Three-spherical-mirror test for radius of curvature measurement using a Fabry-Pérot cavity

A three-spherical-mirror test method that uses a Fabry-Pérot (FP) cavity is proposed for a radius of curvature measurement system, especially for radii larger than 10 m. By using the three-spherical-mirror test with mode spacing measurement in an FP cavity, the local value of the radius of curvature of a mirror can be determined in situ and this mirror can then be used as the reference spherical mirror in a radius of curvature measurement system. We demonstrated determinations of radii of curvature of around 10 m using the three-spherical-mirror test with uncertainties of around 1.5 × 10-4 and then measured the radius of curvature of around 20 m with uncertainties of around 3.1 × 10-4 by using the spherical mirror, of which the radius of curvature was determined by the three-spherical-mirror test, as the reference sphere. The proposed system has high practical applicability because measurements can be conducted under usual air conditions and the measurement results are directly traceable to the time standard because beat frequency measurement is used.