A GENERALIZED N-DIMENSIONAL INVERSE FOURIER-TRANSFORM INCORPORATING EXPERIMENTAL ERROR BARS

The inverse Fourier transform is a most prominent and widely used tool in crystallography. Used to retrieve Patterson densities and densities from measured intensities or phased structure factors, it is well known to suffer from major drawbacks among which is the neglect of known error bars. In this paper, it is shown how to incorporate measured experimental error bars in the computation of the Fourier syntheses. This simple novel procedure should be useful when a proper maximum-entropy analysis proves infeasible, due to either a high dynamical range of the data or a high dimension of the direct space in which the density is sought (at least five or six dimensions for quasicrystallography).