Phase problem

In physics, the phase problem is 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 of phase retrieval have been developed over the years. 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 (related to the direction), and polarization which are 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. phase retrieval There are several ways to retrieve the lost phases. The phase problem must be solved in x-ray crystallography, neutron crystallography, and electron crystallography. Not all of the methods of phase retrieval work with every wavelength (x-ray, neutron, and electron) used in crystallography. If the crystal diffracts to high resolution (

Super Resolution Phase Retrieval for Sparse Signals

Martin Vetterli, Juri Ranieri, Gilles Baechler, Amina Chebira, Miranda Krekovic

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light

Ferroelectric Self-Poling in GeTe Films and Crystals

Super Resolution Phase Retrieval for Sparse Signals

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light

Ferroelectric Self-Poling in GeTe Films and Crystals

Super Resolution Phase Retrieval for Sparse Signals