C-axis determination of a uniaxial crystal with high-repeatability common-path heterodyne retardation measurement

We developed an ultra-precise retardation-measurement system based on optical-heterodyne interferometry with a 3σ repeatability of λ/360, 000 for zero retardation, where the frequency shift for the optical-heterodyne interferometry was generated by a rotating half-waveplate, and both polarizations for the retardation measurement were always exactly on a common path. Using this system, the direction of the c-axis of a sapphire window was determined by analyzing the incidence-angle dependence of the retardation. The possible resolution of the c-axis direction of the sapphire window was estimated to be 0.9 arcmin from the retardation-measurement repeatability. This c-axis determination method will be applicable to, for example, high-precision sapphire-mirror production/evaluation for gravitational-wave detection.