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Morphologies of caustics studied by catastrophe charged-particle optics
Tom Fraysse1, Robin Cours1, Hugo Lourenço-Martins1
1CEMES-CNRS, Université de Toulouse, CNRS, Toulouse, France.
Ultramicroscopy
|January 10, 2026
Summary
This study uses catastrophe theory to analyze caustics in charged particle instruments. It reveals universal mathematical relationships between aberration coefficients, aiding in the design of corrected optical systems.
Area of Science:
- Optics
- Geometric Optics
- Charged Particle Optics
Background:
- Caustics are complex geometrical figures observed in optical instruments.
- Understanding caustic behavior is crucial for improving instrument performance.
- Charged particle instruments like electron and ion microscopes exhibit various caustic topologies.
Purpose of the Study:
- To explore caustic topologies in charged particle instruments using catastrophe theory.
- To analytically reproduce caustic behaviors and uncover hidden mathematical relationships.
- To provide a universal approach for analyzing optical aberrations.
Main Methods:
- Application of catastrophe theory to analyze caustic phenomena.
- Analytical reproduction of various caustic behaviors.
- Definition of a control space for universal analysis.
Main Results:
- Demonstrated the universal nature of caustic behavior independent of specific optical configurations.
- Extracted mathematical relationships between aberration coefficients.
- Revealed hidden relationships through the set of catastrophes in the control space.
Conclusions:
- Catastrophe theory offers a powerful, universal framework for understanding caustics in charged particle optics.
- The derived mathematical relationships can guide the development of new, corrected optical systems.
- This approach is particularly promising for advancing ion-based optical devices.
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