Comparative assessment of freeform polynomials as optical surface descriptions

Area of Science:

• Optics and Optical Engineering
• Computational Design
• Materials Science

Background:

• Freeform optics, non-rotationally symmetric surfaces, are enabled by advanced manufacturing like diamond turning and lap polishing.
• Polynomials are essential for defining freeform optical surfaces in design and fabrication.
• Common methods involve adding orthogonal polynomials to conic sections.

Purpose of the Study:

• To comparatively investigate recently introduced gradient-orthogonal polynomials against widely known Zernike polynomials.
• To assess the numerical robustness and accuracy of these polynomial sets for describing freeform surfaces.
• To establish the equivalence and quantify the accuracy of both freeform surface descriptions.

Main Methods:

• Utilized recurrence relations for numerical robustness with higher-order polynomials.
• Performed comparative analysis of gradient-orthogonal polynomials and Zernike polynomials.
• Evaluated accuracy under stringent conditions for freeform surface description.

Main Results:

• Established the equivalence of gradient-orthogonal and Zernike polynomials in accurately describing freeform surfaces.
• Demonstrated that both polynomial sets can represent complex optical surfaces under demanding conditions.
• Quantified the accuracy of these two distinct freeform surface description methods.

Conclusions:

• Gradient-orthogonal polynomials offer an accurate and robust alternative to Zernike polynomials for freeform optics.
• Accurate quantification of freeform surface descriptions is vital for future optical system design and fabrication.
• This research supports the advancement of freeform optical manufacturing and application.