Abstract:Cryogenic technology is one of the key technologies for the next generation of Laser Interferometer Gravitational-Wave detector. The Japanese gravitational wave interferometer KAGRA (Kamioka Gravitational Wave Detector), as the pathfinder of this technology, will operate in a 20 K cryogenic environment and use a sapphire single crystal with less thermal noise at low temperatures as the test mirror. However, sapphire crystals with high quality, large size, and low absorption rate are extremely difficult in manufacturing. In addition, due to the inhomogeneity of lattice structure in the sapphire crystal, it is easy to cause unnecessary birefringence effects, thereby affecting the target sensitivity of the detector. Based on the above problems, this paper developed two large-size optical measurement systems, and for the first time studied the optical characteristics of KAGRA cryogenic sapphire test mirrors systematically. First of all, according to the requirements of the detector for the thermal noise of the test mirror, we developed an optical measurement system based on the photothermal common-path interferometer technique, which can characterize the optical absorption of the test mirror and the surface coating of the test mirror effectively. Secondly, based on the optical absorption measurement system, we developed the birefringence effect measurement system, which can characterize the uniformity of birefringence in the test mirror. At present, the construction and testing of these two measurement systems have been completed, and the measurement sensitivity of the optical absorption of the sapphire test mirror has reached 1.5ppm/cm. As for the birefringence measurement system, its spatial resolution is less than 0.3mm $\times $ 0.3mm. This work is of high significance for reducing the birefringence effect of large-size cryogenic test mirrors and improving the sensitivity of the detector.