Astronomical observations in the far-infrared are critical for investigation of cosmic microwave background (CMB) radiation and the formation and evolution of planets, stars and galaxies. In the case of space telescope receivers a strong heritage exists for corrugated horn antenna feeds to couple the far-infrared signals to the detectors mounted in a waveguide or cavity structure. Such antenna feeds have been utilized, for example, in the Planck satellite in both single-mode channels for the observation of the CMB and the multi-mode channels optimized for the detection of foreground sources. Looking to the demands of the future space missions, it is clear that the development of new technology solutions for the optimization and simplification of horn antenna structures will be required for large arrays. Horn antennas will continue to offer excellent control of beam and polarization properties for CMB polarisation experiments satisfying stringent requirements on low sidelobe levels, symmetry and low cross polarization in large arrays. Similarly for mid infrared systems multi-mode waveguide structures will give high throughput to reach the required sensitivities. In this paper we present a computationally efficient approach for modelling and optimising horn characteristics. We investigate smooth-walled profiled horns that have a performance equivalent to that of the corrugated horns traditionally used for CMB measurements. We discuss the horn optimisation process and the algorithms available to maximise performance of a merit parameter such as low cross polarisation or high Gaussicity. Â© 2013 Copyright SPIE.