Orthonormal polynomials describing polarization aberration for M-fold optical systems

Area of Science:

• Optics and Photonics
• Optical Engineering
• Materials Science

Background:

• Polarization aberration (PA) degrades imaging quality in high numerical aperture optical systems.
• Existing research primarily focuses on rotationally symmetric systems, leaving a gap in understanding asymmetric aberrations.
• Factors like birefringence in cubic crystalline materials and manufacturing tolerances introduce asymmetry.

Purpose of the Study:

• To extend the previously developed orthonormal polynomials for describing PA.
• To generalize the polynomial description from rotationally symmetric to M-fold symmetric optical systems.
• To provide a mathematical framework for analyzing PA in non-rotationally symmetric systems.

Main Methods:

• Development of M-fold generalized orthonormal polynomials.
• Application of the extended polynomial set to analyze PA in M-fold optical systems.
• Verification through two distinct case studies.

Main Results:

• Successful extension of orthonormal polynomials to describe PA in M-fold systems.
• Demonstration of the polynomials' efficacy in characterizing asymmetric PA.
• Validation of the generalized approach with practical examples.

Conclusions:

• The M-fold generalized polynomials offer a robust method for analyzing polarization aberration in asymmetric optical systems.
• This work enhances the understanding and correction of PA, crucial for advanced optical designs.
• The extended framework is vital for deep ultraviolet optics and systems with manufacturing tolerances.