Ultrasound imaging is widely used in medicine because of its benign characteristics and real-time capabilities. Physics theory suggests that the application of tomographic techniques may allow ultrasound imaging to reach its full potential as a diagnostic tool allowing it to compete with other tomographic modalities such as x-ray computer tomography, and MRI. This paper describes the construction and use of a prototype tomographic scanner and reports on the feasibility of implementing tomographic theory in practice and the potential of ultrasound (US) tomography in diagnostic imaging. Data were collected with the prototype by scanning two types of phantoms and a cadaveric breast. A specialized suite of algorithms was developed and utilized to construct images of reflectivity and sound speed from the phantom data. The basic results can be summarized as follows. (i) A fast, clinically relevant US tomography scanner can be built using existing technology. (ii) The spatial resolution, deduced from images of reflectivity, is 0.4 mm. The demonstrated 10 cm depth-of-field is superior to that of conventional ultrasound and the image contrast is improved through the reduction of speckle noise and overall lowering of the noise floor. (iii) Images of acoustic properties such as sound speed suggest that it is possible to measure variations in the sound speed of 5 m/s. An apparent correlation with x-ray attenuation suggests that the sound speed can be used to discriminate between various types of soft tissue. (iv) Ultrasound tomography has the potential to improve diagnostic imaging in relation to breast cancer detection.

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The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.

We show that the time reversal operator for a planar time reversal mirror (TRM) can have up to four distinct eigenvalues with a small spherical acoustic scatterer. Each eigenstate represents a resonance between the TRM and an induced scattering moment of the sphere. Their amplitude distributions on the TRM are orthogonal superpositions of the radiation patterns from a monopole and up to three orthogonal dipoles. The induced monopole moment is associated with the compressibility contrast between the sphere and the medium, while the dipole moments are associated with density contrast. The number of eigenstates is related to the number of orthogonal orientations of each induced multipole. For hard spheres (glass, metals) the contribution of the monopole moment to the eigenvalues is much greater than that of the dipole moments, leading to a single dominant eigenvalue. The other eigenvalues are much smaller, making it unlikely multiple eigenvalues could have been observed in previous experiments using hard materials. However, for soft materials such as wood, plastic, or air bubbles the eigenvalues are comparable in magnitude and should be observable. The presence of multiple eigenstates breaks the one-to-one correspondence between eigenstates and distinguishable scatterers discussed previously by Prada and Fink [Wave Motion 20, 151-163 (1994)]. However, eigenfunctions from separate scatterers would have different phases for their eigenfunctions, potentially restoring the ability to distinguish separate scatterers. Since relative magnitudes of the eigenvalues for a single scatterer are governed by the ratio of the compressibility contrast to the density contrast, measurement of the eigenvalue spectrum would provide information on the composition of the scatterer.