Optical parameter design model of hemispherical laser retroreflector arrays for satellite laser ranging

A laser retroreflector array (LRA) with multiple retroreflectors is used to directionally reflect an incident laser beam and aims to enhance the received signal strength into laser ranging ground stations. A comprehensive mathematical equation of the received photons is established by modelling the LRA far field diffraction intensity (FFDI) and the satellite velocity aberration position. Based on this received photon model, a novel method on designing the dihedral angle offset and the aperture of retroreflectors is proposed, which maximizes the received photon under the minimal elevation angle of the ground station. Taking the hemispherical structure parameters of Chinese HY-2 satellite LRA and the specification parameters of the Shanghai Astronomical Observatory, the optimal aperture and the dihedral angle offset of the HY-2 laser retroreflectors are 17 mm and 1.6^″, respectively. These two optimal optical parameters make the received photon under the elevation angle of 0° reach ∼0.9 count per laser shot. Until now, ∼851,400 successful observations have been successfully obtained by global ground stations since the first launch of HY-2 satellite series in 2011, which guarantees the high-precise orbit determination of HY-2 satellite series.