The temporal spread of optical pulse signals due to reflection from multiple onboard reflectors is now a critical problem in satellite laser ranging. The full rate residual profile of single-photon laser ranging can be used to model the response function of geodetic satellites, resolving the uncertainty of far-field diffraction. We constructed the response function model for three types of laser ranging targets already in Earth orbit, the LAGEOS, AJISAI, and ETALON satellites. The center-of-mass correction depends on the ranging system and observation policy at terrestrial stations and varies about 1 cm for LAGEOS and 5 cm for AJISAI and ETALON.