The differential scattering cross section for the interaction of optical photons with relativistic electrons is calculated from quantum electrodynamics. The cross section is confirmed by scattering monochromatic electromagnetic radiation from 50-keV electrons. The classical calculation of the differential scattering cross section which agrees with the quantum electrodynamic calculation and with experiment is one which takes into account the fact that scattering electrons enter and leave the scattering volume during the period of observation. These results are important for the proper intepretation of laser scattering measurements of plasma distribution functions when electron temperatures are ≥ 10 keV.