Back reflection of ultrasonic waves from a liquid-solid interface

Abstract

The problem of back reflection of ultrasound from a liquid-solid interface is considered analytically. In experiments it has been observed that the back reflected energy radiates from the interface at the Rayleigh critical angle, irrespective of the incident angle. Mathematically, this radiation corresponds to the complex leaky Rayleigh wave pole of the reflection coefficient. The back-reflected amplitude is proportional to the Fourier transform of the incident field on the interface evaluated at the pole wavenumber. The transforms are calculated for several different ultrasonic beam profiles. The beams are characterized by the field on the transmitting transducer. A Gaussian profile is shown to produce a very small back reflection. Similar results hold for a beam composed of an array of Gaussian beams. This beam has the useful property that as limiting cases it reduces to a simple Gaussian beam and a regular SINC beam. Other beam profiles are examined which give a larger effect than these. The role that the radiation function of the transmitter plays in the back reflection is discussed.