Characterisation of birefringence inhomogeneity of KAGRA sapphire mirrors from transmitted wavefront error measurements

Cooling down test masses to cryogenic temperatures is a way to reduce the thermal noise of gravitational wave detectors. Crystalline materials are considered the most promising materials for fabricating cryogenic test masses and their coatings because of their excellent thermal and optical properties at low temperatures. However, birefringence owing to local impurities and inhomogeneities in the crystal can degrade the performance of the detector. The birefringence measurement or mapping over a two-dimensional area is thus important. This study describes a method for fast birefringence measurements of a large sample by simply combining a series of transmission wavefront error measurements using linearly polarised light with Fizeau interferometers. Using this method, the birefringence inhomogeneity information of KAGRA's two input test masses with a diameter of 22 cm was fully reconstructed. The birefringence information was then used to calculate the transverse beam shapes of the light fields in orthogonal polarisation directions when passing through the substrate. It was possible to find a calculated beam shape consistent with in-situ measurements using the KAGRA interferometer. This technique is crucial for birefringence characterisation of test masses in future detectors, where even larger sizes are used.