Design constraints on Cherenkov telescopes with Davies–Cotton reflectors

Abstract

This paper discusses the construction of high-performance ground-based gamma-ray Cherenkov telescopes with a Davies-Cotton reflector. For the design of such telescopes, usually physics constrains the field-of-view, while the photo-sensor size is defined by limited options. Including the effect of light-concentrators in front of the photo sensor, it is demonstrated that these constraints are enough to mutually constrain all other design parameters. The dependability of the various design parameters naturally arises once a relationship between the value of the point-spread functions at the edge of the field-of-view and the pixel field-of-view is introduced. To be able to include this constraint into a system of equations, an analytical description for the point-spread function of a tessellated Davies-Cotton reflector is derived from Taylor developments and ray-tracing simulations. Including higher order terms renders the result precise on the percent level. Design curves are provided within the typical phase space of Cherenkov telescopes. The impact of all design parameters on the overall design is discussed. Allowing an immediate comparison of several options with identical physics performance allows the determination of the most cost efficient solution. Emphasize is given on the possible application of solid light concentrators with their typically about two times better concentration allowing the use of small photo sensors such as Geiger-mode avalanche photo diodes. This is discussed in more details in the context of possible design options for the Cherenkov Telescope Array. In particular, a solution for a 60 mm 2 photo sensor with hollow cone is compared to a 36 mm 2 with solid cone.

A compact and light-weight refractive telescope for the observation of extensive air showers

“…According to the manufacturer, the focal length is 502.1 mm for perpendicular photons at (546 ± 27) nm. This results in F/D ∼ 1.1 which is ideal for wide field-of-view telescopes as image distortion significantly increases for larger apertures [40]. Ten grooves per millimeter cover the surface of the lens providing the required imaging quality of 90 % light contained in one pixel.…”

“…This optimizes the fill factor for the hexagonal camera layout and reflects the quadratic photo sensitive area. A comprehensive review on a further optimization of an optical system including light-collectors can be found in [40].…”

Design, optimization and characterization of the light concentrators of the single-mirror small size telescopes of the Cherenkov Telescope Array

“…The set-up is located in a dark room in order to protect against ambient light. The light concentrator is placed in a motorized rotational stage 5 . This rotational mount offers high-precision motion and it is used to study the angular dependency in the collection efficiency of the light concentrator.…”

“…We compare this design with the Compound Parabolic Concentrator (CPC), also called Winston's Cone [7]. Even if solid concentrators can achieve larger compression factors than hollow ones [3,4,5], the former start to suffer from limited transmissivity due to the thickness of ∼37 mm necessary in this design for the SST. In addition, hollow cones allow us to use a reflective coating optimized for high reflectivity in the wavelength region of interest.…”

Calibration and performance of the photon sensor response of FACT — the first G-APD Cherenkov telescope

“…Although current sensors usually have a sensitive area of not more than 60 mm 2 , the rapidly decreasing prices allow for several sensors to be put together in a single channel. This enables their application also in large scale detectors such as the large-size telescopes planned for CTA as shown in [5].…”