= £((x, y, (n — 1)qo)) exp(iVpt(x, y)) x £^exp^^(x2 + y2)

With fast Fourier transforms the computation time can be remarkably reduced in comparison with the convolution. For the calculation of the images, phase changes due to defocus and spherical or chromatic aberrations must be considered. These effects are not considered here but are discussed in detail by Fejes [28].

For the calculation of the projected potentials, the atomic positions, and hence the structures of the samples, must be known. The calculation is performed by using atomic form factors as published, for instance, by Doyle and Turner [29]:

where /t are the atomic form factors of atoms at position rn. The whole procedure is described in more detail by Nihoul et al. [3o].

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