Metrology of hydrogen atom: Determination of the Rydberg constant and Lamb shifts

We present the optical frequency measurements of the 2S-8S/D and 2S-12D two-photon transitions in hydrogen and deuterium. From an analysis taking into account these results and the very accurate measurements of the 1S-2S transition, we show that the optical frequency measurements have superseded the microwave determination of the 2S Lamb shift and we deduce optimized values for the Rydberg constant and for the 1S and 2S Lamb shifts. We report also the recent development of our 1S-3S experiment.