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Phasing of Three Dimensional Diffraction Patterns from Finite-Sized ObjectsPowerPoint Presentation

Phasing of Three Dimensional Diffraction Patterns from Finite-Sized Objects

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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

Outline Finite-Sized Objects

- Coherence in Diffraction
- The Phase Problem
- Nanocrystal Shapes
- Crystallization of Proteins
- Applications at LCLS

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

Tomato Bushy Stunt Virus Finite-Sized Objects1980

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

Goals of Coherent Diffraction Finite-Sized Objects

- 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

Lensless X-ray Microscope Finite-Sized Objectsbased on diffraction from crystal lattice

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

Coherence at the APS Finite-Sized ObjectsTypical 3rd Generation (undulator) Synchrotron SourceLCLS coherence will be better

Coherent region defined by slits

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

Diffuse Scattering acquires Structure using CXD Finite-Sized Objects

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

Phase Problem: Finite-size Effect Finite-Sized Objects

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

Generic “Error Reduction” method Finite-Sized Objects

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

“ER” Methods in Crystallograhy Finite-Sized ObjectsR. 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

I. K. Robinson, SSRL Imaging Workshop, October 2002 Finite-Sized Objects

Diffraction as a Surface Integral Finite-Sized Objects

Annalen der Physik [5] 26 55 (1936)

“Stacheln”

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

I. K. Robinson, SSRL Imaging Workshop, October 2002 Finite-Sized Objects

SEMS Finite-Sized Objects

- Au blanket film
- Quartz substrate
- Annealed at 950°C for 70 hrs.

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

Micron-sized gold crystal: Finite-Sized Objects(111) Bragg reflection

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

Symmetrized Data Finite-Sized Objectsand two best fitsChisq=0.0005

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

2D Reconstructions Finite-Sized Objectschisquare = 0.0005

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

3D Diffraction Method Finite-Sized Objects

kf

Q=kf - ki

ki

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

In-situ Study of Crystallization Finite-Sized Objects

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

Experiment at APS Sector 34 Finite-Sized Objects

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

“Pink beam” sees CTRs Finite-Sized Objects

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

Ferritin (111) Powder Ring Finite-Sized Objects

- 50 frames
- 30sec exposure
- 0.3sec playback
- 150x200 pixels of 22.5μm

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

Conclusions and Outlook Finite-Sized Objects

- “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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