Optimization of spherically arranged lens arrays based on class II and III geodesic polyhedra

Spherical arrangement is a common way to pack lens arrays. Due to the restriction of original structures, the previous optimization methods based on icosahedral subdivision are only applicable to a few types of lens arrays adopting different numbers of sub-lenses. In order to design more types of lens arrays, an optimization packing method is proposed with the vertices of class II and class III geodesic polyhedra as the arrangement positions of sub-lenses. The vertices of the geodesic polyhedron are generated by projecting grid nodes on each face of the ortho-icosahedron to a sphere. The vertex translation function is established in a barycentric coordinate system, and then the chord ratio and packing density are used as evaluation functions to optimize the vertices' positions. The universality of the optimization method is tested, and its robustness is certified by analyzing the optimization results of different original structures with the same number of vertices. Finally, the effectiveness and feasibility of the optimization method in engineering applications are demonstrated in a monocentric multi-scale imaging system. The optimization method proposed in this paper can significantly increase the types of lens arrays from 9 to 37 types, adopting different numbers of sub-lenses within 1000 and effectively improved the distribution uniformity of lens arrays.