plane wave echo particle image velocimetry
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Plane Wave Echo Particle Image Velocimetry. Samuel Rodriguez, Xavier Jacob, Vincent Gibiat PHASE University Paul Sabatier. Basics of topological optimization applied to acoustic waves. Plane Wave Echo Particle Image Velocimetry. - PowerPoint PPT PresentationTRANSCRIPT
Plane Wave Echo Particle Image Velocimetry
Samuel Rodriguez, Xavier Jacob, Vincent GibiatPHASE University Paul Sabatier
Basics of topological optimisation applied to acoustic waves
• Topological optimisation: optimisation of a physical domain for a given set of loads and boundaries
• Numerical applications for electromagnetic and ultrasonic imaging [Pommier and Samet, Bonnet, Malcolm and Guzina, Dominguez and Gibiat, Sahuguet Chouippe and Gibiat]
• An experimental application with a transducer array: the TDTE method [Dominguez and Gibiat, Dominguez Gibiat and Esquerre]. Use of a time-domain finite-difference model.
• The Fast Topological Imaging method is an adaptation in the frequency domain of the TDTE method that aims at reducing the computation cost.
2
S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image VelocimetryBasics of topological optimization applied to acoustic waves
3S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image Velocimetry
• Topological optimization
Initial domain
Parameterization
Shape optimization
Topological optimization
Figure adapted from [J. Pommier, “L’asymptotique topologique en electromagnétisme”, PhD thesis]
Basics of topological optimization applied to acoustic waves
4S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image Velocimetry• Topological optimization
Figure adapted from [J. Pommier, “L’asymptotique topologique en electromagnétisme”, PhD thesis]
Solution without a “hole”
Solution with a “hole” Cost
Cost
Calculation of the gradient
Basics of topological optimization applied to acoustic waves
5S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image Velocimetry
Referencee0
u( ,t)
Inspected Med.
?m
um( ,t)
2- Numerical computation of the reference field and measure ofu(r,t)
Adjoint Prob.
(um-u)( ,t)
(um-u)( ,T-t)
0
3- Difference between ref and inspected
then time reversal to compute
Adjoint
v( ,t)
Calcul of topological derivative in time domain
4- the adjoint field v(r,t)
1- Echographic measure of um(r,t)
Basics of topological optimization applied to acoustic waves
How does it work in “true life”
• Experimental conditions– 32-transducer array. Resonance freq 5 MHz. 0.8 mm pitch.– Lecoeur OPEN system 80 MHz.– Plane wave. 3-period sinus.
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Transducer array
Tim
e
Gelatin cylinderArray
Water
Plane Wave Echo Particle Image VelocimetryExperimental static results
7S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image Velocimetry
How to take into account the geometry and the radiation of the transducers?
How to compute efficiently (fast and accurate) the direct and adjoint fields ?
A solution is to transpose the time domain to the frequency one
TDTE versus FTIM
Experimental static results
• we have the physical information that comes from :– The experimental data:
– Dimensions of the transducers and a theoretical or a numerical model (as near as possible from the reality) of the wave propagation in the medium
1 ) Computation of the radiation patterns of every transducer j and every frequency :
8
),,( kj fyxH
)( kj fS
)( kj fM
FT signal emitted by transducer j
FT signal measured with transducer j
Transducer
COMPUTED ONCE AND FOR ALL
Plane Wave Echo Particle Image VelocimetryExperimental static results
2. Computation of the solutions with simple multiplications (time-domain convolutions) :
9
jkjkjk
jkjkjk
fMfyxHfyxV
fSfyxHfyxU
)(),,(),,(
)(),,(),,(
*
X
X
X
+
+
Transducer array Transducer array
Plane Wave Echo Particle Image VelocimetryExperimental static results
3. Computation of the topological derivative of the FTIM method
10
N
kkke fyxVfyxUyxG
1
),,(),,(),(
Tim
e
Dep
th
Transducer array Transducer array
Envelope of RF signals FTIM
Plane Wave Echo Particle Image VelocimetryExperimental static results
Application to an anisotropic solid medium
• Composite material sample
• Radiation patterns computed with a FE model.
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TDTE FTIM²
100 TIMES FASTER
Plane Wave Echo Particle Image VelocimetryExperimental static results
12S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image VelocimetryExperimental dynamic results
Small water tank
Put marble powder « beatite from Saint Béat »
Let the bigger particles sediment
Particles smaller than 40 micrometers (invisible) remain in water
Insonification from the bottom
Image of a slice of the water tank
13S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image VelocimetryExperimental dynamic results
Sedimentation of marble powder
Water level
Bottom
Top
14S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image VelocimetryExperimental dynamic results
Passage of a single wave at the water surface
The interface water/air acts as a mirror
Water level
Top
15S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image VelocimetryExperimental dynamic results
• Water rotated with a magnetic agitator and seeded with small particles (about 40 micrometer big), mimicking contrast agents.
• PRF=250 images/s, and horizontal insonification• video_vortex_flow
16S. Rodriguez, X. Jacob, V. Gibiat
Plane Wave Echo Particle Image Velocimetry
Conclusion
Instead of Time Domain Topological Energy (10 minutes/image)Frequency Domain alternative is possible (FTIM) (6 seconds/image)
Through FTIM algorithm it is possible to record sequences at frequency varying between 250 Hz and 1000 kHzto derive dynamic ultrasonic images of moving very small particles
Everywhere such “reflecting” objects exist it is possible to imageTheir movements
FTIM is a credible alternative to PIV each time it is not possible tooptically Illuminate the medium