The theory of coherent shift-and-add imaging is summarised, is extended to be more generally applicable than in Parts 1 and 2, and is illustrated with the results of computer simulations and laboratory experiments. 2-dimensional images of collections of cylindrical objects (immersed in a water tank into which plastic containers filled with animal offal can be introduced) are reconstructed by shift-and-add (in both its elementary and extended forms) from wideband ultrasonic signals scattered over a wide angle.