The luminosity in the ZEUS detector was measured using photons from electron bremsstrahlung. In 2001 the HERA collider was upgraded for operation at higher luminosity. At the same time the luminosity-measuring system of the ZEUS experiment was modified to tackle the expected higher photon rate and synchrotron radiation. The existing lead-scintillator calorimeter was equipped with radiation hard scintillator tiles and shielded against synchrotron radiation. In addition, a magnetic spectrometer was installed to measure the luminosity independently using photons converted in the beam-pipe exit window. The redundancy provided a reliable and robust luminosity determination with a systematic uncertainty of 1.7%. The experimental setup, the techniques used for luminosity determination and the estimate of the systematic uncertainty are reported.
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