Interferometric characterisation of refractive index variations in vitreous silica
The motivation for the measurement of refractive index variations in vitreous silica comes from the NASA/Stanford University Gravity Probe-B experiment. This experiment proposes to measure directly some of the predictions of the General Theory of Relativity by observing the extent of precession of a gyroscope in orbit around the Earth. The rotor of the proposed gyroscope will be made of vitreous silica. Screening requirements for the homogeneity of the silica rotor have been indicated in terms of the sensitivity of the mass density distribution measurements as Δp/p = 3 x 10-7 (or equivalently, refractive index sensitivity Δn = 1 x 10 -7), with a spatial resolution (to allow control of low order multi-pole moments) to better than 5mm. The thrust of the thesis is towards improvement of existing instrumentation, actual screening of samples, and spectral characterisation of the samples in the spatial frequency domain. After a brief introduction to the instrumentation, a complete matrix analysis of the plane mirror heterodyne interferometer was then developed, using the coherency matrix representation. A detailed analysis of periodic errors (non-linearity) associated with high precision polarisation heterodyne interferometry was carried out. A worst case peak-to-peak nonlinearity of 6.2nm was calculated for the single pass plane mirror heterodyne system. A simple analogue phase meter was then designed and built; its use resulted in an increase of over an order of magnitude in the resolution of the interferometer from λ/300 (2.2nm) to λ/4000 (0.16nm). High precision measurements of refractive index variations in vitreous silica are also reported for the first time. Measurements are repeatable to the Δn = 10-7 level, with phase meter errors of ±0.7% (i.e. 10-8 sensitivity).