The Lamb-shift polarimeter described here enables the polarization of a beam of hydrogen ͑deuterium͒ atoms, or of a slow proton ͑deuteron͒ beam, to be measured with an absolute precision better than 1% within a few seconds. The polarimeter measures the intensity ratios of Lyman-␣ transitions after Stark quenching of metastable hyperfine substates that were selected in a spin filter. For that purpose the hydrogen ͑deuterium͒ atoms are ionized in a Glavish-type ionizer. By charge exchange of the protons ͑deuterons͒ in cesium vapor, atoms in the metastable 2S state are produced. For a hydrogen beam of 3ϫ10 16 atoms/s, ϳ3ϫ10 6 photons/s are registered in a photomultiplier, i.e., the polarimeter efficiency is about 10
Ϫ10. The signal-to-background ratio in the Lyman-␣ spectrum is excellent, thus beam intensities of one to two orders of magnitude less would still be sufficient to carry out a precise measurement. The different components of the polarimeter affect the measured polarization in several ways. It was, therefore, crucial to determine precisely the associated correction factors in order to derive the nuclear polarization from the measured Lyman-␣ spectra.