Towards a precise measurement of the He+ 2S lamb shift

In this thesis we shall describe the design and realisation of an experiment with the ultimate aim of testing the theory of quantum electrodynamics at the level of 100 kHz. This we hope to achieve by making the first observation of the two-photon excitation of the 2S-3S transition in singly-ionised helium. This has involved the design and construction of the exciting laser using second-harmonic generation of UV light, the development of an optical enhancement cavity to further increase the UV power, the assembly of a reference laser stabilised to an iodine transition, the design and construction of a beam source of He+ 2S metastable ions and the integration of all of these systems with a computer control system. These separate components are now finished and all that remains is to put them all together. Thus with the work presented in this thesis we have progressed from the status of an essentially empty laboratory to being in a position where we can realistically expect to observe and measure the transition at the requisite level of precision in the very near future. (author)