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The TMS optical system is based on a decentered dual-reflector system in a Gregorian configuration to observe with an angular resolution of less than 2°. The primary goal of the present study is to evaluate the final design and verify that it satisfies the design requirements. We aim for low cross-polarization (-30 dB), low sidelobe (-25 dB) levels, and a stable beam in terms of shape (low ellipticity) and size over a full octave bandwidth (10–20 GHz). We performed both ray-tracing and full-wave simulations using the CST Studio software in order to investigate the system behaviour. We gave special attention to the beam frequency variation and polarization leakage. We have characterized the effects on the radiation pattern produced by the cryostat window. We present the final design of the TMS optical system, as well as a complete study of the system's performance in terms of cross-polarization, sidelobes, ellipticity and beamwidth. We discuss the effects of sidelobes and study the need for a baffle.