Absolute length measurement with sub-nanometer accuracy using frequency standard

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Since the free spectral range (FSR) of a Fabry-Perot cavity (FP cavity) is defined by a half of light velocity in vacuum (c/2) divided by product of the geometrical distance between the two mirrors (L) and the refractive index in the FP Cavity (n), the FSR measurement is a potential method to measure the absolute length L. In this study, we have developed a method to measure the FSR of a FP cavity using frequency modulation with an electric optical modulator (EOM) and the null method. We have determined the FSR with the measurement uncertainty of order 10^<-8>. From this result, it is possible to measure absolute length of 1m order with uncertainty of nm or less. Using the same method, we have demonstrated the active suppression of air refractive index fluctuation.