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Phase-space distributions for high-frequency fields.

M A Alonso1, G W Forbes

  • 1Department of Physics, Macquarie University, Sydney, NSW, Australia. alonso@ics.mq.edu.au

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
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This study characterizes the localized form of phase-space distributions like the Wigner distribution function and Gaussian windowed Fourier transforms at high frequencies. These findings enhance understanding of optical modeling using phase-space methods.

Area of Science:

  • Optics and Photonics
  • Mathematical Physics

Background:

  • Phase-space distributions, such as the Wigner distribution function (WDF) and windowed Fourier transforms (WFTs), are crucial for linking ray and wave optics.
  • High-frequency limits reveal localization properties of these distributions for simple wave fields, enabling the definition of associated ray families.

Purpose of the Study:

  • To characterize the localized form of the Wigner distribution function and Gaussian windowed Fourier transform in the high-frequency limit.
  • To provide a clearer intuition of phase-space-based methods for optical modeling.

Main Methods:

  • Analysis of the Wigner distribution function and Gaussian windowed Fourier transform.
  • Investigation of distribution localization in the high-frequency regime.
  • Development of a geometric construction for estimating the Wigner distribution function.

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Main Results:

  • The localized forms of the Wigner distribution function and Gaussian windowed Fourier transform are precisely characterized.
  • The study provides a geometric construction for estimating the Wigner distribution function, revealing its structured nature.

Conclusions:

  • The characterization of localized phase-space distributions deepens the understanding of their properties.
  • These results offer improved intuition for phase-space optical modeling and highlight the complex structure of the Wigner distribution function.