Low-level reflections are particularly troublesome in sensitive high-resolution spectral line receivers in the submillimetre and terahertz wavebands, giving rise to baseline ripple on spectra which is hard to distinguish from wide lines. In typical systems for submillimetre-wave astronomy, for example, a lens or flat dielectric plate is often used as a cryostat window placed close to a feed horn. Partial reflection from such interfaces can give rise to return loss at the horn throat, which is considerably higher than for the horn radiating into free space. A full scattering matrix approach based on a combination of standard waveguide modes and quasi-optical Gaussian beam modes can be used to analyse standing waves due to partial reflections, in which track is kept of both the backward and forward going components of the propagating fields. In this paper, we consider how such an analytical tool can be set up and we present typical examples of interest in which horn antennas feed simple components including windows, lenses and reflecting central blockages. (C) 2003 Elsevier Science B.V. All rights reserved.