Surface discretization in optical aspheres production.

Area of Science:

• Optical Engineering
• Surface Metrology
• Computational Geometry

Background:

• Highly aspherical optical surfaces are increasingly common.
• Surface discretization is essential for optical manufacturing and characterization.
• Standard uniform sampling methods fail for highly aspherical surfaces, leading to non-uniform point distributions.

Purpose of the Study:

• To evaluate and compare different surface discretization methods for optical aspheres.
• To identify methods that provide uniform or near-equilateral grid cell sampling.
• To address the limitations of traditional projection-based discretization.

Main Methods:

• Circle Involute (CI) method for surface discretization.
• Laplace-Beltrami (LB) partial derivatives system for mapping.
• Optimal Mass Transportation (OT) for mapping.
• Comparison with trivial uniform x-y projection.

Main Results:

• The CI and OT methods yield the most uniform surface sampling.
• The CI and LB methods result in grid cells that are closer to equilateral.
• Both CI and OT outperform the trivial projection method in achieving desired sampling properties.

Conclusions:

• CI and OT are recommended for achieving uniform discretization of aspherical optical surfaces.
• CI and LB are suitable when near-equilateral grid cells are the primary quality target.
• These advanced methods overcome the limitations of simple projection for complex optical designs.