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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
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.
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:
- 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.