Electrical tomography lecture v3

Industrial Tomography Slide 1

Tony PeytonManchester University

School of Electrical and Electronic Engineering

[email protected]

Industrial Tomography

Electrical Tomography for Industrial Applications


Electrical TomographyOverview of the course:

• Introduction to tomography• Overview of sensing modalities• Hardware design• Image reconstruction techniques • Industrial applications • Conclusions


Introduction

GEhttp://www.ge.com/medical/

Analogichttp://www.analogic.com/Level3/CT%20III.html

Siemenshttp://www.med.siemens.com/


IntroductionIndustrial tomography

• High resolution (spatial or contrast) may not be essential• High imaging speeds may be required

(e.g. 100’s frames/sec for fast flow applications)• Rugged operating conditions

(temperature and pressure)• Safety considerations• Greater inhomogeniety• Wide range of material properties• Cost


IntroductionExamples of industrial techniques 1

Microstructural characterisation Magnetic resonance imaging (MRI).of components, particles, pastes, Neutron tomography.foams, filters X-ray micro-tomography.(1—10000 μm) Optical tomography

Liquid mixing and Optical tomography. multi-phase flow Electrical resistive tomography. (0.01—0.5 m) Electrical capacitance tomography.

Ultra-sonic / acoustic tomography

Powder mixing, transport and Positron-emission tomography (PET).conveying Electrical capacitance tomography. (0.01—0.5 m) γ-ray transmission.

Electro-dynamic tomography.


Fluidisation and trickle bed γ-Tomography.reactor studies X-ray tomography.(0.01—3.0 m) Positron-emission tomography (PET).

Electrical capacitance tomography.


Thermal mapping of reactors, Infra-red emission imaging.objects and atmospheres Electrical resistance tomography.(0.01 m to 5 km) Microwave tomography.

Groundwater monitoring Electrical impedance tomographyand soil remediation(1 m to 2 km)



Atmospheric pollution Laser absorption imagingmonitoring(50 m to 10 km)

Ore deposit and oilfield Acoustic velocity imaging.reservoir exploration Acoustic diffraction tomography(50 m to 50 km)

Air traffic control RADAR(100 m to 50+ km)


Sensing Techniques

• Electromagnetic (hard field)• Electromagnetic (soft field)• Particle• Other

• Hybrids• Multi-modal systems


Sensing techniques:Basic principles

Excitation (array) Detection arrayProcess

Images are formed by projections:

Rotate

• Mechanical rotation• Excitation and detection array


Sensing techniques:EM (hard field)

Type Comments

γ-ray - Radio-active sources. - Mechanically scanned or fixed

arrays. - Potentially fast.

X-ray - High resolution. - Mechanically scanned. - Radiation confinement.

UV Optical Infra red

- Fast. - Optical access. - Use spectrometry to give

component specificity. Millimeter wave

- System components emerging.

f

1010


Sensing techniques:EM (soft field)

Type Comments Micro-wave - Hard or soft.

- Fast. - Moderate resolution

(wavelength dependant) - Attentuation, reflection,

defraction Electrical

- Capacitance (ECT)- Resistance (ERT) - Inductance (EMT)

- Low resolution - Fast - Low cost - Robust

f

1010

0


Sensing techniques:Nuclear particle

Type Comments Positron emission (PET)

- Uses labelled particles. - Not on-line.

Neutron - High resolution. - Spectrometry (TOF) for

element specificity. - Pulse or radioactive

sources. - Radiation confinement.


Sensing techniques:Others

Type Comments Nuclear magnetic resonance

- Fast - High performance. - Large high stabiltiy

magnet. - “Gold” standard

Ultra-sound (sonic) - High resolution. - Frame rate determined by

speed of sound. - Phased arrays for beam

steering. Thermal conduction (heat flux)

- Slow - Soft field


Sensing techniques: PETPositron emission tomography (PET, positron emission computed tomography, PECT) a technique in nuclear medicine for cross-sectional imaging that enables a non-invasive assessment and localization of metabolic activity to be made. Emission of a positron by a radioisotope results in annihilation of the positron on collision with an electron, and the creation of two gamma rays of known energy travelling in exactly opposite directions. The PET scanner has detectors on each side of the patient to detect the simultaneous arrival of the gamma rays. Images are created using reconstruction algorithms similar to CT scanning. Fluorodeoxyglucose (FDG), using fluorine-18, is used to examine glucose metabolism, and ammonia, using nitrogen-13, gives information on perfusion. Carbon-11 and oxygen-15 can also be used as radioisotopes for PET scanning. Some diseases result in decreased uptake of the radio-labelled material due to decreased function; others, including many tumours, show increased glucose metabolism and concentrate the isotope avidly. In this way functional activity of the tissues can be compared with anatomical images obtained by CT or MRI scanning. Originally used to study activity in the brain, PET is now also used for investigating the chest and abdomen. See also tomography. Compare computerized tomography."positron emission tomography" Concise Medical Dictionary. Oxford University Press, 2002. Oxford Reference Online. Oxford University Press.


Sensing techniques: MRIThis diagnostic imaging technique is based on nuclear magnetic resonance (NMR), in which protons interact with a strong magnetic field and with radio waves to generate electrical pulses that can be processed in a similar way to computerized tomography. Images produced by MRI are similar to those produced by computerized tomography using X-rays, but without the radiation hazard.

A major factor in the high costs of MRI is the need for a superconducting magnet to produce the very strong magnetic fields (0.1–2 tesla). Superimposed on this large magnetic field are smaller fields, with known gradients in two directions. These gradient fields produce a unique value of the magnetic field strength at each point within the instrument (see illustration).Some nuclei in the atoms of a patient's tissues have a spin, which makes them behave as tiny nuclear magnets.

The purpose of the large magnetic field is to align these nuclear magnets. Having achieved this alignment, the area under examination is subjected to pulses of radio-frequency (RF) radiation. At a resonant frequency of theRF pulses the nuclei under examination undergo Larmor precession. This phenomenon may be thought of as a ‘tipping’ of the nuclear magnets away from the strong field alignment. The nuclear magnets then precess, or ‘wobble’, about the axis of the main field as the nuclei regain their alignment with that field.

The speed at which the nuclei return to the steady state gives rise to two parameters, known as relaxation times. Because these relaxation times for nuclei depend on their atomic environment, they may be used to identify nuclei. Small changes in the magnetic field produced as the nuclei precess induce currents in a receiving coil. These signals are digitized before being stored in a computer.

MRI has produced spectacular results in studies of the brain and central nervous system, providing excellent images of delicate structures without the risk of the damage associated with ionizing radiation. Systems using very strong fields, in the region of 2 tesla or above, produce images of extremely high quality.

MRI: the way unique field strengths are produced at differentpoints in a specimen.

"nuclear magnetic resonance" A Dictionary of Physics.Ed. Alan Isaacs. Oxford University Press, 2000.

Oxford Reference Online. Oxford University Press.


Transducer

Incident Wave

Reflected Wave

Time delay proportional to distance between

source and reflector

Sonics Principles – Active Sonar(Courtesy J&S Marine Ltd)

Dense reflecting object

Mismatch in acoustic impedance


Object

Transmitter

Receiver

Sonics Principles – Types of Scan

A – Scan:


Object

Z modulation

Time baseX Axis

Scan mechanism

Y Axis

Receiver

Transmitter


B – Scan:


Object

Z modulation

TimebaseX Axis

Y Axis

Beam scanned over object

Scan control


Medicalscan:


Ө


Phasedarray:


Two mechanisms result in need for Time Varied Gain (TVG)

1) Spherical spreading 2) AbsorptionLoss (dB) = 40 log (R) Loss (dB) = 2 α R

R = distance from transducer to reflector

Sonics Principles – Time Varied Gain (TVG)


Fixed gain

preamps

TVG amplifiers

Quadraturedetectors

Analog to Digital

Converters

FIFO memory

DSP

System Timing

generator

TVG generattion

DDS signal generators

Fixed transmit power

amplifier

Steered transmit power

amplifiers

Phased array signal

generators

RS485 serial link

To AUV control PC

Sonar System Overview(Courtesy J&S Marine Ltd)


Method Sensor elements

Typical arrangement

Measure values

Typical material properties ??

Typical material

ECT

Capacitive plates

CapacitanceC

εr 1 – 100 σ < 10-1 S/m (low)

Oil, water, non-metallic

powders, polymers, burning gasses

ERT (EIT)

Electrodes

Resistance (Impedance)

R / Z

σ 10-1 - 107 S/m (wide) εr 100 - 102

Water / saline, biological tissue, rock /geological

materials, semi-conductors e.g. silicon

EMT (MIT)

Coils

Self/ mutualInductance

L / M

σ 102 - 107 S/m (high) μr 1 to 10,000

Metals, some minerals, magnetic materials and

ionised water ?

Sensing techniques:Electrical techniques


1

2

34 5

6

7

8

91011

12

Measure:

C1-2C1-3etc...C1-12

C2-3C2-4etc...C2-12

then

( )2

1−nn. independent measurements

Sensing techniquesOperation of ECT


Excitation coils

Detection coils

Sensor array Conditioning electronics

Host computer

D1D2D3....DM

I1I2I3...IN

CM1CM2CM3...CMN

C21C22C23...C2N

C11C12C13...C1N

.

.

.

.

.

.

.

.

.

.

.

.

.

.

=

Reconstruction algorithm

AC magneticfield

Field control&

Measured signals

Data&

Control

Sensing techniquesHardware

“Typical” electrical tomography system:


Image of 3 copper bars.(15 mm dia, 10% of object space)

Image of 2 copper bars & 1 ferrite.(15 mm dia, 10% of object space)

Sample images(SIRT & ART)

Designed and built experimental systems

Sensing techniquesExample of an EMT system


Example of Hardware Design: ECT

Typical ECT sensor

• 11 times excitation• 66 measurements• Circular or square Measurement

electrode

Insulating pipe

1

234

5

6

7

8

Earthed screen

Radial screen

9 1011

12

Imaging area


Capacitance Values

Requires:

• Highly sensitive circuit • Large measurement range (>100 times)• Stray-immune (150 pF stray C)

0

0.02

0.04

0.06

0.08

0.1

2 3 4 5 6 7 8 9 10 11 12

Detection electrode number

Cap

acita

nce

(pF)

Change in C (<0.1 pF)

0

0.2

0.4

0.6

2 3 4 5 6 7 8 9 10 11 12

Detection electrode number

Cap

acita

nce

(pF)

Standing C (<0.5 pF)


Switched Capacitor Input Circuit

V1 V2

SW, frequency fSW

C

ICharge transferred each cycle ΔQ = C.(V1 – V2)

Current, I = ΔQ.fSW = C. fSW.(V1 – V2)

Equivalent resistance,SW

EQ fCR

.1

=

Simple schematic of a switched capacitor C to V converter:

VREFVOUT

fSW

C

-

+

RF

REFSWOUT VfCV ..−=

A major practical difficulty is the effects of charge injection


C

R

V

C C

VCx

f

foi

s1 s2

1C Rf f

ω

VV

o

i

-90

-45

0

0.01 0.1 1 10 100

Vj C R

j C RVo

x f

f fi= −

+ω

ω 1

Charge amplifier:

AC-based Input Circuit


221)(

ωω++

−=sRsC

RsCsV

ff

fxo

Output Laplace transform with a sine wave input, frequency, ω

( )ωα ff RC1cot−=( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎟⎠

⎞⎜⎜⎝

⎛−−

+= αω

ω

ωt

RCt

RC

RCtV

ffff

fxo sinexp

1)(

2

Time domain response:

ff RC=τTime constant

Transient Analysis

fRC<<

ω1 V

C

CVo

x

fi= −

Capacitive feedback,

• Independent on frequency, good for spectroscopy

• Large τ = RfCf >> 1/ω→ long transient process

ff C

Rω

1<< ifxo VRCjV ω−=

• Stable frequency required• Small τ = RfCf << 1/ω→ short transient process

Resistive feedback,


• DDS signal generators (AD7008) – A, f, φ programmable• AC-PGA necessary (SNR of multiplier)• Multiplier-based demodulator – no odd harmonics• 4th order Butterworth low-pass filter -- 80 dB/decade• C+R• Spectroscopy

Block Diagram of one Channel

ACPGA

Analoguemultiplier

Low-passfilter

DDS signalgenerator

DDS signalgeneratorClock

digital controlsignal

capacitancemeasurement

CxCf

Cs1 Cs2

Rf

latch

latch

Vi

VoVd


System Block Diagram

• Standing capacitance compensation• DC PGA for large measurement range• PCI data acquisition card

M

Electrode 1

Capacitancetransducer

Capacitancetransducer

DDS signalgenerators

Differentialamplifier PGA ADC

DAC PC

Digitaloutputport

Data acquisitioncard

DC

offset voltage

digital control signals

Electrode NUX


Circuit Details - Demodulation

What is the output for a purely resistive object?How would you measure R?

( ) ( )[ ]αωααωω +−=+= tS

ABttBAS

Vd 2coscos2

sinsin1

( )[ ]tS

ABVd ω2cos12

−=

SABVd 2

=

In phase component,

After low-pass

Multiplier-based demodulator

Electrical Tomography:How could you modify the system for ERT or EMT?


C

VoVi

RR

2C

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

=++

=

nn

nn

n

i

o

jjjjV

jV

ωωξ

ωωωωξωω

ωωω

21

12)()(

)(222

2

RCfo 22

1π

=ξ = 0.707 Derive f0 →

Feature → maximally flat in the pass band

Circuit Details -Butterworth low-pass filter


Circuit Details –Excite / Detect Switching

DDS signalgenerator

1

2Electrode

Switch couplingcapacitance

Principle

Minimises problems due to parasitic “off” capacitance

T-configuration switch:

DDS signalgenerator

1 2

3

4Electrode Switch coupling

capacitances

Practical


⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

=+4096

5.040961 DV

KK

FFE

KCC ref

dgcpx

System Model

K K+ + +-

AC-basedcircuit with PGA amp

4096

FE

ADC

Offset signal

Diff.amp

DC

c d

D

4096

Reference voltage, Vref

Cx

Cp

AC PGA

K

DC

generator

g+

0.5F

+


Calibration:

> 0max.↨ (0-4096)0Parasitic< 4095↨ (1-16) keep samemax.Full pipe> 0max.↨ (0-4096)max.Empty pipe

ADC, D3PGA, D2Offset, D1Excitation

DAC

PGA ADC

D1

D2

D3Vx

Simplified System Model


Image reconstruction techniques

• Basic concepts of image reconstruction• Difficulties• Sensitivity maps• reconstruction algorithms• Sample images


Image reconstructionSome basic conceptsBasic concepts

Permittivity

distribution

Capacitance

measurements

Conductivity

distribution

Resistance

measurements

Permeability

distribution

Inductance

measurements

Forward problemInverse problem

)),(( yxfC ε= )),(( yxfR σ= )),(( yxfI μ=

)(),( 1 Cfyx −=ε )(),( 1 Rfyx −=σ )(),( 1 Ifyx −=μ


Image reconstructionSome basic concepts

Projections

X

Y

Objectdistributions

Reconstructedimages

X

Y

ProjectionPoint

distribution

Radial projections Point spread function

X

Y

Clearly we need sufficient projections to obtain a unique solution:


Image reconstructionDifficulties

Several difficulties associated:

“Soft field” effect

Ill-condition of the problem (ill posed)

Limited number of independent measurement

Non-linearity


Image reconstruction:The “soft field” effect

Aluminium targetThe magnetic field cannot penetrate the target due to eddy current effects

(d)

Ferrite targetFlux lines drawn into the target

(c)(b)

Air targetObject does not affect the lines of magnetic flux

aluminium

Model

Ferrite μR = 1000

insulator

target

(a)

Object space diameter, 150 mm excitation frequency 100kHz

The distribution of the excitation field lines is determined by the object material

Simple model of an EMT sensor:


Image reconstruction:The “soft field” effect – ERT example

2

1

2

1

)tan()tan(

σσ

αα

=2

1

2

1

)tan()tan(

εε

αα

=2

1

2

1

)tan()tan(

μμ

αα

=

α 1 and α 2 denotes the angles between field lines and the direction normal to interface

In electromagnetic theory, at the interface between two media


• There are only a limited number of independent measurements per frame, i.e. ( )

21nn +

• Cannot expect high resolution images,No. of independent ~ No. of independent

pixels measurements

Image reconstructionLimited independent measurements

• Smoothing used to improve appearance of the image.

( )2

1nn − ( )2

3−nn

EMT ECT ERT


( )2

1nn +

Image reconstructionnumber of independent measurements

( )2

1nn − ( )2

3−nnEMT ECT ERT

Detector channel

Exci

tatio

n so

urceE1

E2

E3

E4

E5

E6

E7

E8

D1 D2 D3 D4 D5 D6 D7D8

( ) 362

88=

+1Ex

cita

tion

sour

ceE1

E2

E3

E4

E5

E6

E7

D2 D3 D4 D5 D6 D7D8

Detector channel

( ) 282

88=

−1 ( ) 202

388=

−

Exci

tatio

n so

urce

E1-2

E2-3

E3-4

E4-5

E5-6

E6-7

D34 D45 D56 D67 D78 D81

8-coils example 8-electrodes example 8-electrodes example

Detector channel

Increase the number of independent measurements?


Image reconstructionIll-conditioning (ill-posed)

0100000200000300000400000500000600000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Elements Across Diameter

Sens

itivi

ty

• Expect blurring images near the center

The spatial sensitivity distribution is highly non-uniform, i.e. the sensitivity near the wall is very high and the sensitivity near the centre is very low, which is linked with an ill-conditioned sensitivity matrix. The very large condition number of the sensitivity matrix can result in the magnification of both measurement error and numerical error in the reconstructed image.


Image reconstructionNon-linearity

≠

[ ]TyxfC ..............)),(( 11 == ε

[ ]TyxfC ..............)),(( 22 == ε

[ ]TyxfC ..............)),(( 33 == ε

+

target

(a)

(b)

(c)

+

=


Image reconstructionAlgorithms

Lowercomputationrequirements

Highercomputationrequirements

Rulebased

algorithms

Weightedback-projection

Sensitivitycoefficient

NOSER

ART SIRTNeuralnetworks

Parametricalgorithms

QuantitativeFE based

algorithms

Several approaches:

Non-iterative Iterative


Image reconstructionBack-projection (along field lines)

One of the simplest methods involves projecting back along the field lines:


The main approaches:

1. Measure them.- Tedious unless automated- Only useful for the simpler algorithms- Effectively calibrates offset and gain errors at the same time

2. Sweep a perturbation over the model.- Slow- Subject to FE quantisation error

3. Calculate from field values extracted from the model.• The sensitivity maps are strongly affected by boundaries.• So static sensitivity maps are very poor for looking inside

conductive objects.• Need to know where the “main” boundaries are and

dynamically update the maps.

Determining the sensitivity maps


Sensitivity maps are commonly used.These quantify the response of a particular excite / detector pair to each pixel location

Image reconstructionExamples of sensitivity maps (ECT)

5

4

32

1

8

76

How many sensitivity maps for a ECT sensor with 8 electrodes?


Sensitivity maps are commonly used.These quantify the response of a particular excite / detector pair to each pixel location

Image reconstructionExamples of sensitivity maps (EMT)

Coil 1

Coil 6

Coil 3 Coil

5

Coil 2

Coil 4


Image reconstructionAlgebraic techniques

Algebraic techniques are widely used to in image reconstructionAs a first step both measurement and image values can be re-arranged into a vector format, i.e.

Measured data

Exci

tatio

n so

urce

Detector channel

= D

Shown with common excitation / detection elements, i.e. triangular array

. etc ..

Image(Pixel positions)

= P

. etc ..

M×1 N×1


Image reconstructionBack-projection

P = AT.D

etc.

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

TM

T

T

a

a

a

A.

2

1

m

M

mm dP ⋅= ∑

=1α

A linear combination of sensitivity maps⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

Md

d

d

D.

2

1


Image reconstructionLinear forward model

For small changes in the pixel values or for a first order approximation, we can make a linear approximation:

δD = A.δP

The matrix, A, is know as the Jacobian and represents a linear model of the system. It has M rows and N columns, where M is the number of measurements and N is the number of pixels.For this presentation, we will drop the δ, so

D = A.PThe values in the rectangular matrix A are obtained by re-organizing the M sensitivity matrices (maps) on a row by row basis. The values are re-arranged to be consistent with the organization of the vectors Dand P.


For image reconstruction, we need to determine P from measured data D. Unfortunately, the matrix A cannot be directly inverted.A natural solution would be to choose the Moore-Penrose generalisedinverse, i.e.

A† = (AT.A)-1.AT

P = A†.D is the least squares solutions to D = A.P

Unfortunately the problem is extremely ill-posed and the calculation of (A.AT )-1 or (AT.A)-1 will be swamped by numerical error.

Image reconstructionFormulating an inverse solution


Image reconstructionFormulating an inverse solution

1 2

1 3=

3

4

x

y

x=1

y=1

1 2

1 3=

3.3

4

x

y

x=1.9

y=0.7

0.01 2

0.01 3=

2.01

3.01

x

y

x=1

y=1

0.01 2

0.01 3=

2.211

3.01

x

y

x=61.3

y=0.799 Condition number =1300Condition number =1300

Condition number =14.9Condition number =14.9

Condition number is normally used to describe inevitable loss in solution of linear equations.

the largest singular value the smallest singular valueCondition number =


Image reconstructionRegularising the inverse solution (Tikhonov)

The previous solution, i.e., (AT.A)-1.AT provide a solution of min || D - A.P ||2

This is irrespective of the magnitude of vector P. A better solution would be to seek the minimum of

|| D - A.P ||2 + α2 || P ||2

The coefficient α controls a compromise between fitting the data and controlling the size of the solution. Note, ∑=

kkxx 2

A better solution, called the Tikhonov regularized solution, is given by,P =(AT.A + α.I)-1.AT.D


Image reconstructionRegularising the inverse solution(TSVD)

SVD – singular value decompositionA = U S VT

Where U is an M by M orthogonal matrix, V is am N by N orthogonal matrix and S is M by N matrix with all elements zero except diagonal components (δ1, δ2, .. δp).

P = V S-1 UT . D

A better solution, called the Truncated singular value decompositionP = V S-1 UT

T . D

δ1

δ2

δ3

δp

S =

δ1

δ2

δ3

δr

ST =

rp δδ

δδ 11 >


Some of the most effective algorithms employ iterative schemes:

• Linear model• Finite element model (FEM)• Parametric model• Analytical (rare)

Measurements from the sensor array, D

Latest estimate of the image, P

Σ+

-

APPROXIMATE INVERSE SOLVER

FORWARD SOLUTION

Update / constrain / programme flow

λ

Iterative Image Reconstruction


Linear model,i.e. D = A.P



Σ+

-

APPROXIMATE INVERSE

SOLVER ≈ A-1

FORWARD SOLUTION


λ

Relaxation,often adaptive

Regularisedpseudo-inverse.

Some varietye.g. ART vs. SIRTAdaptable flow

Iterative Linear Schemes


( ) TT s

ssgsgg k

kk

kkkkk ⋅

−−= −

−λ1

1ˆˆˆ

ART (Algebraic reconstruction technique)

Image is updated after each pixel calculation.Converges more quickly.But, more sensitive to noise

ART and SIRT

( )TT

SSSS

diagˆˆˆ 1

dppp kkk

−−=+ λ

A new image is computed before updating.A type of descent gradient method

SIRT (Simultaneous iterative reconstruction technique)




Σ+

-

APPROXIMATE INVERSE

SOLVER ≈ A-1

FORWARD SOLUTION


λ

Parameterised model.Pixels are a very basic form of parameterisation

Based on a priori knowledge

Prior knowledge can be used to

dictate the constraining or regularisation.

Iterative parametric algorithms


Parametric algorithms - Examples

• Linear image reconstruction algorithm• Change threshold to match area

Implicit model

Explicit model

Determine θ, d Determine x, y, r

Requires prior knowledge and accurate forward model




Σ+

-

APPROXIMATE INVERSE

SOLVER ≈ A-1

FORWARD SOLUTION


λ

Full FE (or analytical) modelMesh adapted to pixel geometries

Regularisedpseudo-inverse.as earlier slides

Update the sensitivity maps on each iteration

Iterative FE based algorithms


Image reconstructionFEM – 2D

Simple mesh used for previous examples


Image reconstructionFEM – 3D


Image reconstruction Comparison of algorithms (EMT)

Back-projectionNo Constraining

ART20 iterations

No Constraining

SIRT500 iterations

No Constraining

NOSERNo Constraining

Object space 150 mm diameter, 16 pole system (separate excite and detect coils) 100kHz.Target 15 mm copper tube, at radius 75 mm.


Image reconstruction Illustration of spatial resolution (EMT)

20 mm diameter

ART, 10 it.s, λ = 0.9min. = -0.075max. = 0.3mean = -0.022


25 mm diameter


30 mm diameter

23d

2d

d

Object space 150 mm diameter, 16 pole system (separate excite and detect coils) 100kHz, Aluminium rods


Image reconstruction Comparison of algorithms (ECT)

Back-projection TSVD Tikhonov Iterative


Single object Stratified Annular Two objects

Simulated test object

LBP

SVD

Tikhonov

Iterative

Tikhonov

Projected

Landweber


Two rods

SIRT

Tikhonovregularization

SVD

Single rod Three rods Four rods

EMT Images - Rods


Square Rectangle Quarter cylinder U-shape

Coaxial tube and rod Tube alone Tube with rod Difference image

EMT Images – 8 coil array


Example Applications

•Biomedical experiment •Body composition•Metal production processes•Hydraulic conveying•Hydraulic conveying •Flow monitoring•Bubble Column


LadleLadle shroud

Tundish

Water Cooled Mould

Submerged Entry Nozzle (S.E.N)

Spray Banks

Rollers

Tundish

Submerged Entry Nozzle

EM Imaging of metal production processes


Example of Predicted of Flow Regimes

Full Half-full Annular


Pilot Plant Experiments

Photograph of a pilot plant experiment:

Transparent quartz tube:

Example of flow:


Small bar(19 mm dia.)at the centreof the SEN

Medium bar(25 mm dia.)at the centreof the SEN

Large bar(38 mm dia.)at the centreof the SEN

Sample Images


Tomographic Imaging of Hot Steel


Images of molten steel flow profiles


Opening a taphole: Closing:

Taphole Monitoring

Wear mechanisms:• Aggressive nature of the hot materials• Opening and closing methods• Thermal cycling

Maintenance:Outer Insert Change - furnace on line,

2-3 hr jobInner Insert Change - furnace shut down,

labour intensive(2 outer changes for every inner changed)

Risks• Unable to plug hole, leading to a run out• Structural integrity of tapping assembly

may be compromised• Contact between molten materials and

cooling water channels


Screened cubical

Weight measurement

Electromagnetic array

Camera system

Embedded PC

Body Composition

Dave


• Mixingliquid-liquid

gas-liquid

solid-liquid

gas-solid-liquid

• Separationhydrocyclone

filtration

• Transportationhydraulic

powder conveying

• On-line monitoringproduct consistency

diffusion in foodstuffs

• Material characterisationmicro-structure

Applications (ITS Ltd)Applications (ITS Ltd)


Liquid mixing example

Outputs Sensor

10mm


Liquid mixing example


Visualization of swirling flow in a hydraulic conveyor

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25

dis tance (L/D)

flow

vel

ocity

(m/s

)Hydraulic conveying example


Hydraulic conveying: Tomographs and Photographs

Visualization of swirling flow in a hydraulic conveyor

Side view

Tomograms


Air-water flows in a horizontal pipeline

Reconstructed 2D images in respect to typical air cavity formation in the flow loop

Photograph of a slug flow


(from Korjenevsky's web site)

Circular MIT sensor

Image of brain

Experimental Biomedical System

Human head cross-section: one of the first in-vivoimages. Two bright spots in the central part may be identified as ventricles of the brain filled with CSF.


Conclusions

• Overview of electrical tomography as applied to industrial applications.

• Summarised- Sensing modalities- Applications- Image reconstruction

Electrical tomography lecture v3

Documents

oxford reference

sonics principles

oxford university

approximate

nuclear magnetic

large magnetic

image reconstruction

image reconstruction