Analysis of an echo signal reflected from a weakly scattering volume by a discrete model of the medium

Abstract

An echo signal reflected from a weakly scattering volume is analyzed by using the wave equation for an inhomogeneous medium and a discrete model of the medium. The discrete model means that the medium is represented by a pile of small cubes which have uniform density and sound velocity, and the size of the cubes is assumed to be much smaller than the wavelength of ultrasonic waves. By adopting the discrete model, simple and understandable relations are obtained from the wave equation for an inhomogeneous medium. The analysis shows that the difference between echo signals scattered by density and velocity fluctuations becomes appreciable when the distance between the scatterer and a transducer is less than a radius of the transducer. The difference was detected experimentally and shows rather good agreement with the theory. Furthermore, relations are obtained which describe echo signals resulting from an arbitrary incident wave in terms of the fluctuation of specific acoustic impedance of medium. These relations are valid in a region a little larger than a radius of the transducer from the transducer. Waveforms of the echo signal reflected from a rod made of silicone rubber are estimated by using the relations and are compared with experimentally obtained echo signals.