Optimization of the Collection Efficiency of a Hexagonal Light Collector using Quadratic and Cubic B\'ezier Curves

TL;DR

This paper introduces optimized hexagonal light collector shapes using quadratic and cubic Bézier curves, improving collection efficiency and background reduction in gamma-ray telescopes beyond traditional Winston cone designs.

Contribution

It presents the first optimization of hexagonal light collectors with Bézier curves for 3D optical systems, surpassing traditional Winston cone performance.

Findings

Higher collection efficiency achieved

Enhanced background reduction rate

Optimized shapes outperform traditional designs

Abstract

Reflective light collectors with hexagonal entrance and exit apertures are frequently used in front of the focal-plane camera of a very-high-energy gamma-ray telescope to increase the collection efficiency of atmospheric Cherenkov photons and reduce the night-sky background entering at large incident angles. The shape of a hexagonal light collector is usually based on Winston's design, which is optimized for only two-dimensional optical systems. However, it is not known whether a hexagonal Winston cone is optimal for the real three-dimensional optical systems of gamma-ray telescopes. For the first time we optimize the shape of a hexagonal light collector using quadratic and cubic B\'ezier curves. We demonstrate that our optimized designs simultaneously achieve a higher collection efficiency and background reduction rate than traditional designs.