Tomography and holotomography - Northwestern University
Transcript of Tomography and holotomography - Northwestern University
Tomography and holotomographySchool on X-ray micro and nanoprobes
P. Cloetens
ESRF, Grenoble, [email protected]
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).