Interferometric measurement of refractive index inhomogeneity on polished sapphire substrates: application to LIGO-II

In order to improve the detection sensitivity of the Laser Interferometer Gravitational-wave Observatory (LIGO) the use of 40 kg sapphire test masses is being considered for the next instrument upgrade. Currently, sapphire material of adequate size is only available with the optical axis aligned with the m axis of the crystal. To determine the material's suitability it is necessary to characterize the refractive index inhomogeneity of the sapphire substrates for two orthogonal directions of polarisation, to a fraction of a part per million (ppm). We report on a method used to measure the refractive index inhomogeneity which requires three separate measurements of the polished sapphire blank in a Fizeau interferometer. These measurements are of the surface shapes or figures of the two polished sides of the blank and that of the wavefront entering side one propagating through the blank, reflected off side two and exiting through side one. The phase maps corresponding to these three measurements are combined to obtain the refractive index inhomogeneity map distribution. Measurements were carried out on two sapphire substrates (m axis) produced by the heat exchange method. The inhomogeneity maps show features which depend on polarisation direction. The physical origin of the inhomogeneities is discussed as well as the probable impact on the detection of a gravitational wave signal.