A ring of transmitter and receiver transducer arrays circumbscribes an object to be scanned. Semicircular wave fronts of ultrasound energy are propagated from different points around the ring of transducers by triggering the transmitter arrays in sequence. The reflected and transmitted ultrasound energy picked up by the receiver arrays is then electronically analyzed and a synthetically focused image corresponding to the scanned object is reconstructed on a display screen. Surprisingly high quality resolution for the reconstructed images is achieved by carefully controlling the type of waveform from which the displayed image is reconstructed. In one embodiment of the invention, the signals received by the receiver arrays are processed by a waveshaping circuit to achieve the desired waveform. In a second embodiment of the invention, the desired waveform is generated by a waveform generator circuit and transmitted by the transmitter arrays. The quality of resolution for the reconstructed image of reflection is further improved by obtaining, through a computer aided ray tracing technique, the connecting rays between each point in the object and each transmitter and receiver array element. Data sampling times for each point in the reconstructed image are then corrected for refraction by computer aided integration of the object's refractive index along each connecting ray. Correction of the sampled data for amplitude attenuation is similarly obtained by computer aided integration of the object's linear attenuation coefficient along the connecting rays.