  Precise luminosity measurements for the OLYMPUS two-photon exchange
experiment at DESY were performed by counting scattering events with
alternating beams of electrons and positrons incident on atomic electrons in a
gaseous hydrogen target. Final products of M{\o}ller, Bhabha, and pair
annihilation interactions were observed using a pair of lead fluoride Cherenkov
calorimeters with custom housings and electronics, adapted from a system used
by the A4 parity violation experiment at MAMI. This paper describes the design,
calibration, and operation of these detectors. An explanation of the Monte
Carlo methods used to simulate the physical processes involved both at the
scattering vertices and in the detector apparatus is also included.
