Alternative computation of the Seidel aberration coefficients using the Lie algebraic method

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Hamiltonian optics provides a framework for analyzing optical systems.
• Lie algebraic methods offer powerful tools for systematic analysis in physics.

Purpose of the Study:

• To introduce and apply Hamiltonian optics and Lie algebraic methods for optical system analysis.
• To systematically determine aberration coefficients of any order for rotationally symmetric optical systems.

Main Methods:

• Describing operators for light propagation, refraction, and reflection in phase space using Lie algebraic methods.
• Linking derived Lie method aberration coefficients to classical Seidel aberration coefficients.

Main Results:

• A systematic method for calculating high-order aberration coefficients for rotationally symmetric systems.
• Demonstrated preservation of the property of summing individual surface contributions within the Lie algebraic theory.
• Validation of the methodology through two examples yielding good results.

Conclusions:

• The Lie algebraic approach provides a systematic and effective method for analyzing optical aberrations.
• This method offers a unified framework for understanding aberration contributions from individual optical surfaces.