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A new three-dimensional (3-D) acoustic image formation technique is proposed that is based on the transmission of wide bandwidth pulse signals and the application of the 3-D fast Fourier transform. A solution to the Helmholtz wave equation has been obtained using the Born approximation. The solution contains analytical expressions for the spatial spectra of the transmit and receive radiation patterns for transducers of various geometries with lenses of fixed focal distances. It has been shown that the proposed algorithms allow for radiation patterns with constant widths at depths both behind and in front of the focal point, starting practically from the plane of the transducer. The theoretical and experimental investigations and computer simulation for both spherical and rectangular transducer shapes have been performed. The results were used to estimate the beamwidths and the side lobe levels. A variant of the linear array has been studied for a cylindrical lens of a fixed focal distance moving in a lateral direction. It has been shown that, in this case, a high resolution (of the order of a few wavelengths) can be achieved along all three Cartesian coordinates at a very high scanning velocity. The influence of the moving scatterers' velocity in inhomogeneous medium on the spatial radiation pattern characteristics has been estimated.