The invention relates to the loading of quartz glass objects with hydrogen in an annealing process in a furnace for improving the homogeneity of the refractive index and the laser resistance while, at the same time, maintaining a specified stress birefringence of each of the glass objects. Initially, the distribution of the refractive index, the stress birefringence, the distribution of the hydrogen and the differences in refractive index, which are to the equalized, are determined in the respective glass object, after which the hydrogen change, which is necessary for equalizing the refractive index, is determined. Furthermore, the annealing temperature and its holding time, as well as the hydrogen concentration and the hydrogen pressure in the furnace are adjusted to achieve a sufficiently equalized distribution of refractive index.