Computing aberration coefficients for plane-symmetric reflective systems: a Lie algebraic approach.

Area of Science:

• Optics and Optical Engineering
• Computational Physics

Background:

• Freeform optics offer advanced design possibilities but pose challenges in aberration analysis.
• Traditional methods for optical aberration analysis can be complex and less systematic for freeform surfaces.

Purpose of the Study:

• To apply the Lie algebraic method for analyzing aberrations in plane-symmetric freeform optical systems.
• To develop a systematic approach for deriving and composing aberration coefficients.

Main Methods:

• Utilizing analytical ray-tracing equations to construct an optical map.
• Employing Lie algebra to expand the optical map and derive aberration coefficients.
• Applying the method to aberrations of arbitrary order.

Main Results:

• Derived aberration coefficients in terms of initial ray coordinates.
• Presented results for second- and third-order aberrations.
• Demonstrated the method's efficacy on three single-mirror examples.

Conclusions:

• The Lie algebraic method offers a systematic and rigorous approach to aberration analysis in plane-symmetric freeform optical systems.
• This method facilitates the derivation, treatment, and composition of optical aberrations.
• The findings are applicable to the design and optimization of complex optical systems.