Characterizing pulses reflected from rough surfaces using ultrasound

Abstract

A model for the scattering of wideband signals from three-dimensional rough surfaces is presented. This development is an extension of the scattering based on the Kirchhoff approximation method for a monochromatic wave source. The usual plane-wave approximation is relaxed and the Kirchhoff method is extended to include spherically diverging waves from the scattering surface. The scattered signal is expressed in terms of the Fourier transform of the acoustic channel. The frequency correlation function of the channel is then derived for a rough surface having the Gaussian spectrum. The coherent and incoherent components of the scattered signal intensity are determined from the frequency correlation function. The theory is applied to the signals produced by the Polaroid transducer operating in air and mounted on a mobile vehicle capable of automatic translation and rotation. Theoretical results are compared with experimental observations from two different rough surfaces. The analytic results are verified over the observable range of incidence angles from 0° to 60°.