Building ThreeDimensional Images Using a TimeReversal Chaotic Cavity

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Building Three-Dimensional Images Using a
Time-Reversal Chaotic Cavity
Gabriel Montaldo, Delphine Palacio, Mickael
Tanter, and Mathias Fink
IEEE Transactions on Ultrasonics,
Ferroelectronics, and Frequency Control, Vol. 52,
No. 9, September 2005
Presented By Thomas Steen October 20th, 2005
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Presentation Outline

• 3D Ultrasonic Imaging
• Application of 1D transducer arrays
• Application of 2D transducer arrays
• Proposed 3D Ultrasonic Imaging Technique
• Introduction to Time Reversal Acoustics
• Applications
• Application of a Chaotic Cavity with Time
  Reversal
• Experimental Setup
• Nonlinear Imaging and Pulse Inversion
• Results
• Improvements and Conclusions

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Paper Preview

• Design of a 2D array for 3D imaging
• Obtain 3D focusing with a small number of
  transducers
• Propose the use of a chaotic cavity
• Creates a large array of virtual transducers
• Utilize time reversal acoustics

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3D Ultrasound (1D Array)

• Series of 2D images produced by conventional 1D
  transducer array
• 1D array moved by practitioner or motorized
  device
• Accurate position and angular data required

Nelson and Pretorius, Ultrasound in Med. Biol.
24 (1998) 1243-1270
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3D Ultrasound (2D Array)

• Electronic scanning of the volume
• Higher frame rate
• No mechanical scanning
• Real-time 3D imaging
• Disadvantages
• High number of elements (100s to 1000s)
• Complex electronic multiplexing

Davidson et al, Ultrasonic Imaging 16 (1994)
143-163
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Proposed Technique

• 2D array with a small amount of transducers
• Chaotic cavity
• Time reversal

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Introduction to Time Reversal

• Time reversibility of the acoustic wave equation

• u(r,t), u(r,-t) are solutions to the wave
  equation due to the reciprocity principle.
• Given that the medium is time invariant, and the
  reciprocity principle applies, we can time
  reverse the measured acoustic field to
  reconstruct the acoustic field at the object
  plane.

Wavefronts from the object
Measurement plane
Transmit time reverse signals u(r, -t)
r
r
Detection Probe points
Acoustic field of the object
Obtain acoustic field of the object
u(r, t)
Forward waves
Time reversed waves
Measured signals show transverse variation in
the acoustic field due to the object
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Application Time Reversal Mirror for Defect
Detection

• Focusing through inhomogeneous medium with
  iterative time reversal process
• Step 1 Transmit a wave front from one array
  element to the target
• Step 2 The backscattered pressure field is
  recorded by transducer array
• Step 3 Transducer sends time reversed field
  that focuses on the target
• In order to accurately recreate the source, all
  reflected wave vectors must be captured
• 100s to 1000s of transducers

Prada et. al, Inverse Problems 18 (2002) 1761-1773
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Proposed Technique

• Solid Chaotic aluminum cavity
• 3D Sinai billiard 50 x 50 x 50 mm3

• The chaotic cavity acts as an ultrasonic
  kaleidoscope
• Waves that enter the cavity go through all
  points of the cavity
• Strong reverberations inside the cavity the
  waves are reflected hundreds of times
• Act as hundreds of virtual transducers
• Experimental setup consists of 31 piezoelectric
  transducers
• 8mm by 5mm
• Center frequency of 1.5MHz

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Chaotic Cavity

• Acoustic source in the medium
• The impulse response received by the ith
  transducer last a very long time (up to 500?s)
• Diffuse acoustic field
• Corresponds to nearly 300 reflections
• When this is time reversed, focusing occurs at
  the source
• Side lobes are noise

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Nonlinear Imaging (Pulse Inversion)

• Nonlinear effects induced by propagation in
  medium
• Harmonic generation
• Take advantage of this to reduce side lobes
• Use Pulse Inversion technique
• Send pulse and its opposite
• Linear part clears up, leaving only harmonic

Verbeek et al, JASA 107 (2000) 2281-2290
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Nonlinear Imaging (Pulse Inversion)
PI
Improved temporal and spatial focusing
PI
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Application of Cavity to Imaging

• Calibrated in water
• Impulse sent into the cavity from 1600 focal
  points on a 40 by 40 grid
• Record the data set of transmit code that allows
  for the focusing to each point

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Imaging

• Chaotic cavity placed in front of object to
  image
• Measure second harmonic component of
  backscattered echoes
• Tissue phantoms

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Results

• Image made by measuring different arrival times
  of surface echoes

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Improvements

• Frame rate
• Using 500?s of signal requires 0.8 seconds to
  make 40 by 40 point image
• Single receiver limits resolution
• Currently designing a kaleidoscope made of 64
  emission and 64 reception transducers
• Improved contrast

Conclusions

• Utilized a chaotic cavity and time reversal
• Reduced necessary transducers
• No need for small transducers or specific shapes
• Application of pulse inversion technique
• Successful construction of images