Optimization of the collection efficiency of a hexagonal light collector using quadratic and cubic Bézier curves

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 Bézier curves. We demonstrate that our optimized designs simultaneously achieve a higher collection efficiency and background reduction rate than traditional designs.

► We optimize the collection efficiency of a hexagonal light collector to be used for very-high-energy gamma-ray telescopes.
► Quadratic and cubic Bézier curves are used for the inner shape of a light collector instead of a Winston cone.
► The efficiency of the optimized design is higher for signal photons and lower for stray light compared to a Winston cone.