Towards the end of the 1960s, a number of quite different circumstances combined to launch a period of intense activity in the digital processing of electron micro­ graphs. First, many years of work on correcting the resolution-limiting aberrations of electron microscope objectives had shown that these optical impediments to very high resolution could indeed be overcome, but only at the cost of immense exper­ imental difficulty; thanks largely to the theoretical work of K. -J. Hanszen and his colleagues and to the experimental work of F. Thon, the notions of transfer func­ tions were beginning to supplant or complement the concepts of geometrical optics in electron optical thinking; and finally, large fast computers, capable of manipu­ lating big image matrices in a reasonable time, were widely accessible. Thus the idea that recorded electron microscope images could be improved in some way or rendered more informative by subsequent computer processing gradually gained ground. At first, most effort was concentrated on three-dimensional reconstruction, particu­ larly of specimens with natural symmetry that could be exploited, and on linear operations on weakly scattering specimens (Chap. l). In 1973, however, R. W. Gerchberg and W. O. Saxton described an iterative algorithm that in principle yielded the phase and amplitude of the electron wave emerging from a strongly scattering speci­ men.