Extending the use of Doppler spectroscopy as an important plasma diagnostic -- by developing a multi-channel system capable of tomography -- is the foundation of this thesis. A system which can simultaneously measure the emissivity, temperature and flow velocity of plasma ions has been installed, calibrated and operated on the H-1NF heliac, yielding comprehensive and interesting results. The measurements are time-resolved, made from a large range of viewing positions and, using scalar tomographic inversion methods, can be unfolded to give two-dimensional images of ion emissivity and temperature. The flow velocity profiles, while not inverted, nevertheless lead to a greater understanding of the plasma behaviour.¶ Fifty-five lens-coupled optical fibres, mounted on a large rotatable stainless steel ring, encircle the plasma poloidally and transport light to a multi-channel Fourier-transform spectrometer. This `coherence-imaging' spectrometer employs an electro-optically modulated birefringent crystal plate to monitor the coherence of an isolated spectral line. Measurement of the intensity, fringe visibility and phase of the resulting interferogram leads to values for the emissivity, ion temperature and flow velocity. Using a multi-anode photomultiplier assembly, allows the time-resolved detection of all optical channels simultaneously.¶ The system has been fully calibrated, including a measurement of the spatial response of each line-of-sight. The calibration procedure accounts for the relative channel sensitivities, the response of the line filter and the removal of detector cross-talk. In situ light sources are installed provide routine and accurate relative intensity calibration of the system.¶ Methods of tomography provide the unfolding of the measured plasma parameters to construct two-dimensional images of ion temperature and emissivity. Methods of inversion include the iterative ART routine -- using projection data gathered with the light-collecting optics rotated to different viewing positions -- and linear composition of Fourier-Bessel basis functions -- with the data obtained from a single unrotated viewing position. ART reconstructions of the emissivity are performed without the need for a priori information while those of the ion temperature are computed using regularising functions to help stabilise the inversion.¶ This new system -- named ToMOSS for Tomographic Modulated Optical Solid-state Spectrometer -- enables a more detailed study of various plasma phenomena observed in H-1NF. Among other results, this thesis presents the first tomographic reconstructions of emissivity and temperature fluctuations associated with a large-scale coherent instability.