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Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle

H T Yura1, L Thrane, P E Andersen

  • 1Electronics and Photonics Laboratory, The Aerospace Corporation, Los Angeles, California 90009, USA. hal.t.yura@aero.org

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
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A new closed-form solution for the Wigner phase-space distribution function is derived for wave propagation through random media. This method offers a novel approach for creating advanced optical coherence tomography (OCT) images.

Area of Science:

  • Optics and Photonics
  • Wave Propagation in Random Media
  • Statistical Optics

Background:

  • Wave propagation through random media is crucial for understanding light scattering phenomena.
  • The Wigner phase-space distribution function offers a comprehensive description of optical fields.
  • Existing studies on the Wigner function primarily focus on transmission geometry.

Purpose of the Study:

  • To derive a closed-form solution for the Wigner phase-space distribution function in diffuse reflection and small-angle scattering.
  • To apply this solution to arbitrary small-angle volume scattering functions and ABCD optical systems.
  • To propose a novel imaging method for optical coherence tomography (OCT) based on Wigner function properties.

Main Methods:

  • Utilized the extended Huygens-Fresnel principle for optical fields.

Related Experiment Videos

  • Derived a closed-form solution applicable to both single and multiple scattering regimes.
  • Employed the ABCD matrix formalism for paraxial optical systems.

    • Main Results:

    • A general closed-form solution for the Wigner phase-space distribution function was obtained for diffuse reflection and small-angle scattering.
    • Analytic results were derived for various scattering functions in the asymptotic limit (s >> 1).
    • Explicit results were presented for optical coherence tomography (OCT) systems, including a novel imaging approach.

    Conclusions:

    • The extended Huygens-Fresnel principle and ABCD matrix formalism are effective for describing wave propagation in random media, including reflection geometry.
    • The derived Wigner function solution is valid for arbitrary scattering functions and optical systems.
    • A new OCT imaging technique based on the momentum width of the Wigner function shows potential advantages over conventional methods.