High resolution determination of radii of curvature using Fabry–Perot interferometry

A spectroscopic approach to measuring the radius of curvature of a concave mirror is presented. The mirror is incorporated into a plano-concave Fabry–Perot cavity and the radius of curvature of the concave mirror is inferred from the mode spacing of the transverse modes relative to the longitudinal modes. No mechanical displacement is entailed and the measurement is easily performed in vacuum. The spectroscopic resolution of the technique is better than 1 µm for a nominal radius of curvature of 1 m, but the accuracy is limited by the figure of the plane mirror in the cavity to approximately 1 mm in the present work. The optical spot size on the mirror under test is of the order of 0.3 mm, so the method should allow the radius of curvature of a mirror to be mapped out spatially with very high resolution