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Hilbert space inverse wave imaging in a planar multilayer environment.
1Lawrence Livermore National Laboratory, L-154, 7000 East Avenue, Livermore, California 94550, USA. lehman2@llnl.gov
The Journal of the Acoustical Society of America
|June 17, 2005
Summary
This study introduces a novel numerical diffraction tomography (DT) algorithm that bypasses the need for homogeneous Green functions (GFs). This advancement enables non-invasive imaging of flaws in multilayer materials using ultrasonic data.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Traditional diffraction tomography (DT) algorithms rely on homogeneous Green functions (GFs), simplifying inversions but limiting applicability.
- Estimating non-homogeneous GFs or integrating them into existing DT algorithms presents significant practical challenges.
Purpose of the Study:
- To develop a purely numerical DT inversion algorithm independent of measurement geometry, frequency, and Green functions.
- To demonstrate the algorithm's efficacy in nondestructive evaluation (NDE) of multilayer materials.
Main Methods:
- Implemented Devaney's numerical DT inversion algorithm, which is independent of Green functions.
- Developed a planar multilayer Green function for use with the Hilbert space algorithm.
- Conducted a proof-of-principle NDE experiment using ultrasonic data from an aluminum/copper multilayer medium.
Main Results:
- Successfully imaged a flaw non-invasively within the aluminum/copper planar multilayer medium.
- Data were collected using a multistatic method without beamforming, with all focusing performed mathematically post-acquisition.
Conclusions:
- The developed numerical DT algorithm offers a robust alternative to traditional methods, overcoming limitations associated with Green functions.
- This approach facilitates advanced NDE of complex multilayer structures.