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When density distributions in crystals are reconstructed from three-dimensional diffraction data, a problem sometimes occurs when the spatial resolution in one given direction is very small compared to that in perpendicular directions. In this case, a two-dimensional projected density is usually reconstructed. For this task, the conventional Fourier inversion method only makes use of those structure factors measured in the projection plane. All the other structure factors contribute zero to the reconstruction of a projected density. On the contrary, the maximum-entropy method uses all the three-dimensional data, to yield three-dimensional-enhanced two-dimensional projected density maps. It is even possible to reconstruct a projection in the extreme case when not one structure factor in the plane of projection is known. In the case of poor resolution along one given direction, a Fourier inversion reconstruction gives very low quality three-dimensional densities `smeared' in the third dimension. The application of the maximum-entropy procedure reduces the smearing significantly and reasonably well resolved projections along most directions can now be obtained from the MaxEnt three-dimensional density. To illustrate these two ideas, particular examples based on real polarized neutron diffraction data sets are presented.
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