Advanced Laser Interferometric Gravitational Wave Detectors, based on current infrastructure (in particular, the Advanced LIGO detectors), are being planned to significantly increase the sensitivity to gravitational wave strain in the near future. To upgrade the existing detectors requests implementing very high optical power, as well as very high circulating power in the arm cavities; these measures will increase the sensitivity at the shot noise floor by one order of magnitude. However, such extremely high power circulation in the cavities will cause optical distortions in the test masses. Thermal distortions arise from the optical power absorption by defects or inhomogeneities in test masses, resulting in wavefront deformations, which have important consequences for the power buildup of the Radio-Frequency (RF) sidebands in the recycling cavities, thus degrading the performance of the detectors. The degree of this sensitivity degradation in the shot noise floor, due to optical distortions induced by defects or inhomogeneities (i.e. imperfections) in test masses in Advanced Laser Interferometric Gravitational-wave Detectors, is dependent on the test mass optical quality; while the sensitivity degradation in the thermal noise floor is dependent on the test mass mechanical properties. For this reason, it is compulsory to use high optical and mechanical quality test mass materials in the advanced interferometer detectors. Fused silica has been used for test masses in detectors, while sapphire has been planned to be used for test mass substrates in the proposed Large-scale Cryogenic Gravitational-wave Telescope (LCGT) project. Other materials, such as calcium fluoride (CaF2), are also attractive, especially for cryogenic detectors. However, for the state-of-theAbstract II art facilities, it is difficult to manufacture very uniform, defect-free, inhomogeneity-free, high-quality, and large-size samples. Thus, the qualities of sapphire and calcium fluoride single crystal samples were investigated and evaluated, to ensure that they have suitable properties for use in interferometer detectors, i.e. with an adequately low level of imperfections, but also with high mechanical quality factor (Q-factor). This thesis describes research done in the endeavour to investigate bulk defects or inhomogeneities in test masses, as well as their induced thermal distortions, which appear at a high optical power in Laser Interferometric Gravitational-wave Detectors. An Automatic Rayleigh Scattering Mapping System (ARSMS) to examine the optical property of large-size test masses is described. This ARSMS enables quantitative high-resolution 3D mapping of defects or inhomogeneities in optical materials. The measured 3D defect distribution mapping of optical materials can assist in the design of suitable configurations of test masses in high optical power interferometers. In addition, a very sensitive Hartmann wavefront sensor was used to actively monitor the thermal distortions due to bulk and coating absorption in test masses. A very strong thermal distortion in these test masses was observed in the Gingin facility, demonstrating that thermal distortions could be a critical issue in advanced interferometer detectors. A negative thermo-optical coefficient material, to be used in a thermal distortion compensation method, was investigated for the compensation of very localised distortions due to imperfections. This thesis also includes experimental and theoretical studies of the scattering, absorption, and birefringence mechanisms, thermal distortion effects, and optimal compensation methods for test masses.