CCAT: Optical Design of the 410 GHz Prime-Cam Module

Prime-Cam is a first-generation instrument for the Fred Young Submillimeter Telescope (FYST), enabling wide-field, multi-frequency observations for cosmology, line-intensity mapping, and galaxy studies. We present an optical performance study for a candidate 410 GHz broadband module designed to field approximately 21,000 polarisation-sensitive kinetic inductance detectors (KIDs). The three-lens silicon design was adapted from the SO LATR design and used for the existing 280 and 350 GHz Prime-Cam instrument modules, as well as this study. At 410 GHz, a shorter wavelength places tighter demands on wavefront quality and beam shape. Using Ansys Zemax OpticStudio and Huygens PSF analysis, we evaluate candidate module positions, compare 350 and 410 GHz performance, and assess field-dependent Strehl ratio, ellipticity, and encircled-energy behaviour. A preliminary tolerancing study, using inverse increment and Monte Carlo methods, tests sensitivity to selected alignment perturbations.