Why phase errors affect the electron function more than amplitude errors

Abstract

If Fexp(iα) are the set of structure factors for a structure f, the amplitudes can be converted to those of an uncorrelated structure g (amplitude swapping) by multiplying each F by the positive number G/F. Correspondingly, the image f is convoluted with k, the Fourier transform of G/F; k has a large peak at the origin, so that f * k ∼ f. For swapped phases, the image f is convoluted with l, the Fourier transform of exp(iΔα), where Δα, the phase difference between F and G, is a random variable; l does not have a large peak at the origin, so that f * l does not resemble f. The paper provides quantitative descriptions of these arguments. © 2008 International Union of Crystallography.