Geometrical and physical optics analysis for mm-wavelength refractor telescopes designed to map the cosmic microwave background

We present a compact two-lens high-density polyethylene (HDPE) $ f/1.6 $f/1.6 refractor design that is capable of supporting a 28-deg diffraction-limited field of view at 1-mm wavelengths and contrast it to a similar two-lens refractor using silicon lenses. We compare the optical properties of these two systems as predicted by both geometrical and physical optics. The presented analysis suggests that by relaxing telecentricity requirements, a plastic two-lens refractor system can be made to have a surprisingly large field of view. Furthermore, this HDPE system is found to perform comparably to a similar silicon system across a wide field of view and wavelengths up to 1 mm. We show that for both telescope designs, cold stop spillover changes significantly across the field of view in a way that is somewhat inconsistent with Gaussian beam formalism and simple $ f $f-number scaling. We present results that highlight beam ellipticity dependence on both pixel location and pixel aperture size-an effect that is challenging to reproduce in standard geometrical optics. We show that a silicon refractor design suffers from larger cross-polarization compared to the HDPE design. Our results address the limitations of relying solely on geometrical optics to assess relative performance of two optical systems. We discuss implications for future refractor designs.