Exact solution of the inverse acoustic scattering problem for the one-dimensional density profile in cylindrical geometry

Abstract The inhomogeneous acoustic wave equation in cylindrically symmetric geometry, is reduced to a one-dimensional Schrodinger equation for time harmonic waves. The scattering potential so formed is uniquely reconstructed by the Gelfand-Levitan theory. In physical terms, the scattering potential is a function of the impedance profile, which is then recovered. If the velocity profile is known (or constant) the density profile, as a function of the radial coordinate, can be deduced. A practical experiment is envisaged whereby the back-scattered time sequence is measured in a pulse-echo mode, and the data are used to reconstruct the density profile.