1

Overview of CT and XRD: Synchrotron applications

S R StockS.R. Stock

Research Professor, Feinberg School of Medicine

Northwestern University, Chicago IL

s-stock@northwestern.edu

Collaborators’ InstitutionsNU = Northwestern UniversityAPS = Advanced Photon Source, Argonne National LaboratoryAU = Aarhus UniversityUB = University of BurgundyULB = Free University of BrusselsSDSU = San Diego State University

APS stations* = 1-ID# = 2-BM¶ = 2-ID-D

Outline

• Introduction

• Why microCT? What’s happening?

• X-rays, diffraction reviewed.

• Reconstruction in absorption microCT

• MicroCT systems; performance

• Phase microCT

• Synchrotron diffraction examples– Mapping with 250 nm beam in dentin

I it id l t i– In situ residual stress mapping

• Synchrotron microCT examples– Absorption contrast microCT

– Phase contrast microCT

– Diffraction tomography

2

• PhD in Metallurgical Engineering.

• 1984-2001, Materials Sci. & Eng., Georgia Tech.

S.R. Stock

• 2001-present, Feinberg School of Medicine, Northwestern Univ.

• X-ray imaging, x-ray diffraction since 1978. Cullity & Stock, Elements of X-ray Diffraction, 3rd Ed.

• X-ray microCT since 1986. MicroComputed Tomography - Methodology and Applications.gy pp

• Interest in studying spatial distribution of defects, structural features and how they influence macroscopic properties, particularly mechanical properties.

Acknowledgments

• 250 nm mapping in dentin (XRD) ¶+ A Veis, A Telser (NU); Z Cai (APS)

• Residual stress measurements (XRD) *Residual stress measurements (XRD) + JD Almer (APS)

• 3D absorption microCT and finite element modeling #+ F Yuan, LC Brinson (NU); TA Ebert (SDSU); F De Carlo (APS)

• Local (absorption) tomography #+ A Veis (NU); X Xiao (APS)

• X-ray phase contrast microCT #y p+ X Xiao (APS); F de Ridder (ULB); B David (UB)

• X-ray diffraction tomography * + JD Almer (APS)+ JD Almer (APS); H Birkedal, H Leemreize (AU)

3

X-ray diffraction

• Periodic atomic arrays in crystals

Atoms scatter in all directions

dhkl sin

• Atoms scatter in all directions

• Scattering reinforced in directions given by Bragg’s Law, cancels in other directions

wavelength

diffracted beam

dhkl

diffracted beam

(hkl)

Signals – Diffraction, tomography

I/I0 – absorption tomographyIhkl – diffraction pattern

Note 2D detector vs θ/2θ detector slit.

4

What is CT, microCT?

• From Greek tomos to slice.

• In computed tomography, the internal structure of a specimen p g p y, pis reconstructed digitally from projections recorded along different viewing directions.

• There are analog tomography methods…– Tomosynthesis a.k.a laminography used for nondestructive

inspection of flat objects such as circuit boards.

– Pre-CT (S. Webb From the watching of shadows ISBN 0-85274-361-0)

• Here we focus on x-ray methods.y

• MicroCT is high resolution CT (arbitrarily assume this means reconstructions with 50 µm or smaller voxels, i.e., volume elements).

Röntgen: The attenuation of x-rays of wavelength λ is

I/I ( ) (1)

X-ray attenuation

I/I0 = exp (- µ x) , (1)

where I0 is the intensity of the unattenuated x-ray beam, I is the beam’s intensity after traversing x thickness of (homogeneous) material with µ being the linear attenuation coefficient.

In terms of the mass attenuation coefficient µ/ρ (units cm2/g)

I/I0 = exp [(- µ/ρ) ρ x)] . (2)

In terms of what happens in each thickness element dx

dI/I = - (µ/ρ) ρ dx . (3)

5

Adding the increments of the attenuation along the direction of x-ray propagation yields the more general form

I = I0 exp [- ∫ µ(s) ds] , (4)

where µ(s) is the linear absorption coefficient at position s along ray s. The problem is assigning the correct value of µ to each position along this ray (and along all the other rays traversing the sample) knowing only the values of the line integral for the various orientations of s, i.e.,

∫ µ (s) ds = ln (I0/I) . (5)dt s

For compounds or mixturesand wt. fractions wi

<µ> = wi (µ/ρ)i <ρ> . (6)Voxel dV

dt

i x-rays

s

How reconstruction works (cartoon)

Along direction 1, the high 1 absorption rectangle makes

a spatially narrow but deep“valley” in the absorption profile Pθ.

Along direction 2, the profilePθ has a spatially wide, but shallow “valley”

1 2

shallow valley .

At intermediate angles theedges of the valley are less sharp.

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Why not automated serial sectioning plus computerized digital micro-imaging of sample?

• With microCT allows multiple 3D observations of undisturbed sample as it evolves.p

• MicroCT is still much more efficient and rapid on a per unit volume basis.

• Registration of sequence of images is an issue with serial sectioning.

• If sample is highly friable service-related cracks will be ascribed to polishing damage.

• X-ray (absorption, phase) contrast shows different things than optical microscopy.

• Now you can buy commercial units as well as do microCT with synchrotron radiation.

History

• 1898: Röntgen’s radiograph Ann Phys Chem 64(1) 1-37.

• 1917: Radon laid out the mathematics.1917: Radon laid out the mathematics.– Ber Sächsischen Akad Wiss 69 262-277 (German).– IEEE Trans Med Imaging (1986) MI-5 (4) 170-176 (English).

• 1963: Cormack demonstrated practicality. J Appl Phys 34 2722-2727.

• 1973: Hounsfield’s medical system Br J Radiol 46 1016-1022 plus patents.

• Early 1980s: First microCT publications• Mid to late 1990s: Commercial lab microCT systems• 2000s: Explosion of papers

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Explosion of microCT publications: Papers in two electronic databases by year since 1998.*

microCT OR microtomography OR (micro computed tomography)

50

100

150

200

250

300 medline

compendex

Dev X-ray Tomo

* Only 27 duplicates in 2007.

0

50

1998 2000 2002 2004 2006 2008

2007: Distribution of biological papers

Non-bio (111)Heart, vessels (14)Lung (7)Oral, craniofacial (19)Bone (99)Plants (2)Implants, scaffolds (52)

111 239

p , ( )Cancer, tumors (17)Techniques (11)Animals (6)Other (12)

8

Changes in technical capabilitites

• Probably 1,000 microCT and nanoCT systems operating at present.

• Many lower resolution systems (peripheral Quantitative CT, etc.) in the clinical setting.

Literature update 2010

• Number and distribution of papers in– Web of Science (WoS)– PubMed– Compendex

Update Aug. 2010: Web of Science

Annual number of publications

450

100

150

200

250

300

350

400

“microtomography”

“synchrotron tomography”

“microCT”

0

50

2008 2009 2010*

* Extrapolation from search on 7/21/2010** Duplicates removed from plot

21 13 35 % duplicates**

9

Comparison for 3 databases for 2009(last complete year)

1000

12 43 12 % d li t (i l d d)**

200

400

600

800

“synchrotron tomography”

“microCT”

12 43 12 % duplicates (included)**

0

200

1 2 3WoS PubMed Compendex

“microtomography”

**Total: 1189 (no duplicates within a database)1090 (no duplicates within, across all 3)

Changes in technical capabilities

• Commercial microCT systems.• Commercial in vivo small animal microCT.• NanoCT (commercial, synchrotron). • Dedicated synchrotron microCT: production mode.• Probably ~1000 micro-, nanoCT systems operating.• Phase imaging and phase microCT.• Local (region-of-interest) tomography.• Huge change in computation power, data storage.

Emphasis shifting toward high definition (more and more about less and less) … large number of high depth voxels (volume elements) per unit specimen diameter … higher temporal resolution.

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X-rays

• X-rays generated by:– Acceleration of charged particlesg p– Electronic transitions between shells– Radioactive decay (γ-rays)

• X-ray tubes in lab– Characteristic lines (e.g., Cu Kα line, 8 keV)– Bremstrahlung spectrum

• Synchrotron x-rays from storage ringT bl di ti ( 8 k V E 85 k V)– Tunable radiation (~8 keV < E < ~85 keV)

– Nearly parallel, orders of magnitude higher intensity than lab source

– Spatially coherent source

Ref. Cullity & Stock, Elements of X-ray Diffraction, 3rd Ed., Ch. 1

X-ray tube (left), spectrum (right)

Effect of filter: narrows spectrum but still many energies present and this range contributes much more to the total intensity than the narrow, but much more intense characteristic line. Note: X-ray tube voltage kVp (volts) differs from the x-ray (photon) energy E (keV).

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Synchrotron radiation (storage ring)

e- electron bunch circulating in ring (7 GeV at APS)BM bending magnet between straight sectionsID insertion device (wiggler undulator)ID insertion device (wiggler, undulator)

BM, ID both produce x-rays

ref. http://www.aps.anl.gov/About/APS_Overviewhttp://en.wikipedia.org/wiki/Synchrotron_radiation

Relative intensities: US x-ray sources(apologies to the other sources around the world that are not listed)

figure produced by Argonne National Laboratory, managed and operated by The University of Chicago for the U.S. Department of Energy under Contract No. W-31-109-ENG-38.

http://www.aps.anl.gov/About/APS_Overview/Insertion_Devices/insertion_device2.html

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Mass attenuation coefficients

• Except at absorption edges, µ/ρ ~ λ3 Z3

(i.e., is a strong function of x-ray wavelength and atomic ( g y gnumber of absorber).

• Optimum imaging with µt < 2 (~14% transmission) through thickest portion of specimen. Beam passing around the specimen must not saturate detector.

• NIST: Tabulated values for elements, some other non-elemental common substances as fn. of energy.http://physics nist gov/PhysRefData/XrayMassCoef/cover htmlhttp://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html

• For polychromatic source, compute effective x-ray energy for source using a known reference sample of dimensions and absorptivity similar to that of the specimens of interest.

{see approach in Stock et al. J Struct Biol 141 (2003) 9-21}.

Mass attenuationcoefficients of somematerials (data fromNIST website)

absorptionedges

TypicalmicroCToperation

Reproduced from SR Stock,MicroComp ted TomographMicroComputed Tomography:Methodology and ApplicationsIn press 2008.© CRC Press/Taylor and Francis

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NDE

Geometry can affect resolution

Finite source size affects resolution through penumbral blurringFinite source size affects resolution through penumbral blurring.• Not an issue for synchrotron microCT • Affects lab systems. (microfocus spot size → 5 – 10 µm).

Phase contrast effects and specimen-detector separationscan affect sharpness of radiographs.

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Fourier method

Reproduced from SR Stock,MicroComputed Tomography:Methodology and ApplicationsIn press 2008.© CRC Press/Taylor and Francis

Equivalent toreciprocal space

• Absorption profile Pθ → sum of waves of different amplitudes, frequencies.• The ampl., freq. are along line in frequency space parallel to t in direct space.• Along B-B’ in frequency space:

• Increasing distance from origin, increasing frequency component.• Value any point (r,θ) is amplitude of wave at that frequency.

Ref. Kak & Slaney, Principles of Computerized Tomographic Imaging, 2001.

Fourier representation of square profilehttp://mathworld.wolfram.com/FourierSeriesSquareWave.html

1

1.5

One term

-1.5

-1

-0.5

0

0.5

-1 -0.5 0 0.5 1 1.5 2

x/L

Series1

Series2

15

Square profile (2)

0

1

1.5Twoterms

-1.5

-1

-0.5

0

0.5

-1 -0.5 0 0.5 1 1.5 2

x/L

Series1

Series2

Series3

0

1

1.5

Series1

Series2

-1.5

-1

-0.5

0

0.5

-1 -0.5 0 0.5 1 1.5 2

x/L

Series3

Series4

Series5

Series6

Series7

Series8

Seventerms

* Many P(θ) cover frequency space → F(u,v)

* Invert to give map µ (x,y) of sample, i.e., within the slice.

* Views required over 180 ° (but can make Views required over 180 (but can make approx. reconstructions with less).

* For M x M voxel (volume element) recon-struction, need (π/4) M**2 independent measurements (Nyquist limit).

* ~10**3 samples/view (1K detector width)

Reproduced from SR Stock* For 1K x 1K reconstructions, record radio-

graphs every 0.25° (~700 views).

* Normalize beam for inhomogeneitiesbefore data to frequency space.

After Kak and Slaney,Principles of Computerized Tomographic Imaging, 2001.

Reproduced from SR Stock,MicroComputed Tomography:Methodology and ApplicationsIn press 2008.© CRC Press/Taylor and Francis

16

Avoid “designing” experiments with:

High aspect ratioHigh aspect-ratio cross-sections

Long, flat faces

Experimental microCT approaches

Pencil beam

Fan beam

Parallel beam(synchrotron)

Cone beam(Scanco MicroCT-40)

a. Very slow, no effect of scatter.b. Somewhat faster than a., scattering affects fidelity.c., d. Fastest, scattering affects fidelity.

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NanoCT

• Synchrotron or tube.T i ll 30 60 l ti l• Typically 30 nm, 60 nm voxels, respectively.

• Other optics: Kirkpatrick-Baez, Bragg magnifier,compound refractive.

(These optics used for 250 nm mapping application).

Size constraints on reconstructions

sample diameter tnumber of detector elements N

t/N smallest voxel size

sample diameter t = 1 mm 1 µm voxels

detector elements N = 1K1 µm voxels

sample diameter t = 10 mm detector elements N = 1K

10 µm voxels

Intrinsic variance* of linear attenuation coefficient μt s c a a ce o ea atte uat o coe c e t μ

σ20 = const v (Mproj <N0>)-1

v : spatial sampling frequencyMproj : number of views<N0> : mean # photons transmitted

through sample center

*ref: A.C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (2001)

18

Comparison of typical lab (left column) and synchrotron (right column) microCT

P

voxel size, field of view (FOV)

X-rays

6 µm, 12 mm

polychromatic

~0.75 µm, ~1.5 mm

monochromatic

(Scanco MicroCT- 40)

y

slices / data set

time / data set

y

40

~ 15 min

2000

~ 30 min

(XOR, 2BM of APS)

Typical x-ray imaging set-up with synchrotron x-radiation

thin singlegcrystal

phosphorCCDopticallens* sample

X-rayslightlight

* Low depth of field, reject scattered light photons.

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Typical operation in microCT: Correction for detector, beam non-uniformity

No beam, CCD non-uniformity Raw radiograph

Beam non-uniformity Corrected view

Sea urchin spine (Diadema setosum)1 K horiz. field of view (FOV), 550 pixel vert. FOV

Reproduced from SR Stock, MicroComputed Tomography Methodologyand Applications, In press 2008. © CRC Press/Taylor and Francis

X-ray phase contrast

• In most materials the index of refraction for x-rays differs slightly from 1 and depends on electron density in a way that is different from absorption.

• If the x-ray wavefield propagating through a uniform solid encounters volumes with different refractive indices, the wavefront is distorted …edge enhancement, multiple fringes. Changes which are too small to be seen with absorption as the source of contrast are readily seen with phase (provided that the incident beam has the proper characteristics).

detector

20

X-ray phase imaging

propagation sampleabsorption phase

analyzer

analyzerxtal

subset l t d

detector

detectordetector

interferometry

selected

S M A

object

X-ray phase imaging (2)grating method for lab or synchrotron

source G0 object G1 G2 detector

G0: source grating…many virtual sourcesG2: analyzer grating…translated to reveal phase shifts of beams

transmitted through specimen

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Comments

• With very small sources, phase enhanced imaging is possible in the laboratory.p y

• Optics in beam line can degrade beam coherence, suppress ability to image with phase methods.

• Three approaches give different information– Propagation (or in-line): Second derivative of phase

– Analyzer: First derivative of phase

– Interferometer: Phase

• Propagation, analyzer are good for objects with sharp boundaries between materials

• Interferometer excellent for gradually changing material

• Can do phase microCT as well as radiography

Alternative to Computed TomographyLaminography a.k.a. tomosynthesis

(see also stereometry in 2nd part)

Reproduced from SR Stock, MicroComputed Tomography Methodologyand Applications, In press 2008. © CRC Press/Taylor and Francis

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250 nm diffraction, fluorescence mappingin bovine dentin

Mineral phase (cAp, carbonated apatite) has c-axis ǁ collagen axis.Tubule have lumen originally filled with odontoblast process. 1 µm thin sections (microtome) mapped; fluorescence simultaneous with diffraction.

2D maps (left), a, b fluorescence; c-f cAp diffraction1D profiles at positions of arrows (right)

Zn observed at active mineralization site (edge of tubule lumen)!!Expected cAp biaxial crystallographic texture.

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• Applied force distorts the shape of cAp unit cells ( lid i iti l d h d fi l

• Divide cAp diff. ring (00.2, 22.2, 00.4) into azimuthal bins (72). plot A. Fit

k ( di l d V i t)

Internal strain quantificationE > 65 keV, < (50 µm)2, < 1.5 s/pattern.

(solid initial, dashed final unit cell in A. below).

• Initially circular Debye cones elongate into ellipses (B. below).

peaks rη (radial, pseudoVoigt).

• Convert rη into dη using reference (ceria); εcAp= (d – dinitial)/dinitial. Absolute error in dη < 10-4.

• For each reflection, r vs η plots for each σapplied intersect at an invariant radius r* (plot B).

J Struct Biol 152 (2005) 14-27.“ 157 (2007) 365-370.

Strain gradients vs. applied stress across the bovine dentinoenamel junction (DEJ)

3

4

n *

10^

3

8

dentin (D) DEJ enamel (E)

-1

0

1

2

-1 -0.5 0 0.5 1

position (mm)

dev

iato

ric

stra

in 20

32

43

55

cAp 00.2

0 5

1

1.5

ain

* 1

0^3

8

20• 00.2: enamel, strong gradients rise with σappl;

-1

-0.5

0

0.5

-1 -0.5 0 0.5 1

position (mm)

dev

iato

ric

stra

32

43

55

cAp 22.2

00.2: enamel, strong gradients rise with σappl; dentin, uniform increasing strain.

• 22.2: enamel, uniform rising strain near DEJfor σappl ≤ 43 MPa, then drops (cracking?);

• 00.2 dentin: Edentin ~ 24 GPa.• 22.2 enamel: Eenamel ~ 82 GPa.

J Biomech 43 (2010) 2294-2300.

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MicroCT (left) vs FE unit cell mesh (right)numerically alter structure &

investigate effect on load distribution

Actual

• Poor meshing (too

2.5

mm

• Poor meshing (toomany sharp angles)

• Irregularities = toomany elements

Approximation

• Central cylinder(perforated)

• Wedges(trapezoidal)

• Bridges (0.15 mmdia. cylinders)

• No thorns

Local (ROI) tomography

• In a. FOV spans entire sample; fixed # detector pixels spread over FOV. Features C, D and E always in FOV.

• In b. FOV restricted; each detector pixel = smaller voxel. C,D always in FOV. E into and out of FOV.

25

ROI microCT: intact sea urchin lantern (jaw) cast in plastic

a. b. c.

t

t

t

t

r

r

r

r

d.L. variegatusTooth t rot la r Lab microCT (a ) dashed

t

t

tr

Tooth – t; rotula – r. Lab microCT (a.), dashedwhite circle – edge of plastic, dia. ~8.9 mm.Red circle shows ROI in b. (dia. ~ 5.9 mm,2.9 µm voxels). Red circle in b. shows ROI inc. (dia. ~ 1.5 mm, 0.75 µm voxels). Green boxin c. shows are enlarged in d., where theprimary plates have just begun to overlap.Whiter pixel = higher absorption.

(a) shows a 3D rendering of a lantern from lab microCT; (b) Synchrotron microCT of the plumula superimposing a grayscale numerical section and 3D views of pairs of primary plates PP1 and PP2, adoral gold = more mature, bl l t 50 i t i i t tblue = less mature, 50 intervening pairs = transparent.

The primary plates in b. are imaged with 0.7 µm voxels and are 3 8 µm center3.8 µm center-to-center. The white arrow shows the growth direction.

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X-ray phase contrast and microCTof sea cucumber in seawater

Plastic tube + spine outside FOV. ~5.8 µm voxels, 26 keV.

30 mm detector- sample distance (vs ~ 5 mm normally)30 mm detector- sample distance (vs ~ 5 mm normally).

fluid plastic tube

calcite

juvenile

(2K)2

j

soft tissueboundary

epithelium

High energy x-ray scattering tomography (using diffraction peaks) AA 6061

matrix

SiC sheath ~140 µm dia.

C core~30 µm

dia.AA 1100

cover sheet

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Data collection at APS

• Scattering (1-ID): E = 65 keV.• First generation (pinhole, translate-rotate) geometry. g (p ) g y• Detectors: GE amorphous Si (diffraction)

PIN diode in beam stop (transmission).• Beam dimensions: 15 (horiz) x 150 (vert) µm2.• Sampling: 90 points separated by 15 µm

91 projections separated 2º~1 s / projection; ~20 s readout.

• FIT-2D + MATLAB + filtered back projection: p j– Azimuthal average – I(2θ). Convert to I (d).– Reconstruct using selected peak’s integrated intensity.– Could also reconstruct with subsections of ring.

• MicroCT (2-BM). Standard set-up, 1.45 µm voxels.

Al(

200)

Mg2

Si

C(1

02)

l(22

0)

iC(1

10)

Al(

111)

Fit peaks and their identification.

d-spacing vs azimuthalangle η

#2

A

#6

M

#5

Si

#3A

l

#4

Si

#1

A g η

Advanced Photon Source

Intensity vsd-spacing foradjacent positions

28

Al SiC

*

*

t SiC

*

trans SiC

*

Diffraction tomography of mussel bysus(mineralized attachment to substrate)

T k t 1 ID O t 2010Taken at 1-ID Oct 2010E=70keV, 50x50um^2 beam

160 positions @ 50um intervals161 projections 0-360 deg at 2.25 deg intervals

GE detector 2048x2048 pixels / exposure (14 bit)

Peak D-spacing

1 3.85

2 3.03

3 3.278

4 2.485

Phase

calcite

calcite

aragonite

mixed

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Transmitted intensity reconstruction

Slice 1 (bottom, y=12.5mm) Slice 2 (middle, y=13.2mm)

Bottom = closet to substrate.

Diffracted intensity recons: Slice 1

30

Diffracted intensity recons: Slice 2