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

Abstract

This paper presents a design strategy for close-packing circular finite-conjugate optics to create a spherical focal surface. Efficient packing of circles on a sphere is commonly referred to as the Tammes problem and various methods for packing optimization have been investigated, such as iterative point-repulsion simulations. The method for generating the circle distributions proposed here is based on a distorted icosahedral geodesic. This has the advantages of high degrees of symmetry, minimized variations in circle separations, and computationally inexpensive generation of configurations with N circles, where N is the number of vertices on the geodesic. These properties are especially beneficial for making a continuous focal surface and results show that circle packing densities near steady-state maximum values found with other methods can be achieved.