In the Sydney University Stellar Interferometer (SUSI), fringes are detected when the optical path-difference between the arriving wavefronts is less than the coherence length for the observation. While observing a star, it is necessary to compensate not only for the changes in pathlength due to the earth's rotation, but also for those due to the effects of atmospheric turbulence. Apertures smaller than r 0 are used and active tilt-compensation is employed so that the wavefronts in the combined beams are made parallel. The remaining path-difference between the wavefronts must then be tracked for an accurate calibration of the fringe visibility. Improved tracking allows larger bandwidths to be used and therefore improves the sensitivity of the instrument. In this thesis a fringe tracking system is developed for SUSI based on group delay tracking with a PAPA detector. The method uses short exposure images of fringes detected in the dispersed spectra of the combined starlight. The number of fringes across a fixed bandwidth is directly proportional to the path-difference between the arriving wavefronts, and a Fast Fourier Transform is used to calculate the spatial power spectrum of the fringes, thereby locating the delay. Several topics are developed in the thesis. The visibility loss due to a non-constant fringe spacing on the detector is investigated, and the improvements obtained from rebinning the photon data are shown. The low light level limitations of group delay tracking are determined, with emphasis on the probability of tracking error, rather than on signalto-noise performance. Experimental results from both laboratory studies and stellar observations are presented. These show the first closed-loop operation of a fringe tracking system based on observations of group delay with a stellar interferometer. A new photon counting PAPA detector is also described, which was developed for use in this work. The design principles of the PAPA camera are outlined, and the potential sources of image artifacts are identified. These artifacts arise from the use of optical encoding with Gray coded masks. The new camera is distinguished by its mask-plate, which was designed to overcome artifacts due to vignetting. New lens mounts are also presented which permit a simplified optical alignment without the need for tilt-plates. The performance of the camera is described and its images are shown to be free of the effects of vignetting. i Declaration of Originality To the best of my knowledge, this thesis contains no copy or paraphrase of work due to any other person, except where duly acknowledged. None of the remaining work has been presented for any degree at the University of Sydney or elsewhere.