Phase problem

In physics, the phase problem is the name given to the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches have been developed over the years that attempt to solve it.

Light detectors, such as photographic plates or CCDs, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other degrees of freedom such as polarization and angle of incidence) because a light wave has not only an amplitude (related to the intensity), but also a phase, which is systematically lost in a measurement. 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. 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.

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