Coherent Xray Science Coherence Imaging Molecules Keith A

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

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…

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

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: Molecular dynamics • Coherent incident field; variation in object

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…

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

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

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

The Shrinkwrap Algorithm

Spherical wave

Fresnel diffraction imaging

Biological Applications

Materials Applications

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…

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.

Including partial coherence

Longitudinal coherent modes

Coherence function Mode occupancy (spectrum) Spatial coherent mode

z

The Complex Degree of Coherence

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

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

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…

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:

The need for short pulses

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.

Major Collaborators • • Garth Williams (UM) Andrew Peele (La Trobe) • • • Ian Mc. Nulty (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)