1. John Miao Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Crystallography without Crystals and the Potential of Imaging Single Molecules

2. Detector Coherent Beam Atoms The trivial phases: The Phase Problem

3. Regular Sampling: Sampling at the Bragg-peak Frequency # of unknown variables # of independent equations 1DNN/2 2DN2N2 N 2 /2 3DN3N3 N 3 /2 # of unknown variables # of independent equations 1D2NN 2D2N 2 N2N2 3D2N 3 N3N3

4. Oversampling: Sampling at Twice of the Bragg-peak Frequency # of unknown variables # of independent equations 1DNN 2DN2N2 2N 2 3DN3N3 4N 3 # of unknown variables # of independent equations 1D2N 2D2N 2 4N 2 3D2N 3 8N 3 Miao, Sayre & Chapman, J. Opt. Soc. Am. A 15, 1662 (1998). Miao & Sayre, Acta Cryst. A 56, 596 (2000).

5. Eq. (2)   > 2: the phase information exists inside the diffraction intensity! The Oversampling Method

6. 1D Case: (  2 N multiple solutions) 2D & 3D Case: (No multiple solutions) Mathematically, 2D and 3D polynomials usually can not be factorized. Bruck & Sodin, Opt. Commun. 30, 304 (1979). Multiple Solutions

7. Coherence Requirements of the Oversampling Method Oversampling vs. temporal coherence: Oversampling vs. spatial coherence: Miao et al., Phys. Rev. Lett. 89, 088303 (2002). : sample size :desired resolution

8. An Iterative Algorithm (I) ( II ) = 0 (III) = FFT -1 ( ) (IV) (V) (VI) = FFT( ) (VII) Adopt from Fienup, Appl. Opt. 21, 2758 (1982). Miao et al., Phys. Rev. B 67, 174104 (2003). with  > 5

9. The First Experiment of Crystallography without Crystals (a) A SEM image (b) An oversampled diffraction pattern (in a logarithmic scale) from (a). (c) An image reconstructed from (b). Miao, Charalambous, Kirz, Sayre, Nature 400, 342 (1999). (d) The convergence of the reconstruction.

10. Phase Retrieval as a Function of the oversampling ratio (  )  = 5 (180 x 180 pixels)  = 4 (160 x 160 pixels)  = 2.6 (130 x 130 pixels)  = 1.9 (110 x 110 pixels) Miao et al., PRB, in press.

11. Imaging Buried Nanostructures (a) A SEM image of a double-layered sample made of Ni (~2.7 x 2.5 x 1  m 3 ) (c) An image reconstructed from (b) Miao et al., Phys. Rev. Lett. 89, 088303 (2002). (b) A coherent diffraction pattern from (a) (the resolution at the edge is 8 nm)

12. 3D Imaging of Nanostructures The reconstructed top pattern The reconstructed bottom pattern An iso-surface rendering of the reconstructed 3D structure

13. Determining the Absolute Electron Density of Disordered Materials at Sub-10 nm Resolution (a) A coherent diffraction pattern from a porous silica particle (b) The reconstructed absolute electron density Miao et al., Phys. Rev. B, in press. (c) The absolute electron density distribution within a 100 x 100 nm 2 area

14. Imaging E. Coli Bacteria (b) A Coherent X-ray diffraction pattern from E. Coli (c) An image reconstructed from (b). (a) Light and fluorescence microscopy images of E. Coli labeled with manganese oxide Miao et al., Proc. Natl. Acad. Sci. USA 100, 110 (2003).

15. 3D Electron Diffraction Microscopy Electron gun Aperture Lens Sample Detector

16. Computer Simulation of Imaging a 3D Nanocrystal ([Al 12 Si 12 O 48 ] 8 ) with coherent electron diffraction (a) A section (0.5 Å thick) viewed along [100] at z = 0 (c) The reconstructed section (0.5 Å thick) of the nanocrystal viewed along [100] at z = 0 (b) One of the 29 diffraction patterns (the 0  projection), SNR = 3 Miao et al., Phys. Rev. Lett. 89, 155502 (2002). SiAl O

17. The Linac Coherent Light Source (LCLS)

18. Peak and Time Averaged Brightness of the LCLS and Other Facilities Operating or Under Construction TESLA

19. A Potential Set-up for Imaging Single Biomolecules Using X-FELs X-FEL Pulses X-ray Lens Molecular Spraying Gun CCD

20. Two Major Challenges Solemn & Baldwin, Science 218, 229 (1982). Neutze et al., Nature 400, 752 (2000). When an X-ray pulse is short enough ( < 50 fs), a 2D diffraction pattern could be recorded from a molecule before it is destroyed. Use the methods developed in cryo-EM to determine the molecular orientation based on many 2D diffraction patterns. Crowther, Phil. Trans. Roy. Soc. Lond. B. 261, 221 (1971). Use laser fields to physically align each molecule. Larsen et al., Phys. Rev. Lett. 85, 2470 (2000). Orientation Determination Radiation Damage

21. An Oversampled 3D Diffraction Pattern Calculated from 3 x 10 5 Rubisco Protein Molecules (a)One section of the oversampled 3D diffraction pattern with Poisson noise (b) Top view of (a)

22. The Reconstructed Electron Density from the Oversampled Diffraction Pattern The reconstructed 3D electron density map The reconstructed active site The 3D electron density map of a rubisco molecule The active site of the molecule Miao, Hodgson & Sayre, Proc. Natl. Acad. Sci. USA 98, 6641 (2001).

23. Summary Proposed a theoretical explanation to the oversampling method. Carried out the first experiment of crystallography without crystals. Opened a door to atomic resolution 3D X-ray diffraction microscopy. Proposed 3D electron diffraction microscopy for achieving sub-atomic resolution. Future application with the LCLS – imaging non-crystalline materials nanocrystals, and large biomoleucles.

24. Acknowledgements B. Johnson, D. Durkin, K. O. Hodgson, SSRL J. Kirz, D. Sayre, SUNY at Stony Brook R. Blankenbecler, SLAC D. Donoho, Stanford University C. Larabell, UC San Francisco & LBL M. LeGros, E. Anderson, M. A. O’Keefe, LBL B. Lai, APS T. Ishikawa, Y. Nishino, Y. Kohmura, RIKEN/SPring-8 J. Amonette, PNL O. Terasaki, Tohoku University

25. Schematic Layout of the Experimental Instrument X-rays Pinhole Corner Sample Beamstop Photodiode CCD 743 mm 12.7 mm 25.4 mm

26. Experimental Demonstration of Electron Diffraction Microscopy Zuo et al., Science 300, 1419 (2003). The recorded diffraction pattern from a DWNT. Left: The reconstructed DWNT image; Right: A structure model of the DWNT.