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. Outline. Coherence in Diffraction

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Phasing of three dimensional diffraction patterns from finite sized objects
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
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 1980
Tomato Bushy Stunt Virus Finite-Sized Objects1980

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


Goals of coherent diffraction
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 based on diffraction from crystal lattice
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
Diffuse Scattering acquires Structure using CXD Finite-Sized Objects

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


Phase problem finite size effect
Phase Problem: Finite-size Effect Finite-Sized Objects

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


Generic error reduction method
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 r p millane j opt soc am a 13 725 1996
“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



Diffraction as a surface integral
Diffraction as a Surface Integral Finite-Sized Objects

Annalen der Physik [5] 26 55 (1936)

“Stacheln”

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



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

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


Symmetrized data and two best fits chisq 0 0005
Symmetrized Data Finite-Sized Objectsand two best fitsChisq=0.0005

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


2d reconstructions chisquare 0 0005
2D Reconstructions Finite-Sized Objectschisquare = 0.0005

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


3d diffraction method
3D Diffraction Method Finite-Sized Objects

kf

Q=kf - ki

ki

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


In situ study of crystallization
In-situ Study of Crystallization Finite-Sized Objects

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


Experiment at aps sector 34
Experiment at APS Sector 34 Finite-Sized Objects

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


Pink beam sees ctrs
“Pink beam” sees CTRs Finite-Sized Objects

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


Ferritin 111 powder ring
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
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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