= Phase problem
{wiki}
The <phase problem> is the loss of the <wave phases> of the <crystal basis structure factors> when an experiment records their squared magnitudes. Write $F_{hkl}=|F_{hkl}|e^{i\phi_{hkl}}$. A <Fourier series> reconstruction of a periodic <electron density> uses both $|F_{hkl}|$ and $\phi_{hkl}$, whereas an ordinary <wave intensity> measurement supplies only $|F_{hkl}|^2$. Estimating the missing phases therefore needs additional constraints or measurements.<Online Dictionary of Crystallography by International Union of Crystallography/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]{ref}
There is also an unavoidable choice of origin. Translating all motif positions by the same <fractional crystal coordinate> vector $t$ multiplies $F_{hkl}$ by $e^{2\pi i(h,k,l)\cdot t}$ without changing $|F_{hkl}|^2$. 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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