Three-dimensional optical transforms

In recent years optical diffraction patterns have been used to assist in the solution of certain X-ray diffraction problems. The most useful technique—which is based partly on the properties of Fourier transforms and partly on optical experiments—is usually known as the optical-transform technique. It has, however, so far been confined to problems involving the projection of crystal structures on to a plane. The present work is aimed at extending the application to full three-dimensional structures. It is shown that this is most simply achieved by controlling the relative phases of beams of light; a method of phase control using circularly polarized light and half-wave plates of mica is described. The theory of the method, experimental details, and the demonstration of its validity are given. In order to gain experience in the use of three-dimensional optical transforms for solving X-ray diffraction problems a known structure has been examined, and the results of this work are included. Although this work has been primarily concerned with applications to X-ray diffraction, it is thought that the method of continuous phase changing, which is simple and linear, may find uses in other fields.