Estimating the measurement resolution of an arbitrary finesse fiber-optic Fabry – Perot interferometer via Cramer – Rao bound

The work is devoted to obtaining an analytical ratio for estimating the resolution of measurements using a fiber-optic Fabry – Perot interferometer with an arbitrary mirrors’ reflectivity and its spectral interrogation. For this purpose, we used the Rao – Cramer formalism. The corresponding analytical expression was first obtained under the assumption that there was no light divergence in the interferometer gap, and then the divergence was taken into account by introducing the effective reflection coefficient of the second mirror. Сharacteristics of the latter we found numerically for a wide range of interferometer parameters. The found relation connects the root-mean-square deviation of the measured values of the interferometer gap with the level of additive noise of the spectral signal of the interferometer and makes it possible to find the optimal parameters of the interferometer that provide the best resolution. Also, expressions for the mean level and standard deviation of the fiber-optic Fabry – Perot interferometer reflectivity characteristic were obtained.