Automatic Three-Dimensional Fourier Synthesis

Formally, Fourier synthesis is performed by visual analysis of two-dimensional Fourier maps. The advantage of this is the use of the analyst's experience and intuition, but this procedure is rather tiresome and time consuming. More attractive is the idea of an automatic analysis of three-dimensional Fourier maps, as these maps provide the fastest access to the physical information. An automatic procedure for finding peaks (positions of atoms in a crystal) of a three-dimensional function F(x,y, z), which is the inverse Fourier transform of the experimental structure factors, is a very convenient, and in computer-based crystallographic data analysis, a quite indispensable tool. This paper describes a method for three-dimensional peak search. Also, interpretation of the practical aspects of Fourier synthesis in terms of discrete Fourier transform is given, which is more appropriate than the continuous approach.