Telescopes measuring cosmic microwave background (CMB) polarization on
large angular scales require exquisite control of systematic errors to
ensure the fidelity of the cosmological results. In particular,
far-sidelobe contamination from wide angle scattering is a potentially
prominent source of systematic error for large aperture microwave
telescopes. Here we describe and demonstrate a ray-tracing-based
modeling technique to predict far sidelobes for a three mirror
anastigmat telescope designed to observe the CMB from the South Pole.
Those sidelobes are produced by light scattered in the receiver optics
subsequently interacting with the walls of the surrounding telescope
enclosure. After comparing simulated sidelobe maps and angular power
spectra for different enclosure wall treatments, we propose a highly
scattering surface that would provide more than an order of magnitude
reduction in the degree-scale far-sidelobe contrast compared to a
typical reflective surface. We conclude by discussing the fabrication
of a prototype scattering wall panel and presenting measurements of
its angular scattering profile.