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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 13129–13137

Solving structure with sparse, randomly-oriented x-ray data

Hugh T. Philipp, Kartik Ayyer, Mark W. Tate, Veit Elser, and Sol M. Gruner  »View Author Affiliations

Optics Express, Vol. 20, Issue 12, pp. 13129-13137 (2012)

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Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing hundreds of thousands of images that contain very few x-rays. Each low-fluence image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of recovering structural information at these extremes using low-fluence images of a randomly oriented 2D x-ray mask. Successful reconstruction is obtained with images averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-fluence data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal.

© 2012 OSA

OCIS Codes
(000.2190) General : Experimental physics
(040.0040) Detectors : Detectors
(040.7480) Detectors : X-rays, soft x-rays, extreme ultraviolet (EUV)
(110.7440) Imaging systems : X-ray imaging
(110.3055) Imaging systems : Information theoretical analysis
(110.4155) Imaging systems : Multiframe image processing

ToC Category:
Imaging Systems

Original Manuscript: March 23, 2012
Revised Manuscript: April 30, 2012
Manuscript Accepted: May 16, 2012
Published: May 25, 2012

Virtual Issues
Vol. 7, Iss. 8 Virtual Journal for Biomedical Optics

Hugh T. Philipp, Kartik Ayyer, Mark W. Tate, Veit Elser, and Sol M. Gruner, "Solving structure with sparse, randomly-oriented x-ray data," Opt. Express 20, 13129-13137 (2012)

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  1. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature406, 752–757 (2000). [CrossRef] [PubMed]
  2. V. Elser, “Noise limits on reconstructing diffraction signals from random tomographs,” IEEE Trans. Inf. Theory55, 4715–4722 (2009). [CrossRef]
  3. N.-T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phys. Rev. E80, 026705 (2009). [CrossRef]
  4. N. D. Loh, M. J. Bogan, V. Elser, A. Barty, S. Boutet, S. Bajt, J. Hajdu, T. Ekeberg, F. R. N. C. Maia, J. Schulz, M. M. Seibert, B. Iwan, N. Timneanu, S. Marchesini, I. Schlichting, R. L. Shoeman, L. Lomb, M. Frank, M. Liang, and H. N. Chapman, “Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns,” Phys. Rev. Lett.104, 225501 (2010). [CrossRef] [PubMed]
  5. H. T. Philipp, L. J. Koerner, M. S. Hromalik, M. W. Tate, and S. M. Gruner, “Femtosecond radiation experiment detector for x-ray free-electron laser (XFEL) coherent x-ray imaging,” IEEE Trans. Nucl. Sci.57, 3795–3799 (2010).
  6. H. T. Philipp, M. W. Tate, and S. M. Gruner, “Low-flux measurements with Cornell’s LCLS integrating pixel array detector.” J. Inst.6, C11006 (2011). [CrossRef]
  7. L. E. Baum, T. Petrie, G. Soules, and N. Weiss, “A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains,” Ann. Math. Statist.41, 164–171 (1970). [CrossRef]
  8. G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol.144, 219–227 (2003). [CrossRef] [PubMed]
  9. R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, and A. Singer, “Graph Laplacian tomography from unknown random projections,” IEEE Trans. Image Proc.17, 1891–1899 (2008). [CrossRef]
  10. D. Giannakis, P. Schwander, and A. Ourmazd, “The symmetries of image formation by scattering. I. Theoretical framework,” arXiv:1009.5035 (2010).
  11. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science321, 379–382 (2008). [CrossRef] [PubMed]
  12. D. H. Bilderback, J. D. Brock, D. S. Dale, K. D. Finkelstein, M. A. Pfeifer, and S. M. Gruner, “Energy recovery linac (ERL) coherent hard x-ray sources,” New J. Phys.12, 035011 (2010). [CrossRef]
  13. C. E. Shannon, “A Mathematical Theory of Communication,” Bell Syst. Tech. J.,27, 379–423, 623–656 (1948).

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