Intensities of positrons specularly diffracted from Cu(111) were measured at the Brandeis positron beam facility and analyzed in the energy range 8 eV<E<l34 eV for angles of incidence θ=25, 30, 35, 40, 45, 50, 52, 57, and 60°. These intensities were calculated for the known geometry of Cu(111) using a dynamical multiple scattering methodology. Above E=50 eV this methodology gives a useful account of the measured intensities using a constant imaginary optical potential of Vi=4 eV. At lower energies strong energy dependences occur, associated both with multiple elastic scattering phenomena within atomic layers of Cu parallel to the surface and with the thresholds of inelastic channels (e.g., plasmon creation). Use of the free electron calculation of Vi shows that energy dependence of inelastic processes is necessary to obtain a satisfactory description of the absolute magnitude of the diffracted intensities below E=50 eV. Detailed comparison of the calculated and observed diffraction intensities reveals the necessity of incorporating surface loss processes explicitly into the model in order to achieve a quantitative description of the measured intensities for E<40 eV and θ>40°.