The rôle of phase in diffuse diffraction patterns and its effect on real-space structure

A previously described method of synthesizing a real-space distribution of scattering points which will give rise to virtually any required diffraction pattern has been investigated from the point of view of trying to establish the rôle that the phase of individual modulations plays in determining the real-space structure. For an object involving continuous random variables, the choice of phase cannot affect the diffracted intensity and phases can be chosen freely. Although such variation of phases does not affect the diffracted intensity, the real-space amplitudes are no longer normally distributed and the structures will in general contain non-zero multisite correlations. For an object involving binary variables (such as site occupancy), it is shown that the phases of individual elementary volumes of reciprocal space not only contain information about multisite correlations, but also contain the information that the object is binary. It is also shown that the information concerning multisite correlations can be, at least partially, transferred to an object giving a different diffraction pattern by using a known set of phases with a different set of amplitudes.