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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12799–12826

The symmetries of image formation by scattering. I. Theoretical framework

Dimitrios Giannakis, Peter Schwander, and Abbas Ourmazd  »View Author Affiliations

Optics Express, Vol. 20, Issue 12, pp. 12799-12826 (2012)

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We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we present an approach to image formation based on the symmetry properties of operations in three-dimensional space. Augmented with graph-theoretic means, this approach can recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. This is critical for the burgeoning field of structure recovery by X-ray Free Electron Lasers, as well as the more established electron microscopic techniques, including cryo-electron microscopy of biological systems. In a subsequent paper, we demonstrate the recovery of structure and dynamics from experimental, ultralow-signal random sightings of systems with X-rays, electrons, and photons, with no orientational or timing information.

© 2012 OSA

OCIS Codes
(140.2600) Lasers and laser optics : Free-electron lasers (FELs)
(180.6900) Microscopy : Three-dimensional microscopy
(290.3200) Scattering : Inverse scattering
(290.5840) Scattering : Scattering, molecules
(290.5825) Scattering : Scattering theory

ToC Category:

Original Manuscript: February 9, 2012
Revised Manuscript: May 11, 2012
Manuscript Accepted: May 16, 2012
Published: May 23, 2012

Dimitrios Giannakis, Peter Schwander, and Abbas Ourmazd, "The symmetries of image formation by scattering. I. Theoretical framework," Opt. Express 20, 12799-12826 (2012)

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