The phase problem is the loss of the wave phases of the crystal basis structure factors when an experiment records their squared magnitudes. Write . A Fourier series reconstruction of a periodic electron density uses both and , whereas an ordinary wave intensity measurement supplies only . Estimating the missing phases therefore needs additional constraints or measurements.[ref]
Phase problem. Online Dictionary of Crystallography by International Union of Crystallography; Definition: missing structure-factor phases prevent reconstruction of atomic positions; Methods of solution: estimates are tested against observations
There is also an unavoidable choice of origin. Translating all motif positions by the same fractional crystal coordinate vector multiplies by without changing . The physical arrangement is unchanged. A reconstructed coordinate list must therefore distinguish a coordinate convention from information actually recovered from the measurements.
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The phase problem is a fundamental issue in the field of X-ray crystallography and other areas of wave physics, where the information about the phase of a wave is lost or not directly measurable. This problem stems from the fact that when a crystal is subjected to X-ray diffraction, the resulting intensity of the diffracted beams can be measured, but the phase of those beams cannot be directly observed.