Improved peak-to-peak method for cavity length measurement of a Fabry-Perot etalon using a mode-locked femtosecond laser

Differing from the conventional peak-to-peak method using two neighboring spectral peaks in the frequency-domain fringe spectrum of the spectral response of a Fabry-Perot etalon to a femtosecond laser, which contains N spectral peaks equally spaced with a spacing of the etalon free spectral range (FSR), the proposed method employs a pair of spectral peaks with a spacing of an integer multiple k (k ≫ 1) of FSR for measurement of the etalon cavity length d with a reduced measurement error. Under the constrain of the total N spectral peaks obtainable in the finite spectral range of the femtosecond laser, the optimized k is identified to be N∕2 in consideration of an averaging operation using N - k samples of d to achieve the minimum measurement error. The feasibility of the proposed method is demonstrated by experimental results with an uncertainty analysis based on "Guides to the Expression of Uncertainty in Measurement".