X-Ray micro-Tomography

Alastair MacDowell,Advanced Light Source, Lawrence Berkeley National Laboratory

Outline

• History• The tomography technique• Application of absorption tomography

– Bone and Hidden Babylonian writing script• Phase contrast tomography• Applications

– NIF target and wood

A Brief History of Tomography

• Johann Radon, Czech mathematician, 1917• Conceived mathematical solution to the problem

• Allan Cormack, S.African physicist, Tufts Univ 1964• Developed initial algorithms

• Godfrey Hounsfield, EMI Research Labs. UK, 1972• Built the first CT scanners• The Beatles gift to Science

• Cormack and Hounsfield received Nobel Prize 1979• Led to revolution in medical imaging

What is Tomography?

Lots of Math

Transforms

Each ccd horizontal lineyields a slice

3d image

0-180 degree series of images of mouse jaw bone ( 10-30 mins)

The reconstruction of an object from its projections“Tomography” the word – derived from the Greek tomos (slice) and graphein (to write)

Macro CT scanning

Helical body scanning Cover off

Detector

X-raysource

( Beer Lambert law)

One line across the ccdu(x,y)=attenuation coefficient at x,y of sample

Coordinate transform

Rewrite line integral using delta function

This is the Radon Transform, or Sinogramwith representing

X-rays

The Radon Transform, or Sinogram

Mouse jaw Sinogram

pixel

0

deg

rees

180

The mathematical problem is inverting this integral to yield

Use reconstruction algorithms

Reconstruction Algorithms

Two main approaches to inverting Radon Transforms

1. Algebraic Approach - Treat the cross section as huge array of unknowns - Set up huge array of algebraic equations to solve- Used by Hounsfield in 1972- Computationally slow

2. Fourier Transform back projection algorithms- Computational fast - Application Specific Integrated Circuits (ASIC)’s can be

programmed up to perform the inversion fast

Filtered Fourier Transform back projection

Based on the Projection slice theorem

Realspace

The Fourier transform of the real projection p(x) is theslice B-B in 2D Fourier space.Weight (filter) each FT slice (B-B) with slope function

X-rays

Tomogram synthesis

Source

-FT each line of Sinogram-Weight each FT-Invert filtered FT – IFT

Back project the IFT’s in real space and sum

Mathematical proof -A. C. Kak and Malcolm Slaney, Principles of Computerized TomographicImaging, Society of Industrial and Applied Mathematics, 2001. http://www.slaney.org/pct/

Number of Projections

Number of Projections needed =pi/2*image-width (in pixels)– usually get away with less

Effect of reconstruction on phantom head with differing number of Images.

18 projections 36 projections 90 projections

Warm Superbendmagnet

Source - Super bend dipole magnet – 6 Tesla peak field

Dipole magnet sits at 4k in liquid He tank

Inside Enclosed in cold shields and container

In the ring tunnel

eV

0 20x103 40x103 60x103 80x103 100x103

Inte

gra

ted

flux (h

v/s

ec/0

.1%

ba

nd

/50

0m

A/v

ert in

teg

rate

d

1e+6

1e+7

1e+8

1e+9

1e+10

1e+11

1e+12

1e+13

1e+14

Superbend 4.37 Tesla

Regular Warm bend magnet 1.27Tesla

Superbend flux for hard x-rays a the ALS 1.9GeV

Flux similar to that from a dipole at 6GeV Advanced Photon Source at ArgonneAllows for hard ray source on a low energy ring (ALS = 1.9GeV)

8.3.2 BEAMLINE LAYOUT

ShieldWall @6m

Monochromator – white light, multilayer or Si(111)

Hutch 20m from source

White Beam line - 5 mm lead shielded throughout

Superbend source

X-rays

Multilayer

Si(111)

Monochromator, Si(111) and Multilayer

Flux at sample on 8.3.2.

2D Graph 3

KeV

10 20 30 40 50 60 70

hv/s

ec/4

00

mA

1e+10

1e+11

1e+12

1e+13

1e+14

KeV vs Flux 400mA

Kev1 vs hv/sec Si111 2 mrad

Kev1 vs Col 14

Kev2 vs Hv/sec/2mrad/ML

Calc Multilayer

Calc Si(111)

Measured Si(111)

Multilayer flux density at Sample = 5x105 hv/umMulilayer bandpass (WB4C) = 1/100Si(111) bandpasss = 1/7000

Beam = 2×0.23 mr @ 20m. Beam size = 40x4.6mmLetter box shapedTo do large sampleneed to vertically tile

Flux is 100-1000xhigher than lab basedsources.Also coherent-phase contrast imaging

Tomography Camera- Schematic

Sample CdW04 scintillator

X-rays

Rotation stage

30 deg mirror

CCD

Lens

CCD out of the orbit plane to avoid gamma rays from SR

Visiblelight

Light tight box

X-rays

Sampleon rotary stage

Sample Scintillator Lens CCD Camera box on rails

Tomography Camera

Xray energy keV

0 5 10 15 20 25 30

0

20

40

60

80

100

Col 1 vs Col 2

Resolution limits

Resolution limited by 1. Resolution of the visible light optics.

Resolution = lambda/2.NA 2. Ultimate resolution limited by Depth of focus (DOF)

issue due to x-ray penetration into scintillator.

A.Koch et al., J.Opt Soc Am.A, 15, 1940-1951 (1998)

So for CdWO4 scintillator with aabsorption depth ~10-40 um, Resolution ~ 2-4um, For better resolution use 5 um thick epitaxial YAG on YAG

Scintillator

CCD

Lens of HighNumerical ApertureNA= sin(a)

ScintillationLight from different depths

1/e depth (microns) for CdWO4

1/e

dept

h (m

icro

ns)

Variation of resolution with NAand DOF of object.No scintillator absorption

Different Scintillator thickness

Reconstruction artifacts

M.Boin et al. Optic Express, 14, 21071-12075 (2006)

Usually get rings due to -pixel response non linearity,-normalization problems due to beam drift

Pixel

Ang

le

Sum of values Smoothed

Before ring removal

After ring removal

Sum all vertical pixels, smooth and renormalize

Application – Trabecular bone decay in vertebrae

Osteoporosisstudies

Osteoporosis isnot entirely

explained by lossof bone mass.Valid for large

populations butnot for the

individual. Bonedensity alone

accounts for 10-90% of the bonestrength on an

individual basis.

Local architectureand local bonedensity tissueneeds to be

understood foraccurate diagnosis

of what is goingon.

30 year old

63 year oldCarbon Sequestration

Different types of bone

1mm

SpongyTrabecularbone

The internal structure ofvertebra is Trabecularbone (spongy bone) –carries 90% of the forceOsteoporis is theweakening and collapseof this structure.

J.Kinney et al.Bone, 36, 193-201 (2005)

Cortical bone

PJ. Thurner, P. Wyss, R. Voide, M. Stauber, M. Stampanoni, U. Sennhauser, R. MüllerBONE 39 (2): 289-299, 2006

3D bone failure mechanism in Trabecular bone

Work at the Swiss Light Source -

Environmental bone compression cell

PiezoCompressor

3D bone failure mechanism in Trabecular bone

Catastrophic failure of Trabeculae

Quantification by crack detection algorithm

3D bone failure mechanism in Trabecular bone

Application: - Archaic Bookkeeping – First human writings

Babylonia

Time line~10,000BC Nomadic to settlement transition in Euphrates delta

Small settlements – easy living – wild grains and wild animals are domesticatedSmall – organized by the memory and verbal traditions of preliterate humans

3000-4000BC – rainfall reduction, irrigation over distance requires organization - human administration is required -age of early civilization

~3100BC – first real human writings appear on clay tablets as record of goods in Cuniform script.The clay tablets do not recycle – many found in landfills, some are sealed. Could smash them open to read the inside – but the trend is not to these days.

Sealed tablet – tax records insideD.Owen, Univ Cornell,

10mm

The internal script reads:- "1 bushel (by royal standard) and 40 liters of barley, thedeficit from the field of Iridu, Lubaba received in the year the city of Urbilum was raided"(= 2nd year of king Amar-Suena, 2044 B.C.E.)

Part of knowledge accumulation as to how early civilization started.

Babylonian sealed Tablet

Sectional slice

10mm

Other cool stuff happening in micro x-ray tomography

Fossil embryos 500M years old

P.Donghue, Nature 442, 680-683 (2006)Swiss Light Source (SLS)

Shanidar Cave, Iraq

D.Hunt Smithsonian InstituteWork at the ALS

Homo Neanderthalensis

Secondary dentine

Phase Contrast Tomography

Solve images for phase, (algorithms are becoming available)Obtain index of refraction Then do tomographic reconstruction

The Edges are enhanced

n=complex index of refractived=refraction decrementB=attenuation decrementz = Sample to detector distance

To image low absorption materials – we use refractive index variation andinterference effects in the far field

Image of a PMMA rotorX-rays = 20keV Very little absorptionSample-detector distance = 970mm

1

For pure phase object -Intensity proportional to second derivative of phase

x y

A.Pelle, RSI 76, 83707 (2005)

Application – Characterization of NIF targets

NIF – National Ignition Facility at Livermore - $3B project, 7 acresSwitch on date -2010

A few statistics192 laser beams Delivers 1.8x106 joules of UV light in 3x10-9 sec Peak power = 5x1014 wattsPrecision Optic area = ¾ acre (33,000 sq ft)Target Expt. chamber – 33 ft diameter, 106lbsAluminum chamber 4” thick

Laser bay #2 beam paths Target chamber

Research program-Nuclear fusion

-Astrophysics-Fusion energy-Stockpile Stewardship

- Material Properties inextreme conditions

-Plasma physics

NIF program

Sample holder (Hohlraum)

Target at ~ 18K needs to be uniform for implosionto work effectively

Be shell2 mm dia

D-T solid-vaporInterfaceCool <20k

Be/D-Tinterface

The Fusion capsule

Injection tube for Deuteriumand Tritium gas

D.Montgomery et al, Rev Sci Instrum 75 3986-3988 (2004)J. K. Hoffer and L. R. Foreman, PRL 60, 1310 (1988)

Phase contrast image from Lab source . B. Kozioziemski, LLNL

•Solid D-T layer inberyllium shell formed byβ-layering

Solid D-T layers must be formed and characterized

• Must demonstrate D-T layer meets NIF roughness spec

Be shellSolid D-T

h

δh

Hohlraum

Mode

(µm)2

R

R

Mode = 5

Mode = 20

Surface roughness and Crack evolution with time

Cracks on surface

2.5 hour movie from lab source shows crack growth and annealingNeed faster collection times – use a synchrotron.

Rough D-T surface

D-T solid-vaporinterface

Be/D-Tinterface

Roughness present on D-T surface -D-T surface is changing-Sample cooled from 0.4K to 1.5K below melting over 2.5 hours

Application : Cellulosic Ethanol Program

-100,000TW of energy received from the sun.-Need to harness 0.013% of the energy falling on the earth to supply thecurrent energy requirements for human civilization (13TW)

The World Energy ProblemBurning carbon based fuels

- results in major dependence on unstable suppliers- results in global warming – this is bad.

Alternatives-Nuclear Fusion or Fission-Coal with Carbon sequestration-Geothermal-Solar

-Wind-Wave-Hydrolectric-Photovoltaic-Biomass Amount of land needed to

capture13TW:1% efficiency Biomass = 4.6%

Cellulosic ethanol is the conversion of the woody part of plants to ethanol

Corn Ethanol vs Cellulosic Ethanol

-Cellulosic ethanol produces 85% less CO2 than regular Gas-Corn starch ethanol produces only 25% less CO2 than regular Gas

-Starch is soft and can be broken down easily to sugars then fermented

- Lignocellulose is more abundant - the woody part of the plantLignocellulose has evolved to resist breakdown – houses stay upconsists of Cellulose 45%, Hemicellulose 30%, Lignin 25%

-Ruminants and termites have evolved cellulase enzymes to deal withlignocellulose

Biomass Fuel Production

Sunlight

Feedstockdevelopment

Biomass

BiomassDepolymerization

Monomers

BiofuelsProduction

Ethanol

Need to develop new Biomass plants– improve with genetic engineering

Currently use high temp and acid,Then enzymes- cellulose to sugarsSlow, expensive- improve Lignocellulose breakdown

Hemicellulose yields pentosesYeast diet only hexoses-improve with genetic engineering

Miscanthus

- Miscanthus– 2% conversion efficiency demonstrated on non-irrigated non fertilized test field in Illinois.-100M acres (4.4% of USA) would yield 200B Gal/year ethanol (US consumption 2030)-$2-3 per gal-Improvements - Genetic engineering and select for lignocellulose content and efficiency.-Poplar tree has been genetically mapped.

Feedstock development

Biomass Depolymerization

50um

-Termites and Cows have developed enzymes to break down lignocellulose-they are slow – enzymes need engineering for speed

-will probably need mechanical mashing of biomass before enzyme processing- micro tomography can monitor decomposition process on micron scale

Phase contrast reconstructed images of wood – recorded at the SLS

A.Groso et al. Optics Express, 14, 8103-8110 (2006)

Summary

-As might be expected the microscopy of the inside of things is applicable to a wide range of problems across many fields-Getting easier as the technique is developed

– faster CCD’s- faster computers- better algorithms

viewing time to see in 3D should be down to minutes soon.

AcknowledgementsEric SchaibleHolly BarthJames NasiatkaStaff of the ALSHelp from SLS, APS, LLNLThe Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.