The results of spectroscopic studies of plasmas generated in dielectric barrier discharges between flat ceramic electrodes supplied by AC voltage in pure hydrogen atmosphere under low-pressure conditions are presented. Stark splitting of the Hα Balmer line was used to measure the electric field strengths in the discharge volume. The optical instrumentation and the detection system allow to perform spatial and time resolved measurements separately for the π and σ Stark components. The measured spatial light intensity distributions are averaged data obtained by integrating signals from many half-periods of the AC voltage supply. This fact has been taken into account when comparing our averaged data with results of theoretical models which are yielding time dependent results.