Abstract: Pulses of acoustic energy are transmitted from a plurality of different directions through a plane of interest, or a number of adjacent planes of interest, of a body to be examined. The body may be biological or non-biological. Time-of-flight of the pulses is measured for individual paths through the body, and from the data thus obtained the spatial distribution of the acoustic velocity through the plane or planes within the body is reconstructed using a mathematical reconstruction technique. The velocity values thus obtained, which are uniquely determinative of the acoustic index of refraction at each point, have diagnostic value, and they can further be displayed by means of a cathode ray tube or other imaging device to provide an image of the internal structure along each plane. The disclosed technique has the advantage of being highly independent of acoustic attenuation and reflections occurring along the paths.