The main topic of this thesis is to examine the design and analysis of millimetre and sub- millimetre optical systems for use in future cosmic microwave background radiation and far infrared space based astronomy missions. Astronomical observations in these regions of the electromagnetic spectrum are vital for studying the formation and evolution of planets, stars, galaxies, and on an even larger scale the origin of the Universe, through an analysis of the Cosmic Microwave Background (CMB) radiation. In order to further our knowledge of these astronomical processes it will be necessary to use highly calibrated instruments with increased sensitivity, and the capability to measure the polarisation signal of the cosmic microwave background radiation. It will also be necessary to design instruments with higher angular resolution so as measurements can be made on a finer scale. This will allow our current understanding of the origin and evolution of our Universe to be better understood by placing further constraints on the various models that currently exist which serve to explain these processes, for example the various in ationary models. Significant efforts are being made to develop and characterise the technology required to realise these ambitions. Examples of missions that are currently being planned are COrE (Cosmic Origins Explorer) Plus and SPICA (SPace Infrared telescope for Cosmology and Astrophysics), which contains an instrument known as SAFARI, a far infrared Fourier transform spectrometer that makes use of a Mach- Zehnder optical configuration. Such missions require high performance focal plane antennas, a position traditionally filled using corrugated horns. Future missions will require large arrays of high performance anten- nas, and the thermal and mechanical penalties associated with high mass corrugated horns (in addition to their cost) can become prohibitive. In this thesis, the design of an alternative smooth-walled profiled horn antenna will be examined. The resulting simple design is eas- ier and cheaper to manufacture than its corrugated counterpart, and carries less mechanical penalties. The horn was designed using a genetic algorithm based optimisation process that was applied to an implementation of the mode matching technique (used to model the perfor- mance of horn antennas) that has been optimised for computational efficiency. A number of improvements in the execution of the mode matching code were made to increase its efficiency and are described, including singular value decomposition analysis and reducing the number of waveguide modes used in the analysis. The limitations of the approach are considered, in- cluding determining the ideal horn performance metric to optimise with respect to in order to maintain the required levels of performance in all of the important characteristics. A further goal of the optimisation process was to use only desktop computing power and to complete the process within a reasonable amount of time (within a day). A further area analysed is the multi-moded detector pixels for use in the SAFARI in- strument. Such pixels are currently being tested in the Space Research Organisation of the Netherlands (SRON), Groningen. Models already exist to attempt to describe such pixels, however in order to attempt to improve the agreement between the measured and simulated results it is necessary to refine the model. Such pixels contain, for mechanical reasons, a sec- tion between the horn and cavity which can be considered to be a free space gap. This thesis considers the implementation of such a gap within the mode matching technique, and examines the impact of the gap on the measured pixel efficiency. This is critical for understanding the optical performance of the receiver system. Future missions will make use of such multi-moded systems as they maximise the amount of power available to the detector, a critical feature when low strength signals are being measured. Measurements of multi-moded horns are not well understood. Consideration is given in this thesis to a method that may be used in the future, with further development, to measure the performance of multi-moded horns. Such measurements will lead to a better understanding of multi-moded systems. A brief descrip- tion of the background science is also described in the first chapter, along with the specific contributions of the author.