Dynamic inversion by the method of generalized projections

John Spence, B. Calef, J. M. Zuo

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A new approach to the inversion problem of dynamical transmission electron diffraction is described, based on the method of generalized projections in set theory. An algorithm is described that projects between two sets of constrained scattering matrices. This iterative process can be shown to converge, giving the required structure factors (for some choice of origin) if the sets are convex. For the dynamical inversion problem, the set topology is that of an N2 torus, the sets are not convex, and traps are therefore sometimes encountered. These can be distinguished from solutions, allowing the algorithm to be restarted until a solution is found. Examples of successful inversion from simulated multiple-scattering data are given, which therefore solve the phase problem of electron diffraction for centrosymmetric or noncentrosymmetric crystal structures. The method may also be useful for the three-beam X-ray diffraction problem.

Original languageEnglish (US)
Pages (from-to)112-118
Number of pages7
JournalActa Crystallographica Section A: Foundations of Crystallography
Volume55
Issue number2 PART I
StatePublished - Mar 1 1999

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Electron diffraction
projection
Electrons
inversions
Multiple scattering
electron diffraction
Set theory
X-Ray Diffraction
Crystal structure
Topology
S matrix theory
Scattering
X ray diffraction
set theory
topology
traps
crystal structure
scattering
diffraction
x rays

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Structural Biology

Cite this

Dynamic inversion by the method of generalized projections. / Spence, John; Calef, B.; Zuo, J. M.

In: Acta Crystallographica Section A: Foundations of Crystallography, Vol. 55, No. 2 PART I, 01.03.1999, p. 112-118.

Research output: Contribution to journalArticle

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