Recovering phase information from intensity data.

The concept of a crystal is that of a solid body in which the atomic or molecular units are so arranged as to form an array having three dimensional periodicity. Because of the periodicity, it is possible to describe the arrangements of the atomic composition by means of Fourier series. The type of Fourier series that is used in crystal structure analysis represents the electron density distribution in a crystal. This is indeed equivalent to representing the structure of a crystal since the atomic locations are represented by the regions of highest electron density in the electron distributions. The experimental technique used for examining the structure of crystals is called diffraction. In a diffraction experiment, rays are made to impinge on a crystalline substance of interest and, given the proper geometric conditions, the rays are scattered as if they were bouncing off large numbers of different planes imagined to be cutting through the crystal. The collected intensities of scattering (often 5000-10000 in number) are called a scattering pattern or diffraction pattern and comprise the experimental data from which the structure of the crystal of interest is to be elucidated. The most commonly used rays are Roentgen rays or X-rays, as they are usually called. Other rays, composed of neutrons or electrons, also have their purposes. It is possible to obtain an insight into the character and sense of a diffraction experiment by imagining some experimental circumstances on the macroscopic scale. Let us suppose that we would like to probe the shape of some large object, hidden from view, by using balls that are hurled in a precise way at the object of interest and interact with the surface with essentially perfect restitution. Let us also suppose that it is possible to minimize and correct for the gravitational effects on the impinging balls. We assume that we can observe the results of the bouncing of the balls from the surface of the object. If a large area were scanned perpendicular to the direction in which the balls were hurled and each time the bouncing pattern were essentially parallel but in the opposite direction to that of the impinging balls, we would conclude that the object had a face with a high degree of flatness that was perpendicular to the direction of the impinging balls. Evidently, by varying the orientation of an arbitrarily