Phase problem

Summary

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. Overview 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 in

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https://en.wikipedia.org/wiki/Phase_problem

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Features of the secondary structure of a protein molecule from powder diffraction data

Sebastian Basso, Philip Pattison

Protein powder diffraction is shown to be suitable for obtaining de novo solutions to the phase problem at low resolution via phasing methods such as the isomorphous replacement method. Two heavy-atom derivatives (a gadolinium derivative and a holmium derivative) of the tetragonal form of hen egg-white lysozyme were crystallized at room temperature. Using synchrotron radiation, high-quality powder patterns were collected in which pH-induced anisotropic lattice-parameter changes were exploited in order to reduce the challenging and powder-specific problem of overlapping reflections. The phasing power of two heavyatom derivatives in a multiple isomorphous replacement analysis enabled molecular structural information to be obtained up to approximately 5.3 A ˚ resolution. At such a resolution, features of the secondary structure of the lysozyme molecule can be accurately located using programs dedicated to that effect. In addition, the quoted resolution is sufficient to determine the correct hand of the heavy-atom substructure which leads to an electron-density map representing the protein molecule of proper chirality.

International Union of Crystallography2010

Molecular envelopes derived from protein powder diffraction Molecular envelopes derived from protein powder diffraction data

Sebastian Basso, Philip Pattison

The preparation of single crystals suitable for X-ray analysis is frequently the most difﬁcult step in structural studies of proteins.With the aid of two examples, it is shown that de novo solution of the crystallographic phase problem can be achieved at low resolution using microcrystalline powder samples via the single isomorphous replacement method. With synchrotron radiation and optimized instrumentation, high-quality powder patterns have been recorded, from which it was possible to generate phase information for structure factors up to 6 A resolution. pH- and radiation-induced anisotropic lattice changes were exploited to reduce the problem of overlapping reﬂections, which is a major challenge in protein powder diffraction. The resulting data were of sufﬁcient quality to compute molecular envelopes of the protein molecule and to map out the solvent channels in the crystals. The results show that protein powder diffraction can yield low-resolution data that are potentially useful for the characterization of microcrystalline proteins as novel micro- and mesoporous materials as well as for structural studies of biologically important macromolecules.

2008

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In this work we demonstrate the advantages of investigating diffractive optical elements in the phase domain. In this regime we can detect features that are not restrained by the diffraction limit and relate them to the geometrical and optical properties of the sample under test. To accomplish that, we use the custom made spectral high resolution interference microscope. Phase map recordings allow for easier and more precise localization of the positions, where phase changes happen. We show the localization capabilities by detecting phase singularities created by a trench. We also apply the concept to abrupt phase jumps of a phase diffractive component and determine the achievable resolution.

SPIE-INT SOC OPTICAL ENGINEERING2019