1. 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

2. 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

3. 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

4. 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)

5. 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)

6. Proposed Technique 2D array with a small amount of transducers
Chaotic cavity
Time reversal

7. 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
Detection
Probe
points r
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

8. 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)

9. 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

10. 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

11. 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)

12. Nonlinear Imaging (Pulse Inversion)PI
Improved temporal and
spatial focusing PI

13. 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

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

15. Results
Image made by measuring different arrival times of surface echoes

16. Improvements Conclusions 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