  A measurement of the integrated luminosity at the ep collider HERA is
presented, exploiting the elastic QED Compton process ep \rightarrow ep. The
electron and the photon are detected in the backward calorimeter of the H1
experiment. The integrated luminosity of the data recorded in 2003 to 2007 is
determined with a precision of 2.3%. The measurement is found to be compatible
with the corresponding result obtained using the Bethe-Heitler process.
