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Wigner distribution function of volume holograms.

Se Baek Oh1, George Barbastathis

  • 1Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA. sboh@mit.edu

Optics Letters
|September 3, 2009
PubMed
Summary
This summary is machine-generated.

We derived the Wigner distribution function (WDF) for a 4f imager with a 3D holographic pupil. This analysis reveals the shift-variant nature of volume holographic elements using WDF shearing properties.

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Area of Science:

  • Optics and Photonics
  • Holography
  • Information Optics

Background:

  • Volume holograms are crucial optical elements.
  • Understanding their shift-variant properties is essential for imaging systems.
  • The Wigner distribution function (WDF) is a powerful tool for analyzing optical systems.

Purpose of the Study:

  • To derive the Wigner distribution function (WDF) of a 4f imager incorporating a volume holographic pupil.
  • To analyze the WDF of the volume hologram itself using shearing properties.
  • To elucidate the shift-variant characteristics of volume holographic elements in common configurations.

Main Methods:

  • Linear systems approach for WDF derivation.
  • Application of WDF shearing properties to volume holograms.
  • Detailed examination of plane and spherical wave reference volume holograms.

Main Results:

  • The Wigner distribution function (WDF) for the 4f imager with a volume holographic pupil was successfully derived.
  • The WDF of the volume hologram was obtained by utilizing its shearing properties.
  • The shift-variant nature of the volume holographic element was clearly demonstrated for both reference wave configurations.

Conclusions:

  • The Wigner distribution function (WDF) provides valuable insights into the behavior of volume holographic elements within 4f imaging systems.
  • The derived WDF confirms the shift-variant properties of volume holograms, regardless of whether plane or spherical waves are used as references.
  • This work offers a theoretical framework for understanding and designing holographic imaging systems.