New Formulation and Solution of the Phase Problem in X-Ray Analysis of Noncentric Crystals Containing Anomalous Scatterers

1956 ◽  
Vol 103 (6) ◽  
pp. 1645-1647 ◽  
Author(s):  
Yoshiharu Okaya ◽  
Ray Pepinsky
Keyword(s):  
Phase Problem ◽  
X Ray ◽  
New Formulation

Solution to the phase problem using x-ray interferometry

1985 ◽  
Vol 31 (10) ◽  
pp. 6420-6423 ◽  
Author(s):  
J. T. Hutton ◽  
G. T. Trammell ◽  
J. P. Hannon
Keyword(s):  
Phase Problem ◽  
X Ray

scholarly journals The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data. II. The Dependence of the Accuracy of the Solution on the Sampling Step of Experimental Data

2015 ◽  
Vol 10 (2) ◽  
pp. 508-525 ◽  
Author(s):  
Н.Л. Лунина ◽  
N.L. Lunina
Keyword(s):  
Experimental Data ◽  
Particle Image ◽  
Expected Improvement ◽  
Problem Solution ◽  
Phase Problem ◽  
X Ray Diffraction ◽  
Sampling Step ◽  
X Ray ◽  
X Ray Crystallography ◽  
Grid Points

Advances in the methodology of the X-ray diffraction experiments leads to a possibility to register the rays scattered by large isolated biological particles (viruses and individual cells) but not only by crystalline samples. The experiment with an isolated particle provides researchers with the intensities of the scattered rays for the continuous spectrum of scattering vectors. Such experiment gives much more experimental data than an experiment with a crystalline sample where the information is limited to a set of Bragg reflections. This opens up additional opportunities in solving underlying problem of X-ray crystallography, namely, calculating phase values for the scattered waves needed to restore the structure of the object under study. In practice, the original continuous diffraction pattern is sampled, reduced to the values at grid points in the space of scattering vectors (in the reciprocal space). The sampling step determines the amount of the information involved in solving the phase problem and the complexity of the necessary calculations. In this paper, we investigate the effect of the sampling step on the accuracy of the phase problem solution obtained by the method proposed earlier by the authors. It is shown that an expected improvement of the accuracy of the solution with the reducing the sampling step continues even after crossing the Nyquist limit defined as the inverse of the double size of the object under study.

Ultrafast Imaging and the Phase Problem for Inelastic X-Ray Scattering

2010 ◽  
Vol 22 (10) ◽  
pp. 1141-1147 ◽  
Author(s):  
Peter Abbamonte ◽  
Gerard C. L. Wong ◽  
David G. Cahill ◽  
James P. Reed ◽  
Robert H. Coridan ◽  
...  
Keyword(s):  
Phase Problem ◽  
X Ray ◽  
Ultrafast Imaging ◽  
X Ray Scattering ◽  
Ray Scattering

X-Ray Crystallography: The Past and Present of the Phase Problem

2015 ◽  
pp. 3-18
Author(s):  
David Sayre
Keyword(s):  
Phase Problem ◽  
X Ray ◽  
X Ray Crystallography ◽  
The Past

Surface structure analysis of Si(111)−Bi by X-ray diffraction — Approach to the solution of the phase problem

1987 ◽  
Vol 191 (3) ◽  
pp. L825-L834 ◽  
Author(s):  
Toshio Takahashi ◽  
Shinichiro Nakatani ◽  
Tetsuya Ishikawa ◽  
Seishi Kikuta
Keyword(s):  
Surface Structure ◽  
Structure Analysis ◽  
Phase Problem ◽  
X Ray Diffraction ◽  
X Ray
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