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

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

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

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

3D Ultrasound (2D Array)

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

• 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

Proposed Technique

• 2D array with a small amount of transducers

• Chaotic cavity

• Time reversal

Introduction to Time Reversal

2

22( ) u u

u

t

• 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.

r

Obtain acousticfield of the object

Time reversed waves

Acousticfield of the object

Detection Probe points

Forward waves

Measurement plane

r

Wavefronts from the object

u(r, t)

Measured signals showtransverse variation in theacoustic field due to the object

Transmit time reverse signals u(r, -t)

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

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

Chaotic Cavity

• Acoustic source in the medium • The impulse response received by the ith transducer last a very long time (up to 500s)• Diffuse acoustic field

• Corresponds to nearly 300 reflections• When this is time reversed, focusing occurs at the source

• Side lobes are noise

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

Nonlinear Imaging (Pulse Inversion)

PI

PI

Improved temporal andspatial focusing

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

Imaging

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

• Tissue phantoms

Results

• Image made by measuring different arrival times of surface echoes

Improvements

• Frame rate• Using 500s 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

• 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

Conclusions