CCAT-prime: The Optical Design for the Epoch of Reionization Spectrometer

The Epoch of Reionization Spectrometer (EoR-Spec) will be an instrument module for the Prime-Cam receiver on the CCAT-prime Collaboration's Fred Young Submillimeter Telescope (FYST), a 6-m primary mirror Crossed Dragone telescope. With its Fabry-Perot interferometer (FPI), EoR-Spec will step through frequencies between 210 and 420 GHz to perform line intensity mapping of the 158 $\mu$m [CII] line in aggregates of star-forming galaxies between redshifts of 3.5 and 8 to trace the evolution of structure in the universe during the epoch of reionization. Here we present the optical design of the module including studies of the optical quality and other key parameters at the image surface. In order to achieve the required resolving power (R$\sim$100) with the FPI, it is important to have a highly collimated beam at the Lyot stop of the system; the optimization process to achieve this goal with four lenses instead of three as used in other Prime-Cam modules is outlined. As part of the optimization, we test the effect of replacing some of the aspheric lenses with biconic lenses in this Crossed Dragone design and find that the biconic lenses tend to improve the image quality across the focal plane of the module.