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Simulation of X-ray in-line
phase contrast M. Langer, Z. Cen, L. Weber, J. M. Letang, S. Rit, F. Peyrin
Université de Lyon, CREATIS ; CNRS UMR 5220 ; Inserm U1044 ;
INSA-Lyon ; Université Lyon 1, Villeurbanne, France.
European Synchrotron Radiation Facility, Grenoble, France
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Background
• Aim: Monte Carlo simulation of X-ray in-line phase contrast – Infrastructure for grid computing exist (VIP, Gatelab, …)
– Focus is for the moment on the physics problems
– Master thesis Zhenjie Cen
– PhD Loriane Weber
• Outline – What is X-ray phase contrast?
– My focus: Image reconstruction – phase tomography
– Application – bone imaging
– Problems – motivation for simulation
– Developments – Deterministic -> Probabilistic
– Future work
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• Acquisition: Propagation-based imaging, using several distances [2, 3]
• High degree of coherence • Parallel-beam set-up • Micrometric resolution
X-ray phase contrast imaging
3
D1 D2 D3
Phase contrast
increases with
the propagation
distance
[2] Cloetens et al., Appl. Phys. Lett., 1999 [3] Zabler et al., Rev. Sci. Inst., 2005 3
19 keV
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X-ray phase contrast imaging 4/54
Absorption Phase
Coherent X-ray beam
• Refractive index 𝑛 𝑥, 𝑦, 𝑧 = 1 − 𝛿𝑛 𝑥, 𝑦, 𝑧 + 𝑖𝛽(𝑥, 𝑦, 𝑧)
𝛿𝑛related to the phase shift 𝛽 related to the absorption
• For hard X-rays,𝛿𝑛/𝛽 > 103[2]
PCI offers higher sensitivity than attenuation-based imaging.
[2] Momose et al., Nature Medicine, 1996. 4
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Phase Retrieval
– Quantitative, non-linear relationship between phase shift and contrast
– Phase retrieval: inverse problem of calculating phase shift from phase contrast images at different distances
Phase map
2
( ) Fr [T ( )]D D,λ A,
I x x
D
22
,, )(-)]([TFrminarg)( xxx DAD I
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Phase Tomography
•Phase shift is projection through refractive index
•Refractive index can be reconstructed by tomography
•Phase tomography usually divided into a two-step process
• Phase retrieval (2D)
• Repeated for each projection angle, tomography (3D)
• Refractive index proportional to electron density
• I.e. mass density for most materials
Introduction
D
6
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X-ray phase contrast imaging 7/54
• Coherence Spatial point-likeness of the source Temporal monochromaticity
• Synchrotron Radiation [1]: Intense Stable Coherent
ID19: micro-CT ID16A: nano-CT
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X-ray Phase Nano-Tomography
R Mokso, P Cloetens, E Maire, W Ludwig, JY Buffière, APL, 2007, 90, 144104 8
Zoom non-destructively into a region of interest of a tissue, cell, ... Ideal for multi-scale approaches Magnified phase contrast imaging
Quantitative reconstruction of the electron density Very high sensitivity High resolution (X-ray wavelength limited)
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Nano-Imaging end-station ID16B
sample
nano-spindle
Exit KB
35 mm
9 Resolution >40 nm
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Nano-imaging end-station ID16A
• Imaging in vacuum @ 17 & 33 keV
• Cryo-cooling capability
• Target resolution <20 nm 10
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Projection Microscopy
D ≈ 44 mm
Sample
Cone beam
Magnified in-line holograms of Au Xradia test pattern E = 17.3 keV
11 11
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Magnified in-line holograms of Au Xradia test pattern E = 17.3 keV
D ≈ 34 mm
Projection Microscopy
Sample
Cone beam
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D ≈ 30 mm
Projection Microscopy
Sample
Cone beam
Magnified in-line holograms of Au Xradia test pattern E = 17.3 keV
13 13
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D ≈ 29 mm
Projection Microscopy
Sample
Cone beam
Magnified in-line holograms of Au Xradia test pattern E = 17.3 keV
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Projection Microscopy: phase retrieval
Phase map
rad
X-radia gold test pattern Innermost line width: 50 nm Energy = 17.3 keV Field of view: 80 µm Pixel size: 53 nm
10 mm
Au Fluorescence; 25 nm
9 µm 15
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Phase nanotomography of bone
Pacureanu et al., Med. Phys. 2012
16
µCT
120 µm
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3D reconstruction
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3D volume rendering
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Analysis of the Lacuno-Canalicular network
• Can easily be segmented
• 10-20 cells/volume 19
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• Example on human femoral bone data
Healthy Osteoporotic Osteoarthritic
Phase nano-CT: application on bone
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Motivation: Low frequency noise 21/54
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X-ray phase contrast imaging: image formation
[8] Cloetens et al., Appl. Phys. Lett., 1999. [9] Zabler et al., Rev. Sci. Inst., 2005
• Fresnel model: 𝐼𝐷 𝐱 = 𝑃𝐷 𝐱 ∗ 𝑢0 𝐱 ²
• First order terms [8]: Linearized with respect to the object
𝐼 𝐷 𝐟 = 𝛿𝐷𝑖𝑟𝑎𝑐 𝐟 − 2 cos 𝜋𝜆𝐷 𝐟 2 𝐵 𝐟 + 2sin 𝜋𝜆𝐷 𝐟 2 𝜑 𝐟
slowly-varying phase
weak attenuation
• Problem:
Combine several distances (‘holotomography’) [8, 9]
Zero-crossings
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Motivation: Low frequency noise •Problem: transfer function goes to 0 in the low frequencies
• Motivation Simulation of artefacts e.g. LF noise
Test new reconstruction algorithms
Reduce need for synchrotron beam time
Optimize the experimental acquisition parameters
• Previously: Deterministic simulation • Wave-object interaction
• Propagation
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Simulation: Wave-object interaction
•Object described by 3D complex refractive index
•Wave-object interaction described by a transmittance function:
•Induces amplitude (absorption) and phase modulation:
•Both amplitude and phase modulation are projections through n(x)
Absorption
Sample Sample
Phase
uinc(x) u0(x)
uinc(x) u0(x)
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Simulation: Propagation
•Propagation over finite D is described by Fresnel diffraction
•Propagation is a linear system w.r.t. the wave
•Convolution of wave with propagator
•Fourier domain: Multiplication with propagator
•Non-linear w.r.t intensity: squared modulus of wave:
•Quantitative relationship phase -> contrast
D
CCD
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In-line phase contrast simulation tool on VIP 26/54
Implementation on the Virtual Imaging Platform (VIP, Creatis, Villeurbanne), an imaging simulation platform [27]
o MRI o PET o X-rays o Ultrasounds
[27] Glatard et. al, IEEE Trans. Med. Im., 2013. – http://vip.creatis.insa-lyon.fr 26
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In-line phase contrast simulation tool on VIP 27/54
• Existing
phantoms
• Voxellised objects
• Analytical
• Radon
transform
Propagation models: • CTF
• Fresnel
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Deterministic simulation: results
• LF noise not recreated
• Hypothesis: due to scattered radiation – Can be simulated using
Monte Carlo – But…
• Diffraction is a wave phenomenon, scattering is a particle phenomenon
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Ray optical approach
Deterministic process on each ray 29
• Not straight-forward to combine diffraction and scattering
• What can we implement using standard Monte Carlo? – MSc Zhenjie Cen
• Refraction • Reflection
• Implemented in Geant4
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Ray optics: example
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Wave optical approach
• Implemented in GATE (for comparison)
• Uses ITK for computations
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Comparison ray/wave optical approaches
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Perspectives: refraction on voxellised phantoms
• Refraction currently limited to analytical phantoms
• Extension to voxellised phantoms
– Calculation of refractive index gradients
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Perspectives: combine wave and particle effects
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𝑊 𝐱, 𝐩 = 𝑢0 𝐱 + 𝐲/2 𝑢0∗(𝐱 − 𝐲/2)𝑒−𝑖𝐩∙𝐲d𝐲
• Phase as optical path length of each ray – Propagate with Fresnel propagator
• Sample Wigner distribution as initialisation of MC simulation – Phase and absorption as line integrals – Sample W for initial position 𝐱 and momentum 𝐩 of photons – Scattering and propagation in MC
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Conclusions
• Simulation of X-ray phase contrast imaging
• Wave-optical approach implemented in VIP and GATE
• Ray-optical refraction approach implemented in GEANT4
• Available through VIP and GATELab
• Uses EGI
• Perspectives: Unify wave and ray optical approaches
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Acknowledgments
• Creatis
Loriane Weber, Françoise Peyrin,
Cécile Olivier, Pierre-Jean Gouttenoire, Sorina Pop, Zhenjie Cen, Simon Rit,
Jean Michel Letang
• Charité, Berlin
Kay Raum, Peter Varga
• LIB, Paris
Quentin Grimal,
Pascal Laugier
• ESRF Bernhard Hesse, Lukas Helfen, Elodie Boller
ID16
• Labex PRIMES
• You for your attention and questions!
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Simulation of X-ray in-line
phase contrast M. Langer, Z. Cen, L. Weber, J. M. Letang, S. Rit, F. Peyrin
Université de Lyon, CREATIS ; CNRS UMR 5220 ; Inserm U1044 ;
INSA-Lyon ; Université Lyon 1, Villeurbanne, France.
European Synchrotron Radiation Facility, Grenoble, France