Phase recovery for x-ray crystallography

For many years people have believed that in conventional x-ray crystallography one can only record the diffraction intensities but not the phases. In order to obtain the atomic arrangements, one usually has to guess a structure and then fit the intensity data by refining its parameters. Here, we show that the phases are in fact hidden in the intensity data, and can be directly recovered from the peak profiles. This method is demonstrated by the normal two-beam x-ray diffraction of a noncentrosymmetric crystal, and nontrivial phases are recovered from the intensity data alone.