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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.