Coherent X-Ray Diffraction Imaging

1. Coherent X-Ray Diffraction Imaging Kevin Raines University of California, Los Angeles Compton Sources for X/gamma Rays: Physics and Applications Alghero 7-12 September 2008

2. Preliminaries

3. The First Compound Light Microscope Hooke’s compound light microscope and a drawing of cork made by Hooke. • Kepler suggested that a compound light microscope could be • constructed based on a three lenses conformation. • 1665 Hooke built the 1st compound light microscope and imaged • small pores in sections of cork he called “cells”

4. Discovery of X-Rays: RöntgenDevelopment of X-ray Crystallographic Microscope

5. Some Important Dates in the History of Optics Ancient Times – Quantization & Empty Space; Minimization principles ~450 B.C. Empedocles – Speed of light is finite ~100 B.C. Claudius Ptolemaeus – Law of refraction for small angles Pre-modern – Corpuscular theory, Geometrical Optics ~1500 Da Vinci – Camera Obscura ~1660 Hooke – First lensed microscope Early Modern – Wave Theory, Fourier Optics, Ether ~1640 Huygens – Early wave theory advocate ~1800 Fresnel – Diffraction Theory ~1850 Faraday, Maxwell – Electromagnetic theory of light ~1880 Abbe – Early Fourier Optics 1895 Rontgen – Discovery of x-Rays Modern Theory – Quantum, Fourier, & Statistical Optics ~1900 Plank, Einstein – Quantization, special relativity ~1930 Schrodinger, Heisenberg – Quantum mechanics ~1960 Maiman – Laser

6. Fourier Optics + Coherent X-Rays = CXDI • Complex Amplitude from interference of light scattered from each atom (superposition principle) • Only time-averaged intensity of field is measurable – phase information is lost.

7. The Importance of the Phase Information (b) (a)

8. The Importance of the Phase Information (b) (a) Fourier amplitude of (a) + Fourier phases of (b) Fourier amplitude of (b) + Fourier phases of (a)

9. X-ray Diffraction by Crystals Laue, W. Bragg and L. Bragg, 1912 N N |FT| a 1/a Periodic Structure Discrete Bragg Intensities

10. Diffraction by Non-periodic structures N N a 1/a Non-Periodic Structure Continuous Frequency Spectrum

11. Shannon Sampling vs. Bragg Sampling Shannon Sampling Theorem, 1949 1/a Nyquist Frequency FT a FT-1

12. Shannon Sampling vs. Bragg Sampling Shannon Sampling Theorem, 1949 1/a Nyquist Frequency FT a FT-1 1/a Bragg Sampling |FT| a FT-1

13. Bragg-peak Sampling vs. Oversampling Indistinguishable 1/a a |FT| a

14. Bragg-peak Sampling vs. Oversampling Indistinguishable 1/a a |FT| Distinguishable < 1/a a

15. A Pictorial Representation of the Oversampling Method Reciprocal Space Real Space

16. The Physical Explanation to the Oversampling Method Real Space Reciprocal Space Nyquist sampling frequency Oversampling Better coherence More correlated intensity points  Phase information Miao, Sayre & Chapman, J. Opt. Soc. Am. A 15, 1662 (1998). Miao, Sayre & Chapman, J. Opt. Soc. Am. A 15, 1662 (1998).

17. A New Type of Microscopy – Lensless Imaging Coherent Scattering X-rays, electrons or lasers An object Solving the phase problem

18. A Brief History of the Oversampling Method • Sayre, Acta Cryst. 5, 843. • Suggested that measuring the intensity at as well as between the • Bragg peaks may provide the phase information. • 1978 Fienup, Opt. Lett. 3, 27. • Developed an iterative algorithm for phase retrieval of diffraction • intensity. • 1998 Miao et al.J. Opt. Soc. Am. A 15, 1662. • Proposed an explanation to the oversampling method. • 1999 Miao et al., Nature400, 342. • First experimental demonstration of the oversampling method • and lensless imaging.

19. The Guided Hybrid Input-Output (GHIO) Algorithm • i) Start with 16 independent reconstructions. • ii) For each reconstruciton: • Real Space Reciprocal Space • iii) Calculate the R-value, • iv) Select a seed out of 16 images (seed) with the smallest R-value. • v) FFT FFT-1 i = 1, 2, …, 16 Chen, Miao, Wang & Lee, PRB76, 064113 (2007).

20. Image Reconstruction Using the GHIO Algorithm at 0th Generation

21. Image Reconstruction Using the GHIO Algorithm at 8th Generation

22. Temporal (or longitudinal) coherence   180° phase shift lt Spatial (or transverse) coherence x d

23. Young’s Double Slit Experiment

24. Double Slit: Two Sources

25. Oversampling Tightens Coherence Requirements

26. 3D imaging via X-ray Coherent Imaging

27. Diffraction Tomography • Compounded Inverse Problems: • The phase problem – Non-linear inverse problem; diffraction data in principle has less information than a projection. Solve phases – get projections. • The tomography problem – Inverse Radon Transfrom: • - Less meaningful data (i.e. no simple interpretation like a projection.) • Missing Data Problem – Far less data than CT.

28. Diffraction Tomography • Oversampling is the key • Oversampling by greater than 2 uniquely encodes the phases • Iterative computer algorithms efficiently recover the phases • Oversampling + constraints eliminates much of the missing data problem (simulations show only 30% of the data is needed.) • 3 major inverse problem reduced to one straightforward computational problem: interpolation

29. Radiation Studies for Biological Imaging

30. Diffraction Tomography

31. Coherent X-ray Diffraction Pattern from a GaN Quantum Dot Particle Oversampled diffraction pattern from a GaN quantum dot nanoparticle AFM Image of GaN quantum dots, showing the platelet structures.

32. 3D Surface Morphology of the GaN Quantum Dot Nanoparticle

33. Quantitative 3D Internal View of the GaN Quantum Dot Nanoparticle

34. Outline of Current CXDI Projects • - Biological Imaging • i. Whole, unstained cells at ~ 10 nm res. • ii. Single unstained virions at < 1 nm res. • iii. Single biomolecule imaging • - Materials & Dynamic Imaging • i. Femtosecond pulses. • ii. Resonant imaging (atomic specificity) • - Electron Diffraction • - Tabletop Sources

35. Schematic Layout of Resonant X-ray Diffraction Microscopy

36. Coherent X-ray Diffraction Pattern of a Bi Doped Si Crystal with E = 2.55 keV

37. Part of X-ray Diffraction Patterns with E=2.550 and 2.595 keV E=2.550 keV E=2.595 keV

38. Elemental Mapping of Buried Bi Structure Song, Bergstrom, Ramuno-Johnson, Jiang, Paterson, de Jonge, McNulty, Lee, Wang & Miao, PRL100, 025504 (2008).

39. Experimental Setup for Imaging Single Herpesviruses

40. Coherent Imaging of a SingleUnstained Herpesvirus

41. Identifying the Viral Capsid Inside the Herpesvirus AFM image of a herpesvirus prepared at the same conditions Quantitative X-ray diffraction imaging of a single herpesvirus Song, Jiang, Mancuso, Amirbekian, Peng, Sun, Shah, Zhou, Ishikawa & Miao, PRL in press.

42. Experimental Setup of Tabletop Lensless Imaging Using a HHG Source

43. First Experimental Demonstration of Tabletop Lensless Imaging Sandberg et al., PRL99, 098103 (2007).

44. Tabletop Lensless Imaging at 71 nm Resolution (~1.5) with an EUV Laser Source

45. Tabletop Lensless Imaging at 71 nm Resolution (~1.5) with an EUV Laser Source Sandberg et al., PNAS 105, 24 (2008). .

46. A Potential Set-up for ImagingSingle Biomolecules Using X-FELs X-ray Lens Molecular Spraying Gun X-FEL Pulses CCD Radiation Damage Solemn & Baldwin, Science 218, 229 (1982). Neutze et al.,Nature 400, 752 (2000). When an X-ray pulse is short enough ( ~ 10 fs), a 2D diffraction pattern may be recorded from a molecule before it is destroyed.

47. Summary • Oversampling the diffraction intensities  the phase information. • Imaged nanostructured materials and biological structures in two and • three dimensions. • Electron diffraction microscopy  imaging a DWNT at 1 Å • resolution. • Future: imaging single particles by using the X-ray free electron • lasers or electrons.

48. Collaborators UCLA Physics & Astronomy C. Song, H. Jiang, A. Mancuso, R. Xu, K. Raines, S. Salha, B. Amirbekian RIKEN/SPring-8 T. Ishikawa, Y. Nishino, Y. Kumara University of Colorado, Boulder M.M. Murnane, H.C. Kapteyn, R.L. Sandberg Colorado State University J.J. Rocca’s group APS, ANL I. NcNulty, M.D. de Jonge, D. Paterson UCLA, Electric Engineering K. Wang UC, Davis S. Risbud CXO, LBNL A.E. Sakdinawat Academia Sinica, Taiwan C.C. Chen, T.K. Lee UCLA Medical School R. Sun, Z.H. Zhou, P. Li, F. Tamanoi Harvard Medical School M.J. Glimcher, L. Graham

49. Coherent Imaging Group @ UCLA