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Phase extension in crystallography using the iterative Fienup-Gerchberg-Saxton algorithm and Hilbert transforms.

J S Wu1, J C H Spence

  • 1Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287-1504, USA. jinsong.wu@asu.edu

Acta Crystallographica. Section A, Foundations of Crystallography
|October 29, 2003
PubMed
Summary

This study introduces a novel phase extension method for electron crystallography, enhancing iterative algorithms by incorporating discrete Hilbert transforms and known Bragg reflections for improved phase accuracy in crystallographic data.

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Area of Science:

  • Crystallography
  • Materials Science
  • Data Analysis

Background:

  • Electron crystallography often faces challenges with phase determination, limiting structural resolution.
  • Accurate phase information is crucial for reconstructing electron density maps in crystallography.

Purpose of the Study:

  • To develop an advanced phase extension procedure for electron crystallography.
  • To improve the accuracy and performance of iterative phase retrieval algorithms.

Main Methods:

  • Utilizing the iterative Fienup-Gerchberg-Saxton algorithm combined with discrete Hilbert transforms.
  • Introducing oversampling in reciprocal space to satisfy Shannon sampling requirements.
  • Integrating known strong phased Bragg reflections from electron microscopy or direct methods.

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Main Results:

  • The discrete Hilbert transform enables the introduction of fractional indexed reflections.
  • Accurate magnitudes for numerous non-Bragg reflections were calculated, enhancing iterative algorithm performance.
  • Demonstrated applicability of diffuse scattering phasing algorithms to conventional crystallography for high-order phase determination.

Conclusions:

  • The proposed method effectively extends phases in electron crystallography.
  • This technique allows for the determination of high-order beam phases from low-order phases, advancing crystallographic analysis.