We discuss the historical origin of the holographic concept in the field of crystallography and its relation to modern applications of similar ideas to the problem of structure completion in macromolecular x-ray crystallography. For structure completion, the identification of the diffracted amplitude from the known part of the structure with a reference wave enables the recovery of the unknown part of the electron density from the diffraction intensities. In this article, we show how this may be achieved by means of a maximum entropy algorithm.