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

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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

  • 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 Virus1980

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


Goals of coherent diffraction

Goals of Coherent Diffraction

  • 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 Microscopebased on diffraction from crystal lattice

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


Phasing of three dimensional diffraction patterns from finite sized objects

Coherence at the APSTypical 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

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


Phase problem finite size effect

Phase Problem: Finite-size Effect

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


Generic error reduction method

Generic “Error Reduction” method

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 CrystallograhyR. 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


Phasing of three dimensional diffraction patterns from finite sized objects

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


Diffraction as a surface integral

Diffraction as a Surface Integral

Annalen der Physik [5] 26 55 (1936)

“Stacheln”

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


Phasing of three dimensional diffraction patterns from finite sized objects

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


Phasing of three dimensional diffraction patterns from finite sized objects

SEMS

  • 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:(111) Bragg reflection

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


Symmetrized data and two best fits chisq 0 0005

Symmetrized Data and two best fitsChisq=0.0005

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


2d reconstructions chisquare 0 0005

2D Reconstructionschisquare = 0.0005

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


3d diffraction method

3D Diffraction Method

kf

Q=kf - ki

ki

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


In situ study of crystallization

In-situ Study of Crystallization

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


Experiment at aps sector 34

Experiment at APS Sector 34

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


Pink beam sees ctrs

“Pink beam” sees CTRs

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


Ferritin 111 powder ring

Ferritin (111) Powder Ring

  • 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

  • “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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