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Focal shift, optical transfer function, and phase-space representations.

C J Sheppard1, K G Larkin

  • 1Department of Physical Optics, School of Physics, University of Sydney, NSW, Australia. colin@physics.usyd.edu.au

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 11, 2000
PubMed
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This study defines focal shift using the second moment of light intensity, connecting it to optical transfer functions and fractional Fourier transforms. It models Fresnel number effects via phase space rotation and discusses the uncertainty principle.

Area of Science:

  • Optics and Photonics
  • Wave Propagation
  • Image Science

Background:

  • The focal shift of optical systems is crucial for precise focusing.
  • Understanding the influence of the Fresnel number on beam characteristics is essential.
  • Existing models often simplify the complex interplay of wave properties.

Purpose of the Study:

  • To define focal shift using the second moment of intensity distribution for finite Fresnel numbers.
  • To establish connections between fractional Fourier transform, Wigner distribution, and ambiguity function.
  • To model Fresnel number effects through phase space rotation and discuss the uncertainty principle.

Main Methods:

  • Definition of focal shift via the second moment of transverse intensity distribution.

Related Experiment Videos

  • Analysis of the optical transfer function (OTF) and focused amplitude.
  • Application of fractional Fourier transform and phase space rotation models.
  • Calculation of moments using wave modulus and phase; utilization of the Kaiser-Teager energy operator.

    • Main Results:

    • A novel definition for focal shift based on the second moment of intensity.
    • Demonstration of connections between fractional Fourier transform, Wigner distribution, and ambiguity function.
    • A phase space rotation model for Fresnel number effects.
    • Discussion on the uncertainty principle, M2 factor, and optical fiber beam modes.

    Conclusions:

    • The second moment provides a robust definition for focal shift in finite Fresnel number systems.
    • Fractional Fourier transform and phase space concepts offer a unified framework for analyzing beam propagation.
    • The study elucidates the fundamental limits imposed by the uncertainty principle on optical beam quality.