The phase problem might initially seem intractable, since, in the absence of a center of symmetry, the phase of any reflection hk may lie anywhere between 0 β’ and 360 β’ , and there is nothing apparent in the diffraction pattern to indicate the values of any of them. If we can only record intensity information, then how can phases ever be obtained? There are, however, some ameliorating circumstances, chief among them being that we do not, in calculating a Fourier summation, require exact values for phases. If we are close, that is, if we have reasonable estimates, usually that is good enough. We generally have so many Fhk to include in the Fourier summation that we can tolerate rather large phase errors for individual reflections. Many may even be entirely wrong. The Fourier transform has the important property that correct phase (and intensity) information tends to reinforce and sum constructively to present a coherent image. On the other hand, incorrect phase (and intensity) information tends only to sum to a more or less uniform, though fluctuating, background.
How clearly the Fourier image emerges from the background (i.e., the contrast) is principally a function of the quality of the phases, and to a lesser extent the intensities. If phases for only some Fhk are correct, or if most Fhk have a large mean phase error, the electron density image produced by a Fourier will be lost in background noise. If, on the other hand, the average phase error is modest, or if a large number of reflections have accurate phases, then the image will stand out above the background. As will be seen below, in almost all cases where we can solve the phase problem, we do so by somehow obtaining rough estimates of the phases for most of the Fhk , and then gradually improving the quality of the phases by reducing the mean phase error.
Ultimately we can solve the phase problem for a number of reasons: (1) We have chemical and physical information about the structure of the molecules making up the crystal that we can use to interpret and improve even a poor electron density image. (2) Information actually does reside in the intensity distribution alone, cryptic information about the relative phases
Introduction to Macromolecular Crystallography, Second Edition