The invention relates to a method for the manufacture of a lens of synthetic quartz glass with increased H2 content, in particular for a lens for an optical system with an operating wavelength of less than 250 nm, in particular less than 200 nm, with the steps: providing a precursor product of synthetic quartz glass, in particular with a first H2 content of less than 2·1015 molecules/cm3, with a circumferential border surface and two base surfaces lying on opposite sides, wherein at least one partial surface of at least one of said base surfaces has a curvature, and treating the precursor product in an H2-containing atmosphere in order to produce a precursor product of synthetic quartz glass with a second H2 content that is increased in relation to the first H2 content, in particular with a second H2 content of more than 1016 molecules/cm3, and measuring at least one optical property of said precursor product with said second H2 content.