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Resolution revisited: limit of detail in electron density maps

Resolution revisited: limit of detail in electron density maps Application of the Rayleigh criterion for the limit of resolution of a simple lens with axial illumination leads to the value 0.61. In two-dimensional electron density maps based on X-ray data, the limit of resolution has been considered to be 0.61 dmin, the counterpart of the optical case, and in three-dimensional maps 0.715 dmin. It is shown here that point atoms separated by these distances are not resolved in two- and three-dimensional electron density maps. Such maps are amplitude functions rather than intensity functions as in the optical case. Application of the Rayleigh criterion to the three-dimensional amplitude function for point atoms leads to a value of 0.917 dmin, for the limit of resolution in three-dimensional electron density maps. This result is confirmed by superposing both analytic and numeric functions for point atoms and numeric functions for real atoms with B = 0 and 10 A2. Finally, some implications of diffraction effects in X-ray structure analysis are considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

Resolution revisited: limit of detail in electron density maps

Resolution revisited: limit of detail in electron density maps


Abstract

Application of the Rayleigh criterion for the limit of resolution of a simple lens with axial illumination leads to the value 0.61. In two-dimensional electron density maps based on X-ray data, the limit of resolution has been considered to be 0.61 dmin, the counterpart of the optical case, and in three-dimensional maps 0.715 dmin. It is shown here that point atoms separated by these distances are not resolved in two- and three-dimensional electron density maps. Such maps are amplitude functions rather than intensity functions as in the optical case. Application of the Rayleigh criterion to the three-dimensional amplitude function for point atoms leads to a value of 0.917 dmin, for the limit of resolution in three-dimensional electron density maps. This result is confirmed by superposing both analytic and numeric functions for point atoms and numeric functions for real atoms with B = 0 and 10 A2. Finally, some implications of diffraction effects in X-ray structure analysis are considered.

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References (6)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 1984 International Union of Crystallography
ISSN
0108-7673
DOI
10.1107/S0108767384000507
Publisher site
See Article on Publisher Site

Abstract

Application of the Rayleigh criterion for the limit of resolution of a simple lens with axial illumination leads to the value 0.61. In two-dimensional electron density maps based on X-ray data, the limit of resolution has been considered to be 0.61 dmin, the counterpart of the optical case, and in three-dimensional maps 0.715 dmin. It is shown here that point atoms separated by these distances are not resolved in two- and three-dimensional electron density maps. Such maps are amplitude functions rather than intensity functions as in the optical case. Application of the Rayleigh criterion to the three-dimensional amplitude function for point atoms leads to a value of 0.917 dmin, for the limit of resolution in three-dimensional electron density maps. This result is confirmed by superposing both analytic and numeric functions for point atoms and numeric functions for real atoms with B = 0 and 10 A2. Finally, some implications of diffraction effects in X-ray structure analysis are considered.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: May 1, 1984

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