Femtosecond optical two-way time-frequency transfer in the presence of motion

Platform motion poses significant challenges to high-precision optical time and frequency transfer. We give a detailed description of these challenges and their solutions in comb-based optical two-way time and frequency transfer (O-TWTFT). Specifically, we discuss the breakdown in reciprocity due to relativity and due to asynchronous sampling, the impact of optical and electrical dispersion, and velocity-dependent transceiver calibration. We present a detailed derivation of the equations governing comb-based O-TWTFT in the presence of motion. We describe the implementation of real-time signal processing algorithms based on these equations and demonstrate active synchronization of two sites over turbulent air paths to below-1-fs time deviation despite effective velocities of +/- 25 m/s, which is the maximum achievable with our physical setup. With the implementation of the time transfer equation derived here, we find no velocity-dependent bias between the synchronized clocks to within a two-sigma statistical uncertainty of 330 as.