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X-ray and optical microtomography
Alexandra Pacureanu
Instrumental for life science research
Dream:
Visualize the internal structure
without damaging the sample or
altering the observed phenomena
with high accuracy,
high speed at
low cost
Three dimensional imaging
Confocal microscopy versus microtomography
xy
xz
xy
xz
Confocal Micro-CT
Same specimen
0.2x0.2x0.3 μm 0.3 μm isotropic
Stain: FITC No stain
FOV (μm) 200x200x18
FOV (μm) 580x580x580
Note the difference in depth of field (xz)
xy xz
xy xz yz
xy
xz
xy
xz
Co
nfo
cal m
icro
sco
py
X-r
ay m
icro
tom
ogr
aph
y
A closer look: Detailed view of a cell (white cercles) in 3 orthogonal planes.
From literature – images of the same structure
[Ciani, Doty, et al., 2009]
Lin & Xu, 2010
Kubek et al., 2010
SEM
AFM
Confocal
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Today: 3D isotropic tomographic imaging
Tomography – imaging by sectioning, using a penetrating wave
Hard X-rays (~10-10 m) Visible light (~10-7 m)
1895 – Röntgen – X-rays penetrate matter with weak interaction
1917 – Radon – mathematical basis A function can be retrieved from its line integrals
1964 – Cormack – theoretical basis for CT – X-rays
1973 – Hounsfield – built the first CT machine
1973: 1st brain scanner (Massachusetts General Hospital)
1974: 1st body scanner X (Georgetown Univ Med Center)
1979: The Nobel Prize in Physiology and Medicine awarded jointly to Allan M. Cormack and Godfrey N. Hounsfield "for the development of computer assisted tomography“
The beginnings of computed tomography
Interaction wave - matter
𝑛 = 1 − 𝛿+ 𝑖𝛽
Refractive index decrement – phase shift Local electron density
Absorption index – attenuation Local attenuation coefficient:
Interaction of electromagnetic waves with matter: Complex refractive index
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Attenuation / Absorption Phase shift
Photoelectric effect an X-ray photon gives all its energy to an atom which ejects an e--. Other X-rays are emitted isotropically (fluorescence).
Elastic (Rayleigh) scattering: the X-ray
wave induces a vibration of the e-
of the matter, the X-rays keep the
same energy - elastic scattering
Inelastic (Compton) scattering: a X-ray
photon gives part of its energy to an e-,
it is deflected and continues its
trajectory with a different energy -
inelastic scattering
Interactions causing attenuation of the X-ray beam How is the X-ray beam attenuated: Beer-Lambert law
A monochromatic X-ray beam, with wavelength and intensity I0, passing through a
uniform material is attenuated exponentially:
I0
I
L I = I0 exp (- µ L)
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µ - linear attenuation coefficient of the material for the wavelength λ
µtotal = µphotoelectric + µRayleigh + µCompton
µ - is function of energy E (wavelength)
of the X-ray beam, density and atomic number Z of the material
[cm-1] µmass = µ/ρ [cm2/g]
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How is the X-ray beam attenuated: Beer-Lambert law
http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics
I1 = I0 exp (- 1 y1)
I2 = I1 exp (- 2 y2)
.
.
.
In = In-1 exp (- n yn)
In = I0 exp (- i yi)
1
2
n
I
I
0
n
y
y
y
2
n
1
Generalization of the Beer-Lambert law: Object with different materials
1 2 3 0
S D
Polychromatic case
Example : E=13 keV Absorption of 10 cm of air Absorption of 200 nm of Pb
Generalization of the Beer-Lambert law
Monochromatic case
In practice: “flatfield” image
I0
I
Detector
Source
(D)
Summation on the straigth line (D):
projection information
ln (I0 /I ) = (D) (x,y) ds
Measure I & I0 - then take logarithm Image without the beam (dark): d(x,y)
Image with the beam and without the object (reference): I0(x,y)
Image with the beam and the object: I(x,y)
Flatfield image: F(x,y) = ( I(x,y) - d(x,y) ) / ( I0(x,y) - d(x,y) )
Flatfield = ln
Flatfield and Beer-Lambert law
I0
I
d
d
Tomographic reconstruction
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Reconstruct a stack of transverse slices
Parallel beam geometry
Record a set of angular projections (radiographs)
X-ray beam
Beam
Rotation + Spreading + sum+ filter
Rotation + Spreading + sum+ filter
Rotation + Spreading + sum+ filter
Rotation + Spreading + sum+ filter
Rotation + Spreading + sum+ filter
Rotation + Spreading + sum+ filter
Independent 2D reconstruction = 3D reconstruction
Fourier slice theorem
We consider a 2D object as the cross-section of a 3D object
f(x,y) - 2D object (slice in the specimen) R f(, ) - 1D projection or radiograph of f(x,y) at the angle (Radon Transform) F f (,) - 2D Fourier transform of f(x,y) in polar coordinates F R f (,) - 1D Fourier transform of the projection R f(, ) in polar coordinates at the angle Fourier slice theorem F R f (,) = F f (,)
In other words : One can reconstruct the object from its radiographs just by using Fourier transform Collecting projections at a number of angles fills the Fourier space along radial lines
In the central area of the 2D Fourier transform corresponding to the low frequencies, the various spokes are close to each other – more informatuion. At the periphery (the high frequencies area), the spokes are distant – less information. In other words, we have more missing data at the periphery than at the center -> blurring. => Some high pass filter is useful
However, some information is lost
Passing from polar to cartesian grid requires interpolation
q
0°
180°
0,6 0,9 0,3
0
1 circle 2 circles 3 circles
Radon transform - sinogram
A sinogram is an image respresenting the Radon space (i.e. the projection space) Direct space : image (x,y ) Radon space : image (, )
Creating a sinogram
Sinogram
Radon space
Direct space
More about sinograms
x
y
x
y
Rotation axis
Rotation axis
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More about sinograms
Sinogram = set of projections
x
y
Acquisition
Reconstruction Reconstruct a stack of transverse slices
Parallel beam geometry
Record a set of angular projections (radiographs)
X-ray beam
For each horizontal line in the projection image, take all corresponding lines from all recorded angles.
This creates the sinogram for the transverse slice corresponding to that 1D projection
From each sinogram, reconstruct the transverse slice How? With Filtered Backprojection (FBP)
2 projections 0, 90 ° 1000 projections 3 projections 0, 45, 90 ° 30 projections
Use of a high-pass filter to suppress background Intuitively: Rotation, Spreading, Sum and Filter
Filtered backprojection
M=8 M=16 M=32
M=1 M=2 M=4
Backprojection example
Relation Fourier slice theorem - filtered backprojection algorithm
dRfFFyxf
).,(2
1),(
1
Ramp filter
Projection Object
“Spreading+sum” = backprojection
Inverse FFT f(x,y)
Rf(x,y) Data
FR f (,)
| | | |.FR f (,)
F-1[| |.FR f (,)]
Backprojection
Using all angles
Reconstruction steps
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The number of projections
• Number of projections per turn : Fourier slice theorem
– Collecting projections at a number of angles fills the Fourier space along radial lines
1000 projections 30 projections
x
y 20º
40º
60º
80º
100º
120º
140º
160º 180º
Sampling in the Fourier domain .CCD_Size
2Nb_Proj
Nb_ProjPixel_Size2
1
CCD_SizePixel_Size
1
Roughly, one wants =
Synchrotron micro-CT
• Developed in the 1980’s [Flannery et al., 1987]
• Synchrotron light is electromagnetic radiation produced when charged particles are deviated from a circular trajectory (by magnetic fields)
• Synchrotron radiation was first observed in the 1940s and produced in the 1960s by the bending magnets of accelerators built for high energy nuclear physics research (undesired effect). In the 1970s it has been realized that synchrotron radiation can be used as a versatile and highly intense source of X-rays
• Electrons accelerated to nearly speed of light
• High brilliance X-ray beam enables high spatial resolution imaging (1012 times brighter)
• A monochromatic beam can be selected --> quantitative imaging
• Enables 3D studies with unprecedented details
ESRF, Grenoble, France
Electrons are first accelerated in a linear accelerator (Linac), followed by acceleration in a booster synchrotron. Subsequently they circulate with a constant speed in a storage ring from where the synchrotron light is generated through insertion devices. Image credits: ESRF.
Design of a typical beamline at a synchrotron facility. Dedicated hutches are built for the instruments preparing the beam and for the sample and detector stages. The beamline is controlled remotely from the control room. Image credits: Timm Weitkamp, Soleil
In the experimental hutch of a beamline at ESRF
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Tomography setup at beamline ID19
• Long beamline – larger beam at the sample • Parallel beam tomography is possible – reconstruction is exact
• 3 insertion devices and 2 monochromators
• Energy range 12-80 keV
• Spatial resolution 280 nm – 30 µm
Beam hardening
Distortions
Smoothing
1mm
SR-µCT versus Commercial µCT
Commercial µCT: Skyscan, Scanco, Xradia,
Human iliac crest biopsy
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Voxel: 10 µm, 500 views
Acq time < 5 min
Voxel: 10 µm, 500 views
Acq time ~ 150 min
Desktop µCT SR µCT
SR-µCT versus Commercial µCT: in vivo Drawbacks: Radiation damage
Radiation dose damage (MGy)
~ 70 µm
Requires accurate knowledeg of the acquisition geometry
rotation center, angles....
Shift + Shift - Original
Bad rotation center
Attenuation SR X-ray microtomography Osteocyte cell network 300 nm
Phase imaging
• Interaction with matter induces a “phase shift” (slowing down the wave velocity)
• A more sensitive contrast mechanism (1-3 orders of magnitude)
• Reconstruct phase maps from projection images: phase differences are converted into amplitude differences and observed as intensity contrast
• FBP to reconstruct slices
𝑛 = 1 − 𝛿+ 𝑖𝛽
Refractive index decrement – phase shift Local electron density
Absorption index – attenuation Local attenuation coefficient:
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Attenuation / Absorption Phase shift
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Attenuation and phase shift of electromagnetic wave propagating in medium with complex index of refraction n An interference pattern with "Fresnel
fringes" is created. The recorded interference fringes proportional to the second derivative of the phase.
Phase SR X-ray microtomography Brain imaging
Free space propagation Ischemia – Stroke
Free space propagation phase SR μCT - 2 µm Study bone and blood vessels simultaneously
Phase SR X-ray microtomography Rat testis imaging
Gratings interferometry [Zanette et al. 2012]
Free space propagation phase SR nanoCT 60 nm
Magnified holotomography – magnification by divergent beam
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Synchrotron Source ~100 million Euros/year ~ 5 000 Euros / 8 hours OR apply for beamtime
Many specimens relevant to life science are transparent to visible light
• Zebra fish embryos – used as model organisms for disease
studies and drug discovery
• 3D cell cultures – Bridge the gap between cell culture and
live tissue
– Greater similarity with the living organism
• Drosophila melanogaster, etc.
[Pampaloni et al., 2007]
Optical Projection Tomography (OPT) • Same principle as X-ray CT but
– Much more difficult to model than X-rays
– A lot of scattering
– 3 types of photon paths, arriving to the detector at 3 different times (depending of the path length)
• Ballistic (straight line, arrive first)
• Snake (zig zag paths, arrive secong)
• Diffuse (random walks, arrive last)
– Beer Lambert law remains valid
[Arridge 1997, Sharpe 2002]
[Sharpe et al., 2002]
T-Y Chang, C Pardo-Martin, A Allalou, C Wählby,
and MF Yanik, Lab on a Chip, 2012, 12, 711
Optical
Projection
Tomography
in HTS
1 fish processed every 18s
Image pre-processing for
OPT optimization raw
Illumination correction
Vertical and horizontal alignment and
compensation for
change of perspective
Refraction correction
Center of rotation correction
(FBP minimize
entropy).
Final resolution < 10μm Final reconstruction using OSEM,
Hudson & Larkin, IEEE TMI 1994
OPT system for Zebrafish screening at MIT Fairly sophisticated and costly
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In-house optical tomography system
• Microscope ~250 EUR • Programmable rotation motor & sample stage ~250 EUR
Imaging zebrafish embryos with our in-house microtomography system
Angular projection 3D rendering of the reconstructed image
Thank you! Acknowledgments: Francoise Peyrin Pierre Bleuet Peter Cloetens Max Langer Amin Allaou