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Resonator stability subject to dynamic random-tilt aberration.

Max-Olivier Hongler1, Theo Lasser, Gilles Evéquoz

  • 1Institut de Production et Robotique, Laboratoire de Production Microtechnique, and Institut d'Imagerie Optique Appliquée, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland. max.hongler@epfl.ch

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 25, 2003
PubMed
Summary

We studied ray path reflections between mirrors with dynamic random-tilt aberrations. Our approximation shows average exit time follows a 2/3 scaling law with tilt variance for flat mirrors.

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Area of Science:

  • Physics
  • Optics
  • Mathematical Physics

Background:

  • Ray paths between mirrors can be affected by dynamic random-tilt aberrations.
  • Understanding the average exit time (number of reflections before escape) is crucial for optical system stability.

Purpose of the Study:

  • To derive the behavior of the average exit time for ray paths between two mirrors with dynamic random-tilt aberrations.
  • To propose and validate an approximation scheme for this complex problem.

Main Methods:

  • Paraxial approximation was used for calculations.
  • The problem was reduced to studying exit time from an interval for a driven harmonic oscillator.
  • A simple approximation scheme was developed and tested.

Main Results:

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  • For flat mirrors, the average exit time exhibits a 2/3 scaling-law behavior with the variance of random tilts.
  • The proposed approximation scheme successfully reproduced this scaling law, confirming its consistency.
  • Mathematical results were validated through simulation experiments.

Conclusions:

  • The study provides a method to approximate the average exit time of ray paths in systems with dynamic random-tilt aberrations.
  • The identified 2/3 scaling law offers valuable insight into the stability of optical systems under such conditions.