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A new Fabry-Perot interferometer for state-of-the-art displacement measurements is demonstrated. Two different methods for measuring the change in the length of an optical cavity are employed and compared. The “radio frequency” method employs no optical reference and allows us to measure the length of a prototype Fabry-Perot cavity to an rms statistical uncertainty of 560 pm, corresponding to a fractional uncertainty better than 7 ×10-9. The “optical” method employs an atomic Rb transition as an optical reference. The inherent measurement redundancy allows us to confirm that the system is largely free of parasitic Fabry-Perot cavities which are a potentially troublesome source of systematic errors. We currently achieve a measurement uncertainty of 100 pm with the optical method, limited largely by the stability of the aluminum prototype cavity.