The main focus of this thesis is the analysis and optimisation of systems that operate in the terahertz and submillimetre wavebands. Analysis is carried out on the MBI and ALMA interferometers, and on the HIFI instrument on the Herschel Space Observatory (HSO). MBI is a novel instrument designed to test the technique of bolometric nterferometry. ALMA is a 50 element hetrodyne interferometer, currently being constructed in Chile. It is demonstrated that in both MBI and ALMA, the coupling of the signal to the detector horns may be improved by imposing a phase on the field from the sky; a number of possible configurations are considered. HIFI is a high resolution spectrometer, one of three instruments on the HSO. Simulations of the lens antennas used to detect the radiation in the higher frequency channels in HIFI were carried out. A number of methods used to determine the phase centre of the beam from lens antennas are described, and use is made of the same optimisation techniques as for the MBI and ALMA work. As the beams propagating in these systems can be analysed accurately using the paraxial approximation, Gaussian Beam Mode Analysis can be used to simulate the field, and is the main analytical tool used here. Methods of beam shaping are investigated to gain an insight into how coupling may be increased in these systems, and also to design Diffractive Optical Elements (DOEs) for use at terahertz and submillimetre wavelengths in general. The standard methods of the Gerchberg-Saxton Algorithm, and unidirectional optimisation using Differential Evolution and Simulated Annealing are applied to design DOEs. A novel approach using Gaussian Beam Mode Analysis is described. Here, the Gaussian Beam mode coefficients describing a field are optimised to achieve a desired amplitude distribution at a specified plane or planes. This approach was found to achieve highly optimal results, and has a number of benefits over the other methods.