Elimination of minimal FFT grid-size limitations

The fast Fourier transform (FFT) algorithm as normally formulated allows one to compute the Fourier transform of up toNcomplex structure factors,F(h),N/2 ≥h> −N/2, if the transform ρ(r) is computed on anN-point grid. Most crystallographic FFT programs test the ranges of the Miller indices of the input data to ensure that the total number of grid divisions in thex,yandzdirections of the cell is sufficiently large enough to perform the FFT. This note calls attention to a simple remedy whereby an FFT can be used to compute the transform on as coarse a grid as one desires without loss of precision.