X-ray crystallographic imaging

X-ray crystallography is the dominant method for measuring the relative positions in three-dimensional space of each atom in a molecule. This information has long been crucial for many scientific purposes and is increasingly important for the rational design of drugs. The X-ray scattering is the Fourier transform of the electron density. However, only the intensity and not the phase of the scattering can be measured. Therefore, the signal processing is fundamentally phase retrieval. The situation is complicated, however, by the three-dimensional nature of the problem and the periodicity of the crystal. In this paper the underlying physics is sketched, a variety of crystallographic experiments and the resulting types of multidimensional signal processing are described, and the application to drug design is outlined