This paper is concerned with the quasi-optical design and analysis of the Heterodyne Instrument for the Far Infrared (HIFI) on board the European Space Agency’s Herschel Space Observatory, which is due for launch in 2007. The paper begins with an introduction to astronomy at submillimetre wavelengths followed by the science that will be carried out by HIFI. The optical layout of HIFI is presented and the quasi-optical techniques used in the analysis of band 5 of the instrument are discussed, in particular, issues associated with the design and performance of the integrated lens antenna for this band. A power coupling efficiency calculation is carried out and the overall performance of the telescope is analysed.