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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.

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plane wave echo particle image velocimetry
Plane Wave Echo Particle Image Velocimetry

Samuel Rodriguez, Xavier Jacob, Vincent Gibiat

PHASE University Paul Sabatier

basics of topological optimisation applied to acoustic waves

Basics of topologicaloptimizationapplied to acousticwaves

Plane Wave Echo ParticleImage Velocimetry

Basics of topological optimisation applied to acousticwaves
  • Topological optimisation: optimisation of a physicaldomain for a given set of loads and boundaries
  • Numerical applications for electromagnetic and ultrasonicimaging [Pommier and Samet, Bonnet, Malcolm and Guzina, Dominguez and Gibiat, SahuguetChouippe and Gibiat]
  • An experimental application with a transducerarray: the TDTE method [Dominguez and Gibiat, DominguezGibiat and Esquerre]. Use of a time-domainfinite-difference model.
  • The FastTopological Imaging methodis an adaptation in the frequencydomain of the TDTE methodthataimsatreducing the computation cost.

S. Rodriguez, X. Jacob, V. Gibiat

slide3

Basics of topologicaloptimizationapplied to acousticwaves

Plane Wave Echo ParticleImage Velocimetry

  • Topological optimization

Initial domain

Parameterization

Shape optimization

Topological optimization

Figure adapted from [J. Pommier, “L’asymptotiquetopologique en electromagnétisme”, PhD thesis]

S. Rodriguez, X. Jacob, V. Gibiat

slide4

Basics of topologicaloptimizationapplied to acousticwaves

Plane Wave Echo ParticleImage Velocimetry

  • Topological optimization

Solution without a “hole”

Cost

Calculation of the gradient

Solution with a “hole”

Cost

Figure adapted from [J. Pommier, “L’asymptotiquetopologique en electromagnétisme”, PhD thesis]

S. Rodriguez, X. Jacob, V. Gibiat

slide5

Basics of topologicaloptimizationapplied to acousticwaves

Plane Wave Echo ParticleImage Velocimetry

Referencee

Inspected Med.

0

0

m

?

(um-u)( ,t)

u( ,t)

um( ,t)

Adjoint Prob.

v( ,t)

Adjoint

(um-u)(,T-t)

1- Echographicmeasure of um(r,t)

2- Numerical computation of the referencefield and measureofu(r,t)

3- Differencebetweenref and inspected

then time reversal to compute

4- the adjoint fieldv(r,t)

Calcul of topologicalderivative in time domain

S. Rodriguez, X. Jacob, V. Gibiat

how does it work in true life

Experimentalstaticresults

Plane Wave Echo ParticleImage Velocimetry

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.

Transducerarray

Water

Time

Array

Gelatin cylinder

slide7

Experimentalstaticresults

Plane Wave Echo ParticleImage 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

S. Rodriguez, X. Jacob, V. Gibiat

slide8

Experimentalstaticresults

Plane Wave Echo ParticleImage Velocimetry

  • 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 :

FT signal emitted by transducer j

FT signal measuredwithtransducer j

Transducer

COMPUTED ONCE AND FOR ALL

slide9

Experimentalstaticresults

Plane Wave Echo ParticleImage Velocimetry

2. Computation of the solutions with simple multiplications (time-domain convolutions) :

Transducerarray

Transducerarray

X

X

+

X

+

slide10

Experimentalstaticresults

Plane Wave Echo ParticleImage Velocimetry

3. Computation of the topological derivative of the FTIM method

Transducer array

Transducer array

Envelope of RF signals

FTIM

Time

Depth

application to an anisotropic solid medium

Experimentalstaticresults

Plane Wave Echo ParticleImage Velocimetry

Application to an anisotropicsolid medium
  • Composite materialsample
  • Radiation patterns computedwith a FE model.

TDTE

FTIM²

100 TIMES FASTER

slide12

Experimentaldynamicresults

Plane Wave Echo ParticleImage Velocimetry

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

S. Rodriguez, X. Jacob, V. Gibiat

slide13

Experimentaldynamicresults

Plane Wave Echo ParticleImage Velocimetry

Sedimentation of marble powder

Water level

Top

Bottom

S. Rodriguez, X. Jacob, V. Gibiat

slide14

Experimentaldynamicresults

Plane Wave Echo ParticleImage Velocimetry

Passage of a single wave at the water surface

Water level

Top

The interface water/air acts as a mirror

S. Rodriguez, X. Jacob, V. Gibiat

slide15

Experimentaldynamicresults

Plane Wave Echo ParticleImage Velocimetry

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

S. Rodriguez, X. Jacob, V. Gibiat

slide16

Plane Wave Echo ParticleImage 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 kHz

to derive dynamic ultrasonic images of moving very small particles

Everywhere such “reflecting” objects exist it is possible to image

Their movements

FTIM is a credible alternative to PIV each time it is not possible to

optically Illuminate the medium

S. Rodriguez, X. Jacob, V. Gibiat