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Setting Limits on Supersymmetry Using Simplified Models
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Limitations and applicability of the Maréchal approximation.

T Sean Ross1

  • 1Air Force Research Laboratory, Directed Energy Directorate 3550 Aberdeen Avenue SE, Kirtland Air Force Base, New Mexico 87112, USA.

Applied Optics
|April 3, 2009
PubMed
Summary

The Maréchal approximation for Strehl ratio is updated with a complete derivation for wavefront distortion. This provides a more general method for characterizing random phase aberrations in optical systems.

Area of Science:

  • Optical engineering
  • Wavefront analysis
  • Atmospheric optics

Background:

  • The Maréchal approximation is crucial for atmospheric scaling law codes.
  • A complete derivation of the Maréchal approximation is lacking in scientific literature.
  • Understanding Strehl ratio versus wavefront distortion is key for optical system performance.

Purpose of the Study:

  • To provide an updated and complete derivation of the Maréchal approximation.
  • To extend the Maréchal approximation for Gaussian noise to more general cases.
  • To propose a novel method for characterizing random phase aberrations.

Main Methods:

  • Derivation of the first term of the Maréchal approximation.
  • Complete mathematical derivation of the Strehl ratio.

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  • Analysis of the Fourier transform of the probability density function of random phase noise.

    • Main Results:

    • An updated derivation of the Maréchal approximation is presented.
    • A complete derivation reveals the Strehl ratio's proportionality to the squared Fourier transform of phase noise PDF.
    • The generalized formulation is applicable beyond Gaussian noise.

    Conclusions:

    • The presented derivation clarifies the Maréchal approximation for Strehl ratio.
    • A more general formulation enables advanced characterization of random phase aberrations.
    • This work enhances the understanding and application of wavefront distortion analysis in optical systems.