Phase Coherent Vacuum-Ultraviolet to Radio Frequency Comparison with a Mode-Locked Laser

We demonstrate a versatile new technique that provides a phase coherent link between optical frequencies and the radio frequency domain. The regularly spaced comb of modes of a mode-locked femtosecond laser is used as a precise ruler to measure a large frequency gap between two different multiples (harmonics or subharmonics) of a laser frequency. In this way, we have determined a new value of the hydrogen $1S-2S$ two-photon resonance, $f_{1S-2S}=2\mathrm{}466061413187.29\left(37\right)\mathrm{kHz}$, representing now the most accurate measurement of an optical frequency.