [R. Hickling and S. P. Marin, J. Acoust. Soc. Am. 79, 1151 (1986)]. The reflection of focused sound from curved, rigid surfaces using Gaussian beam solutions obtained from the parabolic approximation of the wave equation has been investigated. Both the focusing of the source and the curvature of the target are modeled by quadratic phase factors. A simple closed‐form solution is thus derived for the sound reflected from concave and convex targets in either axisymmetric or nonaxisymmetric configurations. The validity of the solution is restricted to cases in which the focusing gain of the source, and the curvature of nonperpendicularity of the target, are not too large. Propagation curves, beam patterns, and scattering trajectories are used to illustrate the combined effects of diffraction and target curvature on the reflected sound field. Transfer functions are obtained by comparing the received to the transmitted acoustic power for the case of a monostatic acoustic sensor. [Work supported by GM and NSF.]