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) 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

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

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

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 500s) 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 Improved temporal and spatial focusing PI

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 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