Tomography and holotomographySchool on X-ray micro and nanoprobes

P. Cloetens

ESRF, Grenoble, Francecloetens@esrf.fr

June 13, 2007

3D vs 2D Imaging

JJ Blandin, L SalvoConditions : ex situ, E=18 keV abs, 2 µm

Cavitation inducedby superplastic deformation

a single pore in 3D100 µm

3D vs 2D Imaging

0

2000

4000

6000

8000

10000

12000

0.5 1 1.5 2

ε

NV (mm-3)

10-4 s-1

Volume

NV

JJ Blandin, L SalvoConditions : ex situ, E=18 keV abs, 2 µm

Cavitation inducedby superplastic deformation

0

200

400

600

800

0.8 1 1.2 1.4 1.6 1.8

ε

n A (m

m-2

)

NA

Surface

3D observations needed

Outline (Synchrotron based) Tomography

‘Incoherent’ approachesHigh spatial resolutionIn-situ TomographyHigh temporal resolution (Real-time)Edge CTContrast agents

Coherent approachesEdge enhancementHolotomography

Tomography configurations

0D detector

source

1st generationscanner

transl

rot

1 datapoint

2 translations+ 1 rotation

1D detector

source

fan-beamscanner

rot

103 datapoints

1 translation+ 1 rotation

source

cone-beamscanner

2D detector

rot

106 datapoints

1 rotation

G. Peix (INSA-Lyon)

Synchrotron based µCT

source

Parallel beam case .....the whole object

is imaged, slice by slice

New parameters:distance: holotomography, 3DXRDenergy: edge CT, XANES

G Peix, INSA Lyon

Experimental setups

Parallel beam:Absorption TomographyPhase Contrast TomographyResolution limited by detector

500 nm best detector

Coherent X-ray beam

sample

Focused beam:Projection MicroscopyFluorescence mappingResolution limited by focus

3D Imaging from projections

X r

ays

θx

y

n

Px’)θ,(

x’

S)θ,ω(

ω

θ

ω

u

v

g(x,y) G(u,v)

FT-1D

FT-2D

Object: (Fourier transform of

the object)

Projection:

RealSpace

FourierSpace

Fourier-Slice-Theorem

€

ln I0(x ')I(x ')

= µ(x,y)ds∫e.g. absorption

Hard X-ray Tomography

€

N =max. sample thickness

resolution element

AbsorptionDepth of focusMultiple scattering

OpticsInteraction strengthPhoton statistics

3D Imaging from projections

Large N is possible

Depth of focus

€

N =depth of focus

Rayleigh resolution=

λNA2

0.61 λNA

=1

0.61NA=

resolution0.612λ

NA << 1λ << resolution

Hard X-rays particularly adapted to 3D microscopy

Depth of focus

1

10

100

1000

104

0.1 1 10 100

50 nm25 nm10 nm

N

Energy (keV)

Waterwindow

HardX-rays

e.g. 50 nm resolution at end water window: N = 60 7 keV : N = 750

Photonic Noise

€

NPhot∝ DΔx

4 exp(µD)

[µD(σ /µ)]2

Noise is function of the number of photons NPhot

(Flannery, 87)

⇒ high resolution with a high SNR :either long integration time or high photon flux

σ/µ : NSR, Δx : spatial resolution, D: sample diameter

⇒ with D constant : if Δx ↓ then NPhot ↑ as (1/Δx)4

D

µ

Optimal Energy• It has been shown that the SNR is optimized if

µ D ~ 2 (Flannery, 87)µ D ~ 2.22 (Graef & Engelke, 91)

D : sample diameter, µ : linear attenuation (assumes anhomogeneous sample)

• µ D ~ 2.2 ⇔ log (I0/I) ~ 2.2 ⇔ Transmission = I / I0 ~ 11% optimizes the dynamic range of the projection

• In practice, typically 20% of transmission

Parallel Beam Imaging

translationstage

rotationstage

ESRFcamera

Source: ID19: 1 wiggler, 2 undulators distance to source: 145 m (coherence)

Monochromator:double Si crystal (Δλ/λ=10-4)or multilayer (Δλ/λ=10-2)

Sample stagerotation stage (tomography)sample environment

Detectorpixel size: 0.28 µm - 40 µm14 bits CCD, FFM and FTM

Scan time10242 * 900 proj.

~5 minutes, 2GB20482 * 1500 proj.

~15 minutes, 12 GB

X-rays

CCD based detectors

CCD

lightoptics

scintillator

Resolutions down to 5 µmThin powder converter screens (e.g. GADOX)

Resolutions better than 5 µmTransparant crystals (e.g. YAG:Ce, LAG:Eu )with microscope objective

optics

CCD

scintillator

α X-rays

Pb-glass

mirror

(A. Koch, J. Borrel)

X-ray → visible light conversion(De)magnification onto CCD

using light optics or fibre optics

Converter screens: resolution - efficiency

0.001

0.01

0.1

1

10 100

Gadox 5 µm

Gadox 10 µm

YAG 5 µm

YAG 25 µm

LAG 5 µm

LAG 25 µm

abso

rbed

ene

rgy

frac

tion

Energy (keV)

0.001

0.01

0.1

1

10 100

Gadox 5 µm

Gadox 10 µm

YAG 5 µm

YAG 25 µm

LAG 5 µm

LAG 25 µm

abso

rbed

ene

rgy

frac

tion

Energy (keV)

Absorbed fraction

•25 µm thick scintillator - 2 µm resolution - up to 40 keV•5 µm thick scintillator - 1 µm resolution - up to 20 keV•1 µm thick scintillator - 0.5 µm resolution @ 11 keV

New screens: GGG, LSO (Scintax EU project)Move to UV for higher resolution and efficiency?

•YAG:Ce (Y3Al5O12)

•LAG:Eu,Tb (Lu3Al5O12)

•GGG:Eu (Gd3Ga5O12)

•LSO Eu,Tb,Sm (Lu2SiO5)

Rhinoceros molar : 250 Rhinoceros molar : 250 µµmm

Tafforeau, P., Bentaleb, I., Jaeger, J.-J. and Martin, C., Palaeogeography PalaeoclimatologyPalaeoecology. 246: 206-227 (2007)

See also: T. Smith, P. Tafforeau et al, PNAS (2007)

Rhinoceros molar : 10 Rhinoceros molar : 10 µµmm

Rhinoceros molar : 1.4 Rhinoceros molar : 1.4 µµmm

Rhinoceros molar : 0.28 Rhinoceros molar : 0.28 µµmm

Tafforeau, P., Bentaleb, I., Jaeger, J.-J. and Martin, C., Palaeogeography PalaeoclimatologyPalaeoecology. 246: 206-227 (2007)

See also: T. Smith, P. Tafforeau et al, PNAS (2007)

enamel laminations and mineralization in rhinoceros enamel

In-situ TomographyFollow 3D structure and composition as function of

time (fast tomography)temperature (furnace, cryostat)strain (tensile stage)...

Real-time Tomographyscan time << evolution timeHigh Energy Beamline ID15

Sequential Tomographyinterrupt evolution between successive scans

In-situ CT: Damage in Composites

L. Babout, E MaireConditions : in situ, E=30 keV abs/phase, 2 µm

E. I.xy

z

E. I.xy

z

Ep=0,022xy

z

Ep=0,030xy

z

Ep=0,052xy

z

Ep=0,088xy

z

<Ep>=0.126xy

z

Ep

0,1 0,125 0,15

trac

tio

nExample: hard matrixAl2124(T6) + 4%ZrO2SiO2

Failure due tocoalescence of cracksand local configuration

A

C

B

Preferred damage initiation: particle rupture in mode I

Fast Tomography: Liquid Foams

J Lambert, I Cantat, R Delannay, R Mokso, P Cloetens, J Glazier, F Graner, PRL, in press

Coarsening: pressure driven growth or disappearance of bubbles

3D Growth LawDoes the ‘scaling state’ exist in 3D?

2 minutes/scan (2GB data)

Liquid Foams: the scaling state

R. Mokso et al

2048 pixels Plateau borders

Volumes: 2048x2048x1024Acquisition times: 25s (400 proj.) - 54s (900 proj.)

Liquid Foams: the scaling state

First experimental evidence of a scaling state in 3DR Mokso, J Lambert, I Cantat, P Cloetens, R Delannay, J Glazier, F Graner

First evidence by Potts model simulations:G Thomas, R de Almeida, F Graner

Normalized average bubble volumeas a function of the number of faces

Young fast bubbling foamf

Aged shaving foamf

Edge CT: Insect Anatomy

O. Betz (Zoologisches Institut Tuebingen), U. Wegst (MPI Stuttgart), D. Weide et al, sub. JEB

Zinc distributionin mandibles of grass hoppersBi-energy at Zn K-edge

(9.625 9.700 keV)

Zn

500 µmZn concentrationg/cm3

Dual energy Tomography

Insect Anatomy: edge CTZinc distributionin mandibles of grass hoppersDual energy at Zn K-edge

Cortical brain imaging

F. Plouraboue, L. Risser (GEMP, Toulouse), P. Cloetens, C. Fonta, A. Steyer

Cortical brain imaging:Characterisation vascular network Contrast agent

=Barium Sulfate“vascular structure of the cortex’s grey matter

over its entire thickness, on the micrometre scale”

200 µm E = 20 keV

Cortical brain imagingContrast agent

=Barium Sulfate

Color map of local thickness

morphometric information vascular networkphysiological and pathological angiogenesisvascularisation around a tumor

2k camera, 1200 viewsTypical Volume:1500 x 1500 x1500 voxels

F Plouraboué, P Cloetens, C Fonta, A Steyer, F Lauwers and JP Marc-Vergnes, J. Microscopy, 215 (2004)

Cortical brain imaging: analysisVoronoi type graph Fractal analysis

Normal vascular network

Tumorous vascular network

Increase in the scale at which thetransition fractal to homogeneous occurs

Associates a region to eachperforating vessel

Box-counting Sand-box

L Risser, F Plouraboué, A Steyer, P Cloetens, G Le Duc, C Fonta,J. of Cerebral Blood Flow & Metabolism 27, 293-303 (2007)

Phase Contrast vs Absorption

Absorption

Sample Sample

Phase

Simple transmission

• Dream 2: Improve the Sensitivity Absorption contrast too low high spatial resolution

light materialssimilar attenuation

• Dream 1: Zero DoseIncrease the energyAbsorption contrast ↓ replaced by phase contrast

Absorption and Phase

0.1

1

10

100

1000

0.1 1 10 100

110100

δ/β

Energy (keV)

Wavelength (Å)

Soft X-rays(water window) Hard X-rays

Carbon

water vs fat

β = (λ /4π).µ ⇔ amplitude

δ ∝ electron density ⇔ phase

€

B(x,y) =2πλ

β(x,y,z)dz∫

ϕ (x, y) = − 2πλ

δ(x, y, z)dz∫

• Weak interaction with matter• Refractive index n (X-rays):

δ >> β10-6 10-9

n = 1 - δ + i β

with T = e-B.eiϕ

Exit wave gives directlyprojections of the the object

inner layerpolystyrenethickness 30 µm

outer layerparylenethickness 15 µm

850 µm

Absorption

D = 0.03 mλ = 0.7 Å

200 µm

Propagation

D = 19 cm

Polymer sphere with two layers

D = 83 cm

Propagation

Absorption vs Phase

Phase Sensitive Techniques

Phase Retardation

sΔ−=Δ .2

δλπ

ϕΔs

Deflection⇔

Phase gradientsΔα ~ µrad

x∂

∂−=Δ

ϕπλ

α2

At zero distance:Intensity ( )∫−== zIuI dexp.inc

2

00 µ

⇒ all phase information is lost

Phase Contrast Imaging methodsAnalyzer-based PCI

Grating-based PCI

Propagation-based PCI

Medical Imaging

wavefront sensorCh David, F Pfeiffer, SLST Weitkamp, ANKA

Edge enhancementHolotomography

Fresnel diffraction

• In principle: complete object contributes to a point of the image In practice: only finite region: first Fresnel zone

radius

• First Fresnel zone determines the sensed lengthscale Distance to be most sensitive to object with size a:

For example at λ = 0.5Å (25 keV)

D

u0(x,y) uD(x,y)

Dr λ=F

a = 1 µm ⇒ D = 10 mma = 40 µm ⇒ D = 16 m

λ2

2aD =

Spatial Coherence

Hard X-ray / neutron sources are ~ incoherent

Wave is partially coherent when the source is small and far

Transverse coherence length

Illuminated Vill can be much larger than coherent Vcoh

source object detector

s αblurring= z2.α= z2/z1.s

z1 z2

s

zl

2

.

21

coh

λαλ

==

Laboratory: lcoh < 1 µm

ESRF, ID19: s = 25 µm, z1 = 145 mα < 0.2 µrad lcoh ~ 250 µm

edge detection versus holography (Fresnel diffraction)

each edge imaged independentlyno access to phase, only to border

deformed image of whole object access to phase, if recorded at ≠ D’s

λ = 0.7 Å 50 µm

D = 15 cm D = 310 cm

aD <<λ aD ≈λ

towardsFraunhoferdiffraction

Edge Detection

Essentially edge enhancementWeak defocusing (and weak contrast!)

Radiography (2D)

Tomography (3D)

Detection of cracksholesreinforcing fibres, particles

Δ−≈ ),(2

1 . ),( ),( 0 yxD

yxIyxI xyD ϕπλ

absorption image phase term2D Laplacian phase

o(x,y,z) ≈ µ(x, y, z) − D Δ xyzδ(x, y, z)

absorption term phase termLaplacian refractive index

aD <<λ

Edge Detection

U. Wegst

Imaging of a 100 million years old ant preservedin opaque amber from Charentes (France)

From the real object to the virtual oneFrom the real object to the virtual one

Malvina LakMalvina Lak, Paul , Paul TafforeauTafforeau

Insect Anatomy

Virtual slices through heads of tiny staphylinid beetles

100 µm

O. Betz, U. Wegst, D. Weide, M. Heethoff, L. Helfen, W.-K. Lee, P. Cloetens, J. of Microscopy, in press.

Phase Retrieval How to retrieve the phase and

amplitude in the object plane?Image(s) ⇒ Object ???

Inverse Problem

Australian School: K. Nugent, T. Gureyev, D. PaganinTIE (transport of intensity)

€

∂I∂z

= −λ

2π∇(I∇ϕ)

D1 D2 Dn

Series of images recorded atdifferent distances

Each distance is most sensitive to aspecific range of spatial frequencies

Flemish School: D. Van Dyck, JP Guigay, P. CloetensFocus variation / transfer functions

Mixed approachExtends validity of both approaches and reconciles them

JP Guigay, M Langer, P Cloetens, R Boistel, Opt. Lett. 32 (2007)

Contrast Transfer Functions

-2

-1

0

1

2

0 0.5 1 1.5 2 2.5

amplitudephase

Fourier Transform of intensity and of phase are linearly related

phase contrast factor

ID(f) = δD(f) + RD(f) . 2 sin(πλDf 2) . ϕ(f)coherence& detector

frequency

contrastfactor

valid in case of a slowly varying phase

Variable period

2 µm

period ≈ 720 nm

period ≈ 610 nm

Contrast depends strongly on period or spatial frequency

period ≈ 530 nm

Object invisible !

Decreasing linewidthIncreasing spatial frequency

Obtained with KB-mirrors

Phase retrieval

€

˜ I D ( f ) = 2sin(πλDf 2) ⋅ ˜ ϕ ( f )

)sin( 2Dfπλ

“transfer function”

€

˜ ϕ ( f ) =sin(πλDm f 2)

m∑ ⋅ ˜ I m ( f )

2sin2(πλDm f 2)m∑

Linear least squares

Non-iterative (fast!)

∑=

N

mm fD

N 1

22 )(sin21

πλ

⇒ Optimizationof the choice of distances

4 distances

Phase Retrieval: Polystyrene Foam

• non-absorbing foam• 4 images recorded• E = 18 keV D

D = 0.21 m D = 0.51 m D = 0.90 mD = 0.03 m

50 µm

€

variable λD

Holo-tomography

3D distribution of δ or the electron-densityimproved resolutionstraightforward interpretation

processing

2) tomography: repeated for ≈ 1000 angular positions

PS foam

1) phase retrieval with images at different distances

Phase mapD

P.Cloetens et al., Appl. Phys. Lett. 75, 2912 (1999)

Phase Tomography of Arabidopsis seeds

3D structure of Arabidopsis seeds in their native state- wet sample, no preparation- no staining, no fixation, no cutting, no cryo-cooling

Holotomographic approachContrast proportional to the electron density4 distances, 800 anglesE = 21 keV

P Cloetens, R Mache, M Schlenker, S Lerbs-Mache, PNAS (2006) 103, 14626

Phase Tomography of Arabidopsis

In situ 3D imaging of a seed of an Arabidopsis plant

wet sample, no preparation

R. Mache (UJF, Grenoble)

Radiograph D = 10 mm Spectrum – Fourier transform

50 µmContrast factor

-2

-1

0

1

2

0 0.5 1 1.5 2 2.5

amplitudephase

Phase Tomography of Arabidopsis

In situ 3D imaging of a seed of an Arabidopsis plant

wet sample, no preparation

Radiograph D = 30 mm Spectrum

Contrast factor

Phase Tomography of Arabidopsis

In situ 3D imaging of a seed of an Arabidopsis plant

wet sample, no preparation

Radiograph D = 60 mm Spectrum

Contrast factor

Phase Tomography of Arabidopsis

In situ 3D imaging of a seed of an Arabidopsis plant

wet sample, no preparation

Radiograph D = 100 mm Spectrum

Contrast factor

Phase Tomography of ArabidopsisHolotomographic approachFour distancesE = 21 keV

Seed of Arabidopsis

30 µm

Tomographic Slices

Cotyledon

P Cloetens, R Mache, M Schlenker, S Lerbs-Mache, PNAS (2006) 103, 14626

Phase Tomography of ArabidopsisSeed of Arabidopsis

protoderm

organites(protein stocks)

tegumenintercellular spaces

10 µm

Tomographic Slice

5 µm

Phase Tomography of Arabidopsis

three-dimensional network of intercellular air space

gas exchange during germinationand/orrapid water uptake during imbibition

Role?

Seed of Arabidopsis

P Cloetens, R Mache, M Schlenker, S Lerbs-Mache, PNAS (2006) 103, 14626

Frogs: strong absorption / phaseAbsorption (1 scan) Phase (3 scans)

-ρ

Technical issue: simultaneous visualisation of bony parts and soft tissuesScientific case: hearing mechanism of species without middle ear

6 mm Atelopus seminiferus

R Boistel

Vizualization of brain and cartilage R. Boistel

Holotomography and micro-vascularisation

No contrast agent! E = 20.5 keV4 distances

Tumor

2.5 mm

Conclusions• SR based tomography offers different imaging modes

absorption µCT, phase contrast µCT, edge CT, …

• Provides unique information for studying the morphology andcomposition of complex systems…

Quantitative mapping in 2D and 3D

In-situ experiments, fast imaging

• Strong user demand (new SR communities)Micro-tomography: materials science, biology, paleontology, …

AcknowledgementsID19 staff

E Boller, W Ludwig, R Mokso, JP Guigay, M Schlenker, J BaruchelInsect anatomy

U Wegst (MPI Stuttgart), O Betz (U. Tuebingen)Arabidopsis seeds

S Lerbs-Mache, R Mache (UJF, Grenoble), M. Schlenker (INPG)Liquid foams

J Lambert, I Cantat, R Delannay, J Glazier, F GranerFrogs

R Boistel (NCAM, Paris sud)Metal alloys

E. Maire, J.Y. Buffière (GEMPPM, INSA Lyon)Enamel imaging / paleontology

P. Tafforeau, M. Lak

Some references (coherent imaging)

• E. Hecht, Optics, 3th ed. (Addison-Wesley, 1998).• M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon Press, Oxford, New York,

1980).• J.W. Goodman, Introduction to Fourier optics, 2nd ed. (Mcgraw-Hill, 1988).• D. Paganin, Coherent X-ray Optics (Oxford University Press, USA, 2006).

• P. Cloetens, R. Barrett, J. Baruchel, J.P. Guigay and M. Schlenker, J. Phys. D: Appl. Phys.29, 133 (1996).

• K.A. Nugent, T.E. Gureyev, D.F. Cookson, D. Paganin, Z. Barnea, Phys. Rev. Lett. 77,2961 (1996).

• P. Cloetens, M. Pateyron-Salomé, J.-Y. Buffière, G.Peix, J. Baruchel, F. Peyrin and M.Schlenker, J.Appl. Phys. 81, 9 (1997).

• P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, and M.Schlenker, Appl. Phys. Lett. 75, 2912 (1999).

• S. Zabler, P. Cloetens, J.P. Guigay, J. Baruchel, M. Schlenker, Rev. Sci. Instrum. 76,073705 (2005).