Henning Friis Poulsen

NEXMAP

Physics Dept, DTU

hfpo@fyisk.dtu.dk

Imaging: tomography, 3DXRD, x-ray microscopy

Lecture at KTH, Stockholm Dec 2013

• Why imaging, why 4D

• T omography: the math, recent trends and examples

Short break

• 3DXRD microscopy (grain mapping)

• X-ray microscopy: multiscale physics

T he menu

Diffraction Imaging

Atomic structure within crystals Structure on nm – cm scale

Oil/CO2 storage

Fuel cells

Wind energy

Catalysis

3D imaging of energy materials

5

200 µm

Metal structures

5 µm

Example: Al

Model structure evolution in 4D

200 µm

Metal structures

5 µm

Example: Al

Model structure evolution in 4D

But: Bottum-up not yet feasible

Average properties not enough

Multiscale approach required

Mapping:

Phase

position

morphology

orientation of lattice

stress

plastic strain

dislocation densities

…

200 µm

Materials in

2D 4D

5 µm

Tomography:

the principle

Wilhelm Röntgen The first X-ray, Frau

Röntgen´s left hand

Wilhelm Conrad Röntgen discovered X-ray November 8 in 1895

X-ray radiography

Source

Detector Object

r(x,y,z)?

dsµI

I)ln(

0

Isds

dI)(

I0 I

Absorption contrast tomography

q

Inverse problem.

Solution: reconstruction

Radon Transform

Rf = L f(x,y) ds

Rf (w, t) =

f(x,y) d(t = xcos(w)-ysin(w) ) dxdy

Radon Transform: (x,y) -> (t, w)

Inversion:

1917: Johann Radon: On the determination of functions

from their integrals along certain manifolds.

t w x

y

L

Detector

Sample system:

Insert

Filtered Backprojection

Direct space Fourier Space

|k|

Algebraic Reconstruction Technique

Solve: Ax = b

x: density of each voxel

b: detector pixel intensitites

A: geometry of set-up

Iterative solution:

M

j

kj

M

j

k

jkjk

kk

A

xAb

xx

1

2

11

Slower, but freedom to add constraints and choose projections

xi

bj

Discrete tomography

Binary system

known densities, r1 and

r2

Few projections

Materials science: faster

Medicine: reduced dose

Mathematical tomography, other approaches

• Series expansion

• Expectation maximization

• Linear programming, graph theory

• Difference map algorithms

• Total Variation

• Projection onto convex sets (phase retrieval)

Use of Soduku alorithms…

Discrete values

Combinatorial constraints

Finite nr. of projections

Generalised projections

Solution: Difference map algorithm

by Veit Elser, Cornell (2005)

Use for biological imaing using coherent x-rays

D. Shapiro, P. Thibault, T. Beetz, V. Elser et al.

PNAS (2005), 102, 15343–15346

Reconstruction Segmentation Quantification

Fuzzy connectivity Segmentation

Tomography, the math

Basics : • A.C. Kak, and M. Slaney. Principles of Computerized Tomographic Imaging.

(IEEE Press, New York, 1988).

• G.T. Herman. Image Reconstructions from Projections. The Fundamentals of

Compterized Tomography. (Academic Press, New York).

Mathematical:

• S. Helgason (1980). The Radon Transform. Progress in Math., Vol. 5

(Birkhäuser, Boston, 1980).

Discrete Tomography:

• G.T. Herman and A. Kuba, Eds. Discrete Tomography. (Boston, Birkhäuser,

1988).

Segmentation:

• T.S. Yoo. Insights into Images. (Wellesey, Canada, A.K. Peters, 2004).

4D imaging for materials science

at synchrotrons

Resolution: 0.05 – 2.5 µm

Nr of projections: 1000-2000

Reconstructred volume:

~500x500x500 voxels

Tomography for materials science

at synchrotons in Europe*

Some dedicated sources for parallel beam tomography

60-200 keV: ESRF: ID15

20-60 keV ESRF ID19 + BM5

ESRF NINA

PETRA-III

10-30 keV PSI: TOMCAT

Diamond

Soleil

ALBA

Max-IV ?

……

*The list is not complete and numbers are only approximate

Phase Contrast Tomography

Absorption Phase

0.1

1

10

100

1000

0.1 1 10 100

110100

Energy (keV)

Hard X-raysSoft X-rays

(water window)

Wavelength (Å)

d

Aluminium Smallest detectable hole at 25 keV

in a 4 mm thick sample:

Absorption: 20 µm

Phase: 0.05 µm

Phase/

absorption

Ex.: Holotomography of semisolid Al/Si alloy

800 angular positions multilayer monochromator: total time 40 minutes E = 18 keV

Absorption

100 µm

Holotomography

Al/Si Al

Work by P. Cloetens, ID19, ESRF

3DXRD (grains, Flourescence EXAFS and XANES

orientations)

Powderdiffraction SAXS Coherent diffraction

(phases) (nano-particle)

Tomography using other contrast mechanisms

5 nm resolution, Au nanoparticle:

Schroer et al. PRL (2008) 101, 090801

Bleuet et al. Nature Mat. 7, 468 (2008)

Second

half of

talk J.-D.Grunwaldt et al.

J. of Phys. Chem. B 110, 8674 (2006)

white x-ray

beam

sample

in furnace

tomography detector

monochromatic

x-ray beam

2-D diffraction detector

Laue

monochromotar

Laue

monochromator

Ultrafast tomography and diffraction @ID15, ESRF

EVOLUTION OF MICRO-TOMOGRAPHY AT

ID15A

10ms

50ms

1s

10s

10min

4h

0.01

0.1

1

10

100

1000

10000

100000

1999 2001 2003 2005 2007 2009

Year

t (s

)

Time for 500 frames (s)

1999 2005 2009

100000

100

0.01

4 h

10 min

10 s

1 s

50 ms

10 ms

Courtesy of Honkimäki

Applications

PROPAGATION OF LIQUID FRONT

IN GRANULAR MATERIAL

Resolution:

50 ms

2 µm

Cai, Powell, Yue et al. Appl. Phys. Lett. 83, 1671 (2003).

Ultra-fast x-ray tomography

Fuel-spray studies: 5 s time resolution

Observation of shock-waves

People involved:

Risø: Stefan Poulsen, Erik Lauridsen

NU: Peter Voorhees, Julie Fife,

Anthony Johnson, Larry Aagenson

and Michael Miksis

PSI: Marco Stampanoni

Coarsening in solid/liquid AlCu alloys

Al-26wt%Cu (42% solid)

Synchrotron data

Annealing for 6 hours at 850 C

• Time resolution: 2 min

• Resolution: 1 µm

Al-26wt%Cu (Velocity plot)

Interfacial velocities

Common phenomena involving the break up

of a liquid cylinder into droplets

Al-15wt%Cu (74% solid)

Plateau-Rayleigh instability

Rockwool

M.W. Westneat et al. Science, 299, 558-560 (2003)

Beetle Breath

Tomography in materials science

General (in order of increasing complexity)

• J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix. X-ray

tomography in materials science. Hermes Science Publications,

Paris, 2000

• W. Reimers, A.R. Pyzalla, A.K. Schreyer, H. Clemens, Eds. Neutrons and

Synchrotron Radiation in Engineering Materials Science Wiley-VCH, 2008

• J. Banhart, Ed.: Advanced tomographic methods in materials research and

engineering, Oxford Uni. Press, 2008.

Conferences

SPIE conference series

X-TOP conference series

The future

X-rays going nano

An x-ray TEM?

Coherence:

Single particles:

Quantum dots:

Fe

Cu

Tomography going Nano

An Xray TEM

Nano-tomography Coherent scattering

Aim:1 nm

Current resolution: 50 nm

Now: parallel beam geometry:

LIMITATION

Resolution: 0.5 m

Sample size: 1 mm

1000-4000

Current resolution: 5 nm

Farfield

Scintillator based detector

• Resolution: ~ 3 µm

• Efficiency: ~ 1%

CCD

Sample

Flourescence

screen

Conventional

Resolution -> 1 µm

Efficiency improvement by factor 5

Waveguiding

-----

Technique originally developed at KTH

Bridge the length scale

Local tomography:

Problem: no unique, exact solution

But: map the singularities correctly

Open field

Local events at DTU

Extra

3D Imaging center

Start: 4 instruments at DTU

Start-up: Xnovo Technologies

Luggage scanning and transport in airports