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A novel reconstruction method of nanometer micro-displacement of Fabry-Perot[F-P]interference is proposed in this study.Hilbert transforms are performed for F-P interference fringes,and the obtained signal performs tangent operation with the original signal.Finally,the validity of the proposed algorithm and the structure are verified by simulation and several experimental measurements for vibration.Results from the experiments show that the maximum relative error is 4.9％.