Design of a spherical focal surface using close-packed relay optics

Area of Science:

• Optics
• Computational Geometry
• Materials Science

Background:

• Efficiently packing circles on a sphere is a known challenge, often called the Tammes problem.
• Existing methods like point-repulsion simulations are computationally intensive.
• Achieving high packing density is crucial for creating continuous surfaces.

Purpose of the Study:

• To present a new design strategy for close-packing circular finite-conjugate optics.
• To create a spherical focal surface using optimized circle distributions.
• To explore an alternative to existing Tammes problem solutions.

Main Methods:

• Utilizing a distorted icosahedral geodesic to generate circle distributions.
• Leveraging the geodesic's symmetry and minimized separation variations.
• Computationally generating configurations for N circles based on geodesic vertices.

Main Results:

• The proposed geodesic method achieves high degrees of symmetry.
• It minimizes variations in circle separations across the sphere.
• Circle packing densities comparable to steady-state maximums from other methods were achieved.

Conclusions:

• The distorted icosahedral geodesic offers an efficient and advantageous method for circle packing on spheres.
• This strategy is beneficial for constructing continuous spherical focal surfaces.
• The method provides a computationally inexpensive way to generate optimal configurations.