The radiation emitted by 180-GeV/c volume-reflected electrons and positrons impinging on a bent crystal has been measured by the H8RD22 Collaboration on the H8 beamline at the CERN SPS. A dedicated spectrometer has been developed to measure high-energy photon spectra (up to similar to 100 GeV) under volume reflection: photon and charged particle beams have been separated by a bending magnet and leptons were detected and tagged by microstrip silicon detectors and a Pb-scintillator sampling calorimeter. A comparison between the experimental and analytical data for the amorphous and volume-reflection cases is presented and the differences are discussed