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Acoustical diffraction tomography in a finite form based on the Rytov transform.

Zhi-Yong Tao1, Zhen-Qiu Lu, Xinlong Wang

  • 1State Key Laboratory of Modem Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China.

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This study introduces a new finite reconstruction algorithm for acoustical diffraction tomography using the Rytov transform. The method proves effective for cylindrical objects but has limitations with strong scattering.

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Area of Science:

  • Acoustical Diffraction Tomography
  • Wave Scattering Theory

Background:

  • Acoustical diffraction tomography (ADT) aims to reconstruct object properties from scattered wave data.
  • The Rytov transform is a mathematical tool used in wave propagation analysis.

Purpose of the Study:

  • To develop a novel finite reconstruction algorithm for ADT based on the Rytov transform.
  • To analyze the properties of generalized scattering introduced by the Rytov transform.

Main Methods:

  • Application of the Rytov transform to the wave equation.
  • Analysis of generalized scattering and its asymptotic equivalence to physical scattering.
  • Formal parameter expansion to derive a finite form solution.

Main Results:

  • The generalized scattered wave satisfies the Sommerfeld radiation condition.
  • Parameter expansion yields a finite solution by retaining only first- and second-order terms.
  • Computer simulations validate the algorithm for objects with cylindrical symmetry.

Conclusions:

  • The proposed Rytov transform-based algorithm offers a finite solution for acoustical diffraction tomography.
  • The algorithm's effectiveness is demonstrated for specific scattering scenarios.
  • Limitations exist for strong scattering objects, indicating areas for future research.