The use of continuous diffraction data as a phase constraint. I. One-dimensional theory

Intensity can often be measured as a continuous function of scattering angle in diffraction from non-crystalline specimens. An analysis of the amount of information contained in one-dimensional continuous diffraction data is presented here. This analysis, based on the sampling theorem and the theory of entire functions, indicates that there is a limited but often rather large number of possible phase solutions to any given continuous intensity distribution. A refinement technique has been developed which allows phase solutions to be found that are consistent with the diffraction data and with other physical and chemical data. In favourable cases, when diffraction data is used in coordination with other kinds of data, there can be enough information in a diffraction pattern to identify a unique structural solution.