Simulating the optical performance of a small-sized telescope with secondary optics for the Cherenkov Telescope Array

The Gamma-ray Cherenkov Telescope (GCT) is a small-sized telescope (SST) that represents one of three novel designs that are based on Schwarzschild-Couder optics and are proposed for use within the Cherenkov Telescope Array (CTA). The GAmma-ray Telescope Elements (GATE) program has led an effort to build a prototype of the GCT at the Paris Observatory in Meudon, France. The mechanical structure of the prototype, known as the SST-GATE prototype telescope, is now complete along with the successful installation of the camera. We present the results of extensive simulation work to determine the optical performance of the SST-GATE prototype telescope. Using the ROBAST software and assuming an ideal optical system, we find the radius of the encircled point spread function (θ80) of the SST-GATE to be ∼1.3 arcmin (∼0.02°) for an on-axis (θfield=0∘) observation and ∼3.6 arcmin (∼0.06°) for an observation at the edge of the field of view (θfield=4.4∘). In addition, this research highlights the shadowing that results from the stopping of light rays by various telescope components such as the support masts and trusses. It is shown that for on-axis observations the effective collection area decreases by approximately 1 m2 as a result of shadowing components other than the secondary mirror. This is a similar loss (∼11%) to that seen with the current generation of conventional Davies-Cotton (DC) Cherenkov telescopes. An extensive random tolerance analysis was also performed and it was found that certain parameters, especially the secondary mirror z-position and the tip and tilt rotations of the mirrors, are critical in order to contain θ80 within the pixel limit radius for all field angles. In addition, we have studied the impact upon the optical performance of introducing a hole in the center of the secondary mirror for use with pointing and alignment instruments. We find that a small circular area (radius < 150 mm) at the center of the secondary mirror can be used for instrumentation without any significant impact upon optical performance. Finally, we studied the impact of reducing the size of the primary mirror for the prototype telescope and found that this comes at the cost of poorer image quality and light collection efficiency for all field angles, but at a significant cost saving for a one-off prototype.