Coherent X-ray Science: Coherence, Imaging & Molecules

1. Coherent X-ray Science: Coherence, Imaging & Molecules Keith A. Nugent ARC Centre of Excellence for Coherent X-ray Science & School of Physics The University of Melbourne Australia

2. Plan of presentation Develop a view of coherent diffractive imaging including partial coherence. • Describe CDI and identify three limits within the framework of partial coherence • Coherent • Partially coherent illumination • Time varying object • Describe the method • Essential developments • Applications in biology • Applications in materials science • Partial coherence in CDI • How important is it? • How can coherence be measured • Building partial coherence into the reconstruction • Time varying objects as partially coherent diffraction • Some thoughts…

4. Formalism for CDI In far-field: The far-field intensity is therefore

5. Molecular dynamics Three limits 1.CDI with coherent light & static object: • Harmonically varying (ie. coherent) incident field; static object 2.CDI with partially-coherent light & static object: • Random variation in incident field; static object 3.CDI with coherent light & dynamic object: • Coherent incident field; variation in object

6. Plan of presentation Develop a view of coherent diffractive imaging including partial coherence. • Describe CDI and identify three limits within the framework of partial coherence • Coherent • Partially coherent illumination • Time varying object • Describe the method • Essential developments • Applications in biology • Applications in materials science • Partial coherence in CDI • How important is it? • How can coherence be measured • Building partial coherence into the reconstruction • Time varying objects as partially coherent diffraction • Some thoughts…

7. “Conventional” coherent diffractive imaging 1.CDI with coherent light & static object: • Harmonically varying (ie. coherent) incident field; static object

8. Coherent imaging methods are being developed. Coherent Field Impose Measured Intensity, Keep Phase z Impose “support” Guess Phase

9. First Demonstration • Assumes complete coherence • Object must be finite in extent

11. The Shrinkwrap Algorithm

13. Spherical wave

14. Fresnel diffraction imaging

18. Biological Applications

22. Materials Applications

27. Plan of presentation Develop a view of coherent diffractive imaging including partial coherence. • Describe CDI and identify three limits within the framework of partial coherence • Coherent • Partially coherent illumination • Time varying object • Describe the method • Essential developments • Applications in biology • Applications in materials science • Partial coherence in CDI • How important is it? • How can coherence be measured • Building partial coherence into the reconstruction • Time varying objects as partially coherent diffraction • Some thoughts…

28. Conclusion Algorithms implicitly assume a very high degree of spatial coherence. A very high degree of spatial coherence is required for reliable, high-resolution image recovery.

29. Including partial coherence

30. Longitudinal coherent modes

31. Coherence function Mode occupancy (spectrum) Spatial coherent mode

32. z

33. The Complex Degree of Coherence

34. S Flewett, HM. Quiney, CQ Tran and KA. Nugent, Extracting Coherent Modes from Partially Coherent Wavefields, Optics Letters, submitted Three coherent modes

35. The effects of partial coherence can be included in the analysis and provide a significantly greater degree of stability in the reconstruction

36. Plan of presentation Develop a view of coherent diffractive imaging including partial coherence. • Describe CDI and identify three limits within the framework of partial coherence • Coherent • Partially coherent illumination • Time varying object • Describe the method • Essential developments • Applications in biology • Applications in materials science • Partial coherence in CDI • How important is it? • How can coherence be measured • Building partial coherence into the reconstruction • Time varying objects as partially coherent diffraction • Some thoughts…

37. Three limits – Limit Three 3.CDI with coherent light & dynamic object: • Coherent incident field; variation in object Studies have been predicated on the need for the condition:

38. The need for short pulses

41. Summary • Coherent x-ray imaging techniques are well developed. • Methods are emerging that allow the inclusion of the effects of partial coherence. • The imaging of a system that is effected by the pulse can be formulated as a problem of partial coherence. • The recovery of structure in this way might be possible is suitable models can be developed. This will be a challenge.

42. Major Collaborators • Garth Williams (UM) • Andrew Peele (La Trobe) • Ian McNulty (APS) • Harry Quiney (UM) • Lachlan Whitehead (UM) • David Vine (UM) • Rueben Dilanian (UM) • Bo Chen (UM) • Brian Abbey (UM, now at Oxford) • Sam Flewett (UM) • Chanh Tran (La Trobe) • Jesse Clark (La Trobe) • David Paterson (APS, now Australian Synchrotron) • Martin de Jonge (APS, now Australian Synchrotron)