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Phasing of Three Dimensional Diffraction Patterns from Finite-Sized Objects

Phasing of Three Dimensional Diffraction Patterns from Finite-Sized Objects. Ian Robinson Ivan Vartanyants Mark Pfeifer John Pitney Garth Williams Sébastien Boutet. Department of Physics University of Illinois SSRL Imaging Workshop, October 2002. Outline. Coherence in Diffraction

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Phasing of Three Dimensional Diffraction Patterns from Finite-Sized Objects

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  1. Phasing of Three Dimensional Diffraction Patterns from Finite-Sized Objects • Ian Robinson • Ivan Vartanyants • Mark Pfeifer • John Pitney • Garth Williams • Sébastien Boutet Department of Physics University of Illinois SSRL Imaging Workshop, October 2002 I. K. Robinson, SSRL Imaging Workshop, October 2002

  2. Outline • Coherence in Diffraction • The Phase Problem • Nanocrystal Shapes • Crystallization of Proteins • Applications at LCLS I. K. Robinson, SSRL Imaging Workshop, October 2002

  3. Tomato Bushy Stunt Virus1980 I. K. Robinson, SSRL Imaging Workshop, October 2002

  4. Goals of Coherent Diffraction • Thermodynamic fluctuations • No ensemble average in CXD • Probe of structure on nm scale • 1D, 2D and 3D • non-periodic object gives continuous F(q) • Oversampling (in reciprocal space) permits solution of the phase problem I. K. Robinson, SSRL Imaging Workshop, October 2002

  5. Lensless X-ray Microscopebased on diffraction from crystal lattice I. K. Robinson, SSRL Imaging Workshop, October 2002

  6. Coherence at the APSTypical 3rd Generation (undulator) Synchrotron SourceLCLS coherence will be better Coherent region defined by slits I. K. Robinson, SSRL Imaging Workshop, October 2002

  7. Diffuse Scattering acquires Structure using CXD I. K. Robinson, SSRL Imaging Workshop, October 2002

  8. Phase Problem: Finite-size Effect I. K. Robinson, SSRL Imaging Workshop, October 2002

  9. Generic “Error Reduction” method J. R. Fienup Appl. Opt. 21 2758 (1982) R. W. Gerchberg and W. O. Saxton Optik 35 237 (1972) I. K. Robinson, SSRL Imaging Workshop, October 2002

  10. “ER” Methods in CrystallograhyR. P. Millane, J. Opt. Soc Am. A 13 725 (1996) • ‘Positivity’ constraint • Finite support, molecular envelope • Solvent flattening • Molecular replacement • Non-crystallographic symmetry • Basis of ‘direct methods’ (Sayre, Bricogne) • Non-uniqueness is ‘pathologically rare’ (d>1) I. K. Robinson, SSRL Imaging Workshop, October 2002

  11. I. K. Robinson, SSRL Imaging Workshop, October 2002

  12. Diffraction as a Surface Integral Annalen der Physik [5] 26 55 (1936) “Stacheln” I. K. Robinson, SSRL Imaging Workshop, October 2002

  13. I. K. Robinson, SSRL Imaging Workshop, October 2002

  14. SEMS • Au blanket film • Quartz substrate • Annealed at 950°C for 70 hrs. I. K. Robinson, SSRL Imaging Workshop, October 2002

  15. Micron-sized gold crystal:(111) Bragg reflection I. K. Robinson, SSRL Imaging Workshop, October 2002

  16. Symmetrized Data and two best fitsChisq=0.0005 I. K. Robinson, SSRL Imaging Workshop, October 2002

  17. 2D Reconstructionschisquare = 0.0005 I. K. Robinson, SSRL Imaging Workshop, October 2002

  18. 3D Diffraction Method kf Q=kf - ki ki I. K. Robinson, SSRL Imaging Workshop, October 2002

  19. In-situ Study of Crystallization I. K. Robinson, SSRL Imaging Workshop, October 2002

  20. Experiment at APS Sector 34 I. K. Robinson, SSRL Imaging Workshop, October 2002

  21. “Pink beam” sees CTRs I. K. Robinson, SSRL Imaging Workshop, October 2002

  22. Ferritin (111) Powder Ring • 50 frames • 30sec exposure • 0.3sec playback • 150x200 pixels of 22.5μm I. K. Robinson, SSRL Imaging Workshop, October 2002

  23. Conclusions and Outlook • “Diffuse” scattering acquires fine structure • Phase problem solved by oversampling • Images of small particles in 3D • Applications of CXD at LCLS • (physics) fluctuations at the atomic level • (biology) imaging of viruses and proteins I. K. Robinson, SSRL Imaging Workshop, October 2002

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