Editing Phase problem (section)

==Overview==

Light detectors, such as [[photographic plate]]s or [[charge-coupled device|CCD]]s, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other [[degrees of freedom (physics and chemistry)|degrees of freedom]] such as [[polarization (waves)|polarization]] and [[angle of incidence (optics)|angle of incidence]]) because a light wave has not only an amplitude (related to the intensity), but also a phase (related to the direction), and polarization which are systematically lost in a measurement.<ref name=":1" /> In [[diffraction]] or [[microscopy]] experiments, the phase part of the wave often contains valuable information on the studied specimen. The phase problem constitutes a fundamental limitation ultimately related to the nature of [[measurement in quantum mechanics]].

In [[X-ray crystallography]], the diffraction data when properly assembled gives the amplitude of the 3D [[Fourier transform]] of the molecule's [[electron density]] in the [[unit cell]].<ref name=":0" /> If the phases are known, the electron density can be simply obtained by [[Fourier synthesis]]. This Fourier transform relation also holds for two-dimensional far-field [[diffraction]] patterns (also called [[Fraunhofer diffraction]]) giving rise to a similar type of phase problem.