Quantitative phase contrast tomography using coherent synchrotron radiation

1
Quantitative phase contrast tomographyusing
coherent synchrotron radiation
ID19

• P. Cloetens
• J.P.Guigay1, O. Hignette1, W. Ludwig2,M.
  Schlenker3, S. Zabler1
• 1. ESRF, Grenoble, France
• 2. INSA, Lyon, France
• 3. CNRS, Grenoble, France

2
Tomography
Motivation 3D microscopy (non-destructive) in-si
tu experiments (strain, fatigue,
) representative elementary volume input
for calculations ?structure ? properties
Compromise spatial resolution ? field of
view micron (100 nm) millimeter, centimeter
User Facility Need for practical, robust methods
3
Outline

• Coherent synchrotron radiation ? propagation
  technique
• Simulation
• Edge enhancement (qualitative tomography)
• Holotomography (quantitative tomography)
• phase retrieval
• optimisation choice of algorithm, distances,
  energy, practical cases
• X-ray magnification
• projection microscope based on KB mirrors

4
Why Phase Contrast?

• Dream 1 Sensitivity
• Absorption contrast too low high spatial
  resolution light materials similar
  attenuation C-C, Al-Si, Al-Al2O3

5
Absorption vs. Phase
6
Experimental Setup
Implemented on ID19 / ESRF Dedicated
microtomograph (P. Bernard) Monochromator double
Si crystal (Dl/l10-4) or multilayer
(Dl/l10-2) Sample stage rotation stage
(tomography) Detector CCD-based on translation
(propagation) crucial for spatial
resolution Scan time 10242 900 proj. 7
minutes 20482 1500 proj. 20 minutes
ESRFcamera
sample
rotationstage
translationstage
7
edge detection
holography (Fresnel diffraction)
versus
D 15 cm
D 310 cm
each edge imaged independently
deformed image of whole object

no access to phase, only to border
access to phase, if recorded at different
distances
D lt a2/?
D a2/?
8
Image Formation Fresnel diffraction
Intensity
Convoluted intensity
convolution with the projected distribution
of the incoherent source
Fresnel diffraction convolution with propagator
PD
convolution with detector point- spread function
objects complex transmission function j(x) and
B(x)
Source
incoherent emission of spherical waves
Effective propagation distance D z1z2/(z1z2)
z1
z2
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Weak phase object

• Fourier Transform of intensity and of phase are
  linearly related

phase contrast factor
coherence detector
contrastfactor
frequency
a single image is blind to some spatial
frequencies!
10
Variable period
Decreasing linewidth
Increasing spatial frequency
Sample by M. Panitz, University of Goettingen
Contrast depends strongly on period or spatial
frequency
Obtained with KB-mirrors
11
Focus variation method in EM
Defocus series Elimination of microscope by
computer
D. Van Dyck, EMAT, Antwerp
12
Simulation
below K-edge
above K-edge
Wah-Keat Lee (APS), P. Cloetens
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Anomalous Dispersion
d, b
Parameters determined by simulation and fitting
of Fresnel diffraction patterns
r
WK Lee (APS), P. Cloetens, M. Schlenker,
submitted to Phys. Rev. A
14
Anomalous Dispersion
f
f
WK Lee (APS), P. Cloetens, M. Schlenker,
submitted to Phys. Rev. A
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Edge Enhancement

• Essentially edge enhancementWeak defocusing (and
  weak contrast!)
• Radiography (2D)
• Tomography (3D)
• Detection of cracks holes reinforcing
  fibres, particles

absorption image
phase term2D Laplacian phase
absorption term
phase termLaplacian refractive index
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Phase Contrast Liquid Foams
Scientific Case Evolution (coarsening,
drainage) of liquid foams in 3D
F. Graner (UJF), P. Cloetens, ID19
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Phase Contrast Liquid Foams
Coarsening pressure driven growth or
disappearance of bubbles

• 3D Growth Lawvolume individual bubbles in
  time(cfr. grain growth, sintering)? needs to
  be faster image analysis

2 minutes/scan (2GB data)
F. Graner (UJF), P. Cloetens, ID19
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Edge Enhancement limitations
Radiography
100 mm
E 15 keV
D 12 mm
O. Betz
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Holo-tomography

• ) phase retrieval with images at different
  distances

D
Phase map
3D distribution of d or the electron-densityimpro
ved resolution straightforward interpretation
processing
P.Cloetens et al., Appl. Phys. Lett. 75, 2912
(1999)
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Phase Retrieval

• appropriate choice of the phase retrieval
  algorithm
• transport of intensity equation (TIE)
• parabola method (EM)
• slowly varying phase (and weak absorption)
• optimum choice of the propagation distances
• (number and values)
• appropriate choice of the x ray energy

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Test object
Experimental images for 30 distances 12 energies
D15mm
0.4 mm
D190mm
D381mm
D572mm

• assembly of small polymer balls as a test-object
  in order to evaluate the optimisation
• a similar object was created by simulation tools
• the sample is polystyrene (0.1 divinyl benzene)
  pure phase object

S. Zabler
22
Multi-energy TIE
Radiographs at 3 energies yield amplitude and Dj
Poor results on test object ? fibre model
Restricted to weak contrast, change in distance
and energy?
23
Parabola method
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Parabola method
(non-iterative part)
Correct results if phase not too large Problem
forward diffracted beam (a) can become small
Possible improvement use larger distances
(opposite to TIE requirement) consider
interference with range of beams around direct
beam?
25
Slowly varying phase
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Choice propagation distances
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Number of propagation distances
8 distances 4 distances 2 distances 1 distance
Phase retrieval from simulated data Profile
compared with the original phase
retrieved phase
original phase
Quality of phase retrieval seems sufficient (but
not perfect)when using 3-4 propagation distances.
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Choice of the energy

• higher energies favorable because d/b increases
  (dose?)
• not too high E because of decrease in nb. of
  photons, DQE
• approximation of slowly varying phase is more
  valid at higher energies
• phase profiles obtained by using 4 propagation
  distances and a given energy between 14.7keV and
  34.2keV

29
Choice of the energy
Evaluation at the level of a single Fourier
coefficientI(f0)/l should be proportional to
lpDf2(rel. low frequency f0 2104 m-1)
plDf02(mrad)
Non-linear behavior for energies below 20keV
in this case.
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In-situ imaging of organic tissue

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

wet sample, no preparation
R. Mache (UJF, Grenoble)
31
Weak phase and absorption
phase contrast factor
absorption contrast factor
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In-situ imaging of organic tissue

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

wet sample, no preparation
E 21 keV
Radiograph D 10 mm
Spectrum Fourier transform
Contrast factor
R. Mache (UJF, Grenoble)
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In-situ imaging of organic tissue

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

wet sample, no preparation
Radiograph D 30 mm
Spectrum
Contrast factor
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In-situ imaging of organic tissue

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

wet sample, no preparation
Radiograph D 60 mm
Spectrum
Contrast factor
35
In-situ imaging of organic tissue

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

wet sample, no preparation
Radiograph D 100 mm
Spectrum
Contrast factor
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In-situ imaging of Arabidopsis

• Holotomographic approach

Seed of Arabidopsis
Four distances, 800 projections E 21 keV
Tomographic Slices
Cotyledon
R. Mache (UJF, Grenoble)
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In-situ imaging of Arabidopsis
Seed of Arabidopsis
Tomographic Slice
tegumen
intercellular spaces
organites(protein stocks)
protoderm
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Holotomography applied to Materials Science
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Holotomography applied to Materials Science
Proposed solution Numerical immersion
Interest features, not matrix ? extract
contribution of features perturbation
divide raw images by the absorption
imagesubtract contribution due to
matrixcorrect for divergent lens effect
? retrieve phase due to features ? tomographic
reconstruction on phase maps ? density
variations
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Number of distances
Al-Al2O3 composite material
?? 0.3910-6 et ?? - 0.4310-9 gain
1000! Phase retrieval with 2 distances
E 20.5 keV
S. Zabler, A. Borbely (Eotvos Lorand University)
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Number of distances
2 distances
4 distances
-2pd/l
Theory400 cm-1
0.1 mm
S. Zabler, A. Borbely (Eotvos Lorand University)
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Holotomography of semi-solids
Rheology of aluminium alloys in the semisolid
state
4 distances absorption 0.2 m, 0.5 m and 0.9
m 800 angular positionsmulti-layer as
monochromator total time ? 40 minutes
L. Salvo (GPM2, Grenoble)
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Density Resolution
Semi-solidAl / AlSi
Absorption
Phase contrast
Al
Al/Si
?-map
?-map
E 18 keV
??
?? 3.5 10-8 ? ?? 0.05 g/cm3 15 of Si
L. Salvo (GPM2, Grenoble)
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Larger field of view
45
Larger field of view
Breast Biopsy Ø 15 mm pixel size 7.5 mm
Absorption
Holotomography
Lobular tissue
P. Cloetens, E. Pagot
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Sub-micron Tomography

• Improve the spatial resolution l lt 1
  Å resolution ? 0.5 mm with scintillator
  based detectors

X-ray magnification using diffractive optics
(FZP) lenses refractive optics
(CRL) reflective optics (KB) asymmetric
Bragg reflections
X-ray diffraction Fienup, J. Opt. Soc. Am. A
(1987)
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Sub-micron Tomography
Gabors Microscopic principle (Nature, 1948) The
object is illuminated by an electron beam brought
to a fine focus The object is a small distance
behind (or in front) of the point focus, followed
by a photographic plate at a large multiple of
this distance
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Kirkpatrick-Baez focusing
lt 300 mm
150 m
50 mm
focus
mirror 2
slits
mirror 1
Source size Mirror quality Diffraction
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Focusing results at 20.5 keV
Measurement Direct line scan, no
derivation Fluorescence of Au slit
Au thichness lt 70 nm
X-rays
ApertureVH (mm) Spot fwhmVH (nm) Flux (DE/E10-2)ph/s _at_ 80 mA
200 x 50 118 x 109 5 1010
400 x 100 86 x 83 2 1011
600 x 160 116 x 90 4.5 1011
O. Hignette, P. Cloetens
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Projection Microscopy
2 mm pitch grating (Si)C. David, PSI
Mirrors fully illuminated0.2 (H) x 1.1 (V) mm,
E20.5 keV
10 mm
D -10 mm M 230
D -20 mm M 115
D 20 mm M 115
D 10 mm M 230
focus
Exposure time 0.4 s ! (16-bunch, saturation CCD)
P. Cloetens, O. Hignette
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Projection Microscopy
Cu fiber
Optical microscope view
X ray microscope view
Cellular clusters
Cellular imaging
Cancerous cellsS. Bohic
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Projection Microscopy
Cancerous cellsS. Bohic
Towards focus
10 mm
D 50 mm M 45
D 30 mm M 75
D 10 mm M 230
E 20.5 keVExposure time 0.3 s ! (16-bunch)
No X-ray optics behind the sample ? dose
efficient
P. Cloetens, W. Ludwig
53
Applications Fluorescence
Cancerous cells treated with anti-cancer drug
(Cisplatin)
40 mm
Step 0.3 mm, 0.9 sec/pt
K
Pt
Phase Contrast
Fe
P. Cloetens,W. Ludwig,S. Bohic
54
Applications Fluorescence
Cancerous cells (Coll. S. Bohic- ID22)
50 mm
Pt
K
Step 0.5 mm 1 sec/pt
Fe
Traces of Pt-based drug can be imagedNew opens
in elemental cellular chemistry Adapted length
scale for- sub-cellular structures (cell
organelles)- unicellular organisms
(bacteria,certain algae and fungi)
P. Cloetens, W. Ludwig, S. Bohic
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Conclusions

• Tomography more powerful than ever absorption,
  phase contrast, holotomography,
• Quantitative mapping of the phase (2D) and
  density (3D) is possible by combining images at a
  series of distancesPractical solution slow
  phase approximationRemaining problems low
  spatial frequencies apply constrains in 3D
  (gt109 voxels)

• Improve the spatial resolutionProjection
  microscopy by KB focusing Sub (100 nm)2
  focusing made easy High flux
  (1012ph/s) Sub-micron imaging fast
  nano-radiography, nano-tomography fast and
  dose efficient full-field imaging -
  defocused image, distorsions due to mirrors
  Fluorescence probe for sub-micron element
  mapping (2D - 3D)

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Acknowledgments

• European Synchrotron Radiation Facility,
  Grenoble Technical Support
• GPM2, INPG, Grenoble L.Salvo Semi-solids
• EMAT, University of Antwerp D. Van Dyck Phase
  Retrieval
• Lab. Plastes et Différenciation Cellulaire,
  UJF,Grenoble R. Mache Plant cell imaging
• Eotvos Lorand University A. Borbely Al-Al2O3
  composites
• Imaging Group ESRF S. Bohic (ID22) cancerous
  cells S. Fiedler, A. Bravin (ID17) breast biopsy