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A Stable Phantom Material for Optical and Acoustic Imaging
Published on: June 16, 2023
Non-paraxial model for a parametric acoustic array
Milan Cervenka1, Michal Bednarik
1Czech Technical University in Prague, Faculty of Electrical Engineering, Technicka 2, 166 27 Prague 6, Czech Republic. milan.cervenka@fel.cvut.cz
The Journal of the Acoustical Society of America
|August 10, 2013
Summary
This study models parametric radiation using the Westervelt equation, revealing low-frequency fields near the source. Numerical results highlight limitations of the paraxial approximation for accurate acoustic field prediction.
Area of Science:
- Acoustics and wave propagation
- Nonlinear acoustics
- Computational physics
Background:
- Parametric radiation is crucial for generating low-frequency acoustic fields.
- The Westervelt equation models nonlinear acoustic phenomena, including diffraction and dissipation.
- Existing paraxial approximations simplify calculations but may miss near-source effects.
Purpose of the Study:
- To investigate parametric radiation from axisymmetric planar sources.
- To focus on low-frequency difference-frequency fields.
- To analyze the accuracy of the paraxial approximation versus a full 3D numerical calculation.
Main Methods:
- Utilizing the Westervelt equation as the model for acoustic propagation.
- Employing the method of successive approximations for quasi-linear analysis.
- Reducing a multi-layer integral to a 3D integral using multi-Gaussian beam expansion.
- Comparing 3D numerical integration with the simplified 1D paraxial approximation.
Main Results:
- The quasi-linear approximation and successive approximations were used to calculate difference-frequency fields.
- A multi-Gaussian beam expansion simplified the acoustic field calculation integral.
- Numerical results from the 3D integral show nonzero low-frequency fields near the source.
- The paraxial approximation fails to capture these near-source low-frequency field effects.
Conclusions:
- The Westervelt equation effectively models parametric radiation phenomena.
- The 3D numerical calculation provides a more accurate representation of near-source low-frequency fields.
- The paraxial approximation, while efficient, has limitations in describing acoustic fields close to the source.
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