We have performed a pure optical frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, R` 109 737.315 685 16͑84͒ cm 21 (relative uncertainty of 7.7 3 10 212 ) and for the 1S and 2S Lamb shifts L 1S 8172.837͑22͒ MHz and L 2S-2P 1057.8446͑29͒ MHz [respectively, L 1S 8183.966͑22͒ MHz, and L 2S-2P 1059.2337͑29͒ MHz for deuterium]. These are now the most accurate values available. [S0031-9007(99)09458-2] PACS numbers: 06.20.Jr, 21.10.Ft, 31.30.JvFor many years, Doppler free two-photon spectroscopy has been applied to the hydrogen atom in order to test quantum electrodynamics calculations and to improve the precision of the Rydberg constant R` [1]. Recently, the uncertainty of the measurements has been reduced to a level below 10 211 thanks to optical frequencymultiplication chains, which link the measured frequency via intermediate standard lasers to the caesium clock. With such a chain, Hänsch and co-workers have taken advantage of the small natural width of the 1S-2S twophoton transition (1.3 Hz) to measure this frequency with an uncertainty of 3.4 3 10 213 [2]. In our group, we have made absolute frequency measurements of the 2S-8S͞D transitions with an accuracy better than 8 3 10 212 [3]. In this last case, the precision was limited by the line shape analysis which becomes complicated by a large broadening (up to 1 MHz) due to the inhomogeneous light shift. The comparison of the 1S-2S and 2S-8S͞D measurements has provided very precise determinations of R`and of the Lamb shift [2,3]. Nevertheless, in order to confirm our 2S-8S͞D frequency measurements, we have built a new chain to measure the frequencies of another transition, that is the 2S-12D transition. This transition yields complementary information to our study of the 2S-nS͞nD transitions, because it is very sensitive to stray electric fields (the shift due to the quadratic Stark effect varies as n 7 ), and so such a measurement is a stringent test of Stark corrections to the Rydberg levels.In this Letter, we present these new results and make a complete analysis of the optical frequency measurements to determine the best values for R`and the Lamb shifts.Our new frequency chain uses two standard lasers, a laser diode stabilized on the 5S-5D two-photon transition of rubidium (LD͞Rb laser, l 778 nm, n 385 THz) and a CO 2 laser stabilized to an osmium tetraoxyde line (labeled CO 2 ͞OsO 4 , l ഠ 10 mm, n ഠ 29 THz). In 1996, the frequencies of three LD͞Rb lasers, one in the Laboratoire Kastler Brossel (LKB) and two in the Laboratoire Primaire du Temps et des Fréquences (LPTF), were measured with a frequency chain which connected the LD͞Rb laser to the CO 2 ͞OsO 4 standard [4]. More recently, the frequency measurement of this CO 2 ͞OsO 4 standard has been remade with respect to the Cs clock with an uncertainty of 20 Hz (i.e., a relative uncertainty of...