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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
−10
0
10
20
−35
−30
−25
−20
−15
−10
−5
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−40
−35
−30
−25
−20
−15
−10
−5
Aberration and harmonic imaging
6/12
Energy distr. fundamental
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−35
−30
−25
−20
−15
−10
−5
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−40
−35
−30
−25
−20
−15
−10
−5
Aberration and harmonic imaging
7/12
Energy distr. harmonic
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−50
−45
−40
−35
−30
−25
−20
−15
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−55
−50
−45
−40
−35
−30
−25
Aberration and harmonic imaging
7/12
Energy distr. harmonic
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−50
−45
−40
−35
−30
−25
−20
−15
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−55
−50
−45
−40
−35
−30
−25
Aberration and harmonic imaging
8/12
Energy distr.
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−35
−30
−25
−20
−15
−10
−5
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−40
−35
−30
−25
−20
−15
−10
−5
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−50
−45
−40
−35
−30
−25
−20
−15
[mm]
[mm
]
0 20 40 60 80
−20
−10
0
10
20
−55
−50
−45
−40
−35
−30
−25
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
−25
−20
−15
[mm]
Aberration and harmonic imaging
10/12
Energy
20 40 60 80−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
0
[mm]
[dB
]
20 40 60 80
−36
−35
−34
−33
−32
−31
−30
−29
−28
−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
]
20 40 60 80
−36
−35
−34
−33
−32
−31
−30
−29
−28
−27
[mm]0 20 40 60 80
−14
−12
−10
−8
−6
−4
−2
[mm]
[dB
]
0 20 40 60 80
−40
−35
−30
−25
−20
−15
[mm]
Aberration and harmonic imaging
10/12
Energy
20 40 60 80−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
0
[mm]
[dB
]
20 40 60 80
−36
−35
−34
−33
−32
−31
−30
−29
−28
−27
[mm]0 20 40 60 80
−14
−12
−10
−8
−6
−4
−2
[mm]
[dB
]
0 20 40 60 80
−40
−35
−30
−25
−20
−15
[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
10
20
y[mm]−20 −10 0 10 20
−20
−10
0
10
20
−35
−30
−25
−20
−15
−10
−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
