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Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering
1Department of Physics, Washington State University, Pullman 99164-2814, USA. marston@wsu.edu
The Journal of the Acoustical Society of America
|April 28, 2001
Summary
A new generalized optical theorem for acoustic scattering by symmetric targets simplifies complex scattering amplitudes. This theorem, applicable in non-dissipative scenarios, offers insights into forward and arbitrary-direction scattering phenomena.
Area of Science:
- Acoustics
- Wave Scattering
- Theoretical Physics
Background:
- The optical theorem is fundamental in scattering theory, relating total scattering cross-section to the forward scattering amplitude.
- Plane wave scattering by symmetric targets is a common problem in physics and engineering.
Purpose of the Study:
- To generalize the optical theorem for acoustic plane wave scattering by targets with inversion symmetry.
- To express scattering amplitudes in arbitrary directions using angular integration of other scattering amplitudes.
Main Methods:
- Derivation of a generalized optical theorem for non-dissipative scattering.
- Application of the theorem to the backscattering problem of a perfectly soft sphere.
- Numerical analysis of the integrand for the backscattering case.
Main Results:
- A generalized optical theorem is established for targets with inversion symmetry.
- The theorem reduces to the standard optical theorem for forward scattering.
- The integrand in the backscattering example is found to be oscillatory.
Conclusions:
- The generalized optical theorem provides a new framework for analyzing acoustic scattering.
- Potential applications include inverse problems, multiple scattering analysis, and numerical algorithm verification.