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Local time in diffusive media and applications to imaging.

Vincent Rossetto1

  • 1Université de Grenoble I, LPMMC/CNRS, 25 avenue des Martyrs, 38042 Grenoble CEDEX 09, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary

Local time quantifies wave sensitivity in scattering media. This study provides formulas for local time and its fluctuations, enabling accurate mapping of medium property variations.

Area of Science:

  • Physics
  • Wave Propagation
  • Geophysics

Background:

  • Waves in multiple scattering media become diffuse.
  • Local medium properties (absorption, velocity, scattering) affect wave fields.
  • Local time measures wave sensitivity to these properties.

Purpose of the Study:

  • To introduce the concept of local time in wave propagation.
  • To provide mathematical expressions for local time and its fluctuations.
  • To enable inversion algorithms for mapping medium property variations.

Main Methods:

  • Utilizing random walk theory to define local time.
  • Deriving expressions for local time in 1D, 2D, and 3D.
  • Calculating fluctuations of local time.

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  • Employing wave field correlations to measure variations.
  • Main Results:

    • Formulas for local time in various dimensions are presented.
    • Expressions for local time fluctuations are derived.
    • Local time is shown to be proportional to wave field variations.

    Conclusions:

    • Local time is a key metric for understanding wave sensitivity in scattering media.
    • The derived formulas facilitate accurate inversion for medium property variations.
    • This work provides a foundation for estimating the accuracy of such inversions.