Displacement Determination of the Guard Electrode for the New Calculable Capacitor at NIM
We present our continuing work on the displacement determination of the guard electrode for the new vertical calculable capacitor. We describe a method for determining the displacement by actively locking the Fabry-Perot interferometer to a stabilized laser at two cavity lengths of interest. In order to lock the interferometer tightly, the modulation width of the laser is optimized for the full-width at half-maximum at the two different cavity lengths. For each of the cavity lengths, the Fabry-Perot interferometer is maintained at its resonance, and the cavity length is quantized with a space of λ/2. Then, its corresponding ratio between the fixed standard capacitor and the calculable capacitor is accurately measured by a capacitance bridge. The two main parameters for determining the displacement between the two cavity lengths-i.e., the difference in order number (AN) of the interferometer and the laser wavelength (λ)-are obtained from the capacitance bridge measurement based on a 1-pF standard capacitor with a priori value and the accurate wavelength measurement of an iodine laser, respectively. Evaluation of the displacement sensing system confirms a relative uncertainty of 5.2 × 10-9 over a range of 205 mm.
A two terminal-pair coaxial AC bridge with auto source balance at NIM
A two terminal-pair coaxial AC bridge is constructed at NIM for high precision capacitance transfer, in which, an auto auxiliary source balance method is proposed and achieved. The error introduced by auto source balance circuit is at negligible level. The bridge can transfer capacitance from 1 pF to 100 pF with an uncertainty of 1 × 10-8 (k = 1) at low audio frequency.
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.