Spectral analysis of echoes for backscattering coefficient measurement

This paper describes spectral analyses of echoes scattered by a random medium and a plane reflector by using mathematical expressions of echoes which have been proposed by us before [M. Ueda and H. Ichikawa, J. Acoust. Soc. Am. 70, 1768–1775 (1981): 75, 1012 (1984)]. It becomes possible to express the spectrum of echoes scattered by the random medium in terms of a backscattering coefficient of the random medium and a velocity potential of an ultrasonic transducer. The expressions hold for any sound field if a correlation length of the random medium is much smaller than a beamwidth and a radius of the transducer. Then the spectrum of the echo scattered by the plane reflector is expressed in terms of a directivity of the transducer. By using a ratio of the two spectrums an expression which gives the backscattering coefficient of the random medium is formulated. It works in a farfield of a flat circular transducer and at a focal plane of a concave one. It is shown that our formula contains those cases which have been proposed so far as the extreme cases of the conditions. Finally, the backscattering coefficients of sponges are measured with several transducers. The results show that our formula gives the coefficients regardless of the transducer geometry.