# Structure and Order in Coherent Diffractive Imaging

Structure and Order in Coherent Diffractive Imaging

Structure and Order in Coherent Diffractive Imaging – p. 1/35

Structure and Order in Coherent

Diffractive Imaging

Mark A. Pfeifer

La Trobe University

Australian Research Council Centre of Excellence for Coherent X-ray Science

Structure and Order in Coherent Diffractive Imaging – p. 2/35

Outline

• imaging of non-crystalline samples

• coherent x-ray diffractive imaging

• Fresnel coherent x-ray diffractive imaging

• principal

• equipment

• results

• directions in Fresnel CDI

• imaging disorder in crystalline samples

• some annoying math

• three dimensional strain mapping

• directions in Bragg CDI

Structure and Order in Coherent Diffractive Imaging – p. 3/35

CDI background

The wave in the far field of an electron density ρ e (r),

is given by

A(Q) ∝ ρ e (r)e iQ·r dr ∝ F(ρ e (r))

Invoking the convolution theorem

I(Q) ∝ A(Q) ∗ A(Q) = F(F −1 (A(Q) ∗ A(Q)))

∝ F(ρ ∗ e(r) ⊗ ρ e (r))

The measured intensity is proportional to the Fourier

transform of the autocorr. of the electron density

Structure and Order in Coherent Diffractive Imaging – p. 4/35

CDI background

density

7

6

5

4

3

2

1

0

-3 -2 -1 0 1 2 3

Structure and Order in Coherent Diffractive Imaging – p. 4/35

CDI background

density

amplitude

7

2

6

1.5

5

4

1

3

0.5

2

0

1

0

-3 -2 -1 0 1 2 3

-0.5

-3 -2 -1 0 1 2 3

Structure and Order in Coherent Diffractive Imaging – p. 4/35

CDI background

density

intensity

7

2

6

1.5

5

4

1

3

0.5

2

1

0

0

-3 -2 -1 0 1 2 3

-0.5

-3 -2 -1 0 1 2 3

Structure and Order in Coherent Diffractive Imaging – p. 4/35

CDI background

autocorrelation

intensity

7

2

6

1.5

5

4

1

3

0.5

2

1

0

0

-3 -2 -1 0 1 2 3

-0.5

-3 -2 -1 0 1 2 3

Structure and Order in Coherent Diffractive Imaging – p. 5/35

CDI developments

J.Miao,

P.Charalamous,J.Kirz,

D.Sayre, Nature 1999.

D. Shapiro, et al. Proc.

Structure and Order in Coherent Diffractive Imaging – p. 6/35

Quick CDI Review

Consider a wavefield leaving a biological sample

Structure and Order in Coherent Diffractive Imaging – p. 6/35

Quick CDI Review

Consider a wavefield leaving a biological sample

A question of uniqueness

Structure and Order in Coherent Diffractive Imaging – p. 7/35

A question of uniqueness

Structure and Order in Coherent Diffractive Imaging – p. 8/35

A question of uniqueness

Structure and Order in Coherent Diffractive Imaging – p. 9/35

Structure and Order in Coherent Diffractive Imaging – p. 10/35

FCDI – A Unique Solution

complex illumination

Structure and Order in Coherent Diffractive Imaging – p. 11/35

FCDI – A Unique Solution

far-field diffraction

Structure and Order in Coherent Diffractive Imaging – p. 12/35

FCDI – A Unique Solution

high angle scatter (logarithmic scaling)

•requires minutes of acquisitions

•sample must remain stable

FCDI Geometry

Structure and Order in Coherent Diffractive Imaging – p. 13/35

Structure and Order in Coherent Diffractive Imaging – p. 14/35

Recovered complex wavefield

Harry Quiney, Nature Physics 2006.

FCDI Experimental Geometry

Structure and Order in Coherent Diffractive Imaging – p. 15/35

Structure and Order in Coherent Diffractive Imaging – p. 15/35

FCDI Experimental Geometry

zone plate

Structure and Order in Coherent Diffractive Imaging – p. 15/35

FCDI Experimental Geometry

order sorting aperture

zone plate

Structure and Order in Coherent Diffractive Imaging – p. 15/35

FCDI Experimental Geometry

order sorting aperture

zone plate

sample

SXM at 2-ID-B, Advanced Photon Source

Structure and Order in Coherent Diffractive Imaging – p. 16/35

Malaria infected red blood cell

APS 2ID-B

2.1keV

Williams et al. Cytometry

2008

Finding a region of interest

Structure and Order in Coherent Diffractive Imaging – p. 17/35

Fuses on integrated cicruit

Structure and Order in Coherent Diffractive Imaging – p. 18/35

Structure and Order in Coherent Diffractive Imaging – p. 19/35

Fuses on integrated circuit

Brian Abbey, et al. APL 2008.

Fuses on integrated cicruit

Structure and Order in Coherent Diffractive Imaging – p. 20/35

Variable zoom

Structure and Order in Coherent Diffractive Imaging – p. 21/35

Structure and Order in Coherent Diffractive Imaging – p. 22/35

A New FCDI Microscope

Installed at APS 2-ID-B

Structure and Order in Coherent Diffractive Imaging – p. 22/35

A New FCDI Microscope

zone plate

Installed at APS 2-ID-B

Structure and Order in Coherent Diffractive Imaging – p. 22/35

A New FCDI Microscope

zone plate

order sorting aperture

Installed at APS 2-ID-B

Structure and Order in Coherent Diffractive Imaging – p. 22/35

A New FCDI Microscope

zone plate

order sorting aperture

Installed at APS 2-ID-B

sample

Finding a region of interest

Structure and Order in Coherent Diffractive Imaging – p. 23/35

Finding a region of interest

Structure and Order in Coherent Diffractive Imaging – p. 24/35

Structure and Order in Coherent Diffractive Imaging – p. 25/35

Directions for FCDI

• biological imaging

• organelles

• strctures within un-sectioned cells

• hard condensed matter

• burried structures (nano-electronics)

Structure and Order in Coherent Diffractive Imaging – p. 26/35

Bragg CDI

For a discrete charge distribution ρ e (r),

∫ ∑

A(Q) ∝ ρ e (r)e iQ·r dr ∝ δ(r − r n − u(r))s(r)e iQ

n

s(r)=shape function, u(r)=strain

By the convolution theorem

∫ ∑

A(Q) ∝ δ(r − r n )e iQ·r dr ⊗ s(r)e iQ·u(r) e iQ·r dr

n

∝ ∑ ∫

δ(Q − G m ) ⊗ s(r)e iQ·u(r) e iQ·r dr

m

Bragg CDI

Structure and Order in Coherent Diffractive Imaging – p. 27/35

Structure and Order in Coherent Diffractive Imaging – p. 28/35

Diffraction from Pb crystals

Coherent diffraction

from Pb nanocrystals

APS 34ID-C

Structure and Order in Coherent Diffractive Imaging – p. 29/35

Diffraction data

Every third slice through 3D diffraction pattern from

Pb nanocrystal.

Structure and Order in Coherent Diffractive Imaging – p. 30/35

Shape reconstruction

250nm

Structure and Order in Coherent Diffractive Imaging – p. 31/35

Shape reconstruction

250nm

Structure and Order in Coherent Diffractive Imaging – p. 32/35

Phase map

250nm

Structure and Order in Coherent Diffractive Imaging – p. 33/35

Directions in Bragg CDI

• strain from finite size/boundary effects

• strain from chemical inhomogeneity

• electrically/mechanically induced strain

Structure and Order in Coherent Diffractive Imaging – p. 34/35

Acknowledgements

• Individuals

• Garth Williams - CXS, UM

• Brian Abbey - CXS, UM

• Ian McNulty - APS/ANL

• Jesse Clark - CXS, LTU

• Eric Hansen - CXS, LTU

• Lachlan Whitehead - CXS, UM

• Andrew Peele - CXS, LTU

• Leann Tilley - CXS, LTU

• Keith Nugent - CXS, LTU

• Ian Robinson - UCL

• Ross Harder - UCL

Structure and Order in Coherent Diffractive Imaging – p. 35/35

Acknowledgements

• Institutions

• Centre of Excellence for Coherent X-ray

Science

• La Trobe Univrsity

• University of Oregon

• Lawrence Berkeley National Laboratory

• Materials Research Laboratory, University of

Illinois

• Argonne National Laboratory (UNICAT,

XOR

• US Department of Energy

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