Aberration and harmonic imaging

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Aberration and harmonicimagingIEEE Ultrasonics Symposium 2005

Trond Varslot, Svein-Erik Masøy and Bjørn Angelsen

Norwegian University of Science and Technology

Aberration and harmonic imaging

2/12

MotivationGood understanding of wavefront aberrationand linear wave propagation.

time-delays and amplitude filter /generalised screentime-reversal / DORT

"... but harmonic imaging works so well ...why bother ... "

"... harmonic imaging has solved the problemof aberration ... "

Aberration and harmonic imaging

2/12

MotivationGood understanding of wavefront aberrationand linear wave propagation.

time-delays and amplitude filter /generalised screentime-reversal / DORT

"... but harmonic imaging works so well ...why bother ... "

"... harmonic imaging has solved the problemof aberration ... "

Aberration and harmonic imaging

2/12

MotivationGood understanding of wavefront aberrationand linear wave propagation.

time-delays and amplitude filter /generalised screentime-reversal / DORT

"... but harmonic imaging works so well ...why bother ... "

"... harmonic imaging has solved the problemof aberration ... "

Aberration and harmonic imaging

3/12

TheoryWestervelt equation

∇2p −1

c2

∂2p

∂t2=

1

c2

∂2Lp

∂t2− εn

∂2p2

∂t2

Define linear and nonlinear parts in frequencydomain for |pnl| << |pl|

Aberration and harmonic imaging

3/12

TheoryWestervelt equation

∇2p −1

c2

∂2p

∂t2=

1

c2

∂2Lp

∂t2− εn

∂2p2

∂t2

Define linear and nonlinear parts

in frequencydomain for |pnl| << |pl|

p = pl + pnl

∇2pl −1

c2

∂2pl

∂t2=

1

c2

∂2Lpl

∂t2

∇2pnl −1

c2

∂2pnl

∂t2=

1

c2

∂2Lpnl

∂t2− εn

∂2p2

∂t2.

Aberration and harmonic imaging

3/12

TheoryWestervelt equation

∇2p −1

c2

∂2p

∂t2=

1

c2

∂2Lp

∂t2− εn

∂2p2

∂t2

Define linear and nonlinear parts in frequencydomain

for |pnl| << |pl|

p = pl + pnl

∇2pl +ω2

c2pl = −

ω2

c2Lpl

∇2pnl +ω2

c2pnl = −

ω2

c2Lpnl + εnω

2p∗ωp.

Aberration and harmonic imaging

3/12

TheoryWestervelt equation

∇2p −1

c2

∂2p

∂t2=

1

c2

∂2Lp

∂t2− εn

∂2p2

∂t2

Define linear and nonlinear parts in frequencydomain for |pnl| << |pl|

p = pl + pnl

∇2pl +ω2

c2pl = −

ω2

c2Lpl

∇2pnl +ω2

c2pnl = −

ω2

c2Lpnl + εnω

2pl∗ωpl.

Aberration and harmonic imaging

4/12

ObservationsAberration of linear part is well understood

Nonlinear part is governed by the sameequation with additional source term

Source for the nonlinear part is an aberratedlinear part

Expect the nonlinear part to be as aberratedas the linear part.

Aberration and harmonic imaging

5/12

Simulations

F

xd

d

TX frequency : 2.5 MHzFocal depth : 6.0 cmXD : 2.0×2.0 cmWall model : abdominal

2.0 cmTissue : muscleSimulation : 3D

Aberration and harmonic imaging

6/12

Energy distr. fundamental

[mm]

[mm

]

0 20 40 60 80

−20

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0

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]

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Aberration and harmonic imaging

6/12

Energy distr. fundamental

[mm]

[mm

]

0 20 40 60 80

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Aberration and harmonic imaging

7/12

Energy distr. harmonic

[mm]

[mm

]

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]

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Aberration and harmonic imaging

7/12

Energy distr. harmonic

[mm]

[mm

]

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Aberration and harmonic imaging

8/12

Energy distr.

[mm]

[mm

]

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]

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]

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0

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Aberration and harmonic imaging

9/12

Peak pressure

0 20 40 60 80

−14

−12

−10

−8

−6

−4

−2

[mm]

[dB

]

0 20 40 60 80

−40

−35

−30

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[mm]

Aberration and harmonic imaging

10/12

Energy

20 40 60 80−11

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0

[mm]

[dB

]

20 40 60 80

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−27

[mm]

E(z) =

∫ ∞

−∞

∫Tz

|p(r, t)|2dtdr.

20 40 60 80−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0

[mm]

[dB

]

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[mm]

[dB

]

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[mm]

Aberration and harmonic imaging

10/12

Energy

20 40 60 80−11

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−8

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−6

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−4

−3

−2

−1

0

[mm]

[dB

]

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[mm]

[dB

]

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[mm]

Aberration and harmonic imaging

11/12

Beam profiles

−20 −15 −10 −5 0 5 10 15 20−30

−25

−20

−15

−10

−5

0

[mm]

[dB

]

Aberration and harmonic imaging

11/12

Beam profiles

−20 −15 −10 −5 0 5 10 15 20−30

−25

−20

−15

−10

−5

0

[mm]

[dB

]

Aberration and harmonic imaging

11/12

Beam profilesx[

mm

]

y[mm]−20 −10 0 10 20

−20

−10

0

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y[mm]−20 −10 0 10 20

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0

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−5

Aberration and harmonic imaging

12/12

SummarySecond harmonic is governed by the sameequation as fundamental, with additionalsource term

Source for the second harmonic is aberratedfundamental

Aberration of second harmonic is similar tothat of fundamental

Reduced aberration for fundamental at lowerfrequency

Other sources for improved image quality inharmonic imaging

Aberration and harmonic imaging

12/12

SummarySecond harmonic is governed by the sameequation as fundamental, with additionalsource term

Source for the second harmonic is aberratedfundamental

Aberration of second harmonic is similar tothat of fundamental

Reduced aberration for fundamental at lowerfrequency

Other sources for improved image quality inharmonic imaging

Aberration and harmonic imaging

12/12

SummarySecond harmonic is governed by the sameequation as fundamental, with additionalsource term

Source for the second harmonic is aberratedfundamental

Aberration of second harmonic is similar tothat of fundamental

Reduced aberration for fundamental at lowerfrequency

Other sources for improved image quality inharmonic imaging

Aberration and harmonic imaging

12/12

SummarySecond harmonic is governed by the sameequation as fundamental, with additionalsource term

Source for the second harmonic is aberratedfundamental

Aberration of second harmonic is similar tothat of fundamental

Reduced aberration for fundamental at lowerfrequency

Other sources for improved image quality inharmonic imaging

Aberration and harmonic imaging

12/12

SummarySecond harmonic is governed by the sameequation as fundamental, with additionalsource term

Source for the second harmonic is aberratedfundamental

Aberration of second harmonic is similar tothat of fundamental

Reduced aberration for fundamental at lowerfrequency

Other sources for improved image quality inharmonic imaging

Aberration and harmonic imaging

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