next up previous contents
Next:  Sensitivity to the accuracy Up:  Examples Previous:  Positivity and improved resolution   Contents

 Insensitivity to missing data

The second example illustrates the behaviour of the method with respect to missing data. This example was constructed as follows : one-dimensional data were calculated from a hypothetical (1D) structure containing two Gaussians in the asymmetric unit of the pm cell (where p denotes the one-dimensional lattice). This hypothetical structure is shown on the far left panel in the figure below, and the data calculated by Fourier transforming this structure only included 18 strong reflections. The middle column of graphs shows the conventional and GraphEnt syntheses that were obtained when all these 18 reflections were included in the calculation (and, of course, both are essentially identical with the starting structure). When the calculation was repeated with 6 reflections missing from the data set, the conventional map (top, right-hand corner graph) was far from ideal : a new peak appears at x = 0.5, and the relative heights of the two Gaussians are no longer the same. In sharp contrast, the GraphEnt map (lower, right-hand side graph) is almost identical with the synthesis calculated with all data (and with the correct structure).

Figure: Insensitivity to missing data
1D example


next up previous contents
Next:  Sensitivity to the accuracy Up:  Examples Previous:  Positivity and improved resolution   Contents
NMG, Nov 2002