Beam shaping for uplink transmission of a relay mirror system.

We establish the model of a two-Cassegrain-telescope system that is commonly used in a relay mirror system. With this model, uplink transmission of the relay mirror system is theoretically analyzed. We determined that uplink transmission with turbulence completely corrected is not an optimal mode. We improve power coupling efficiency of the two-Cassegrain-telescope system by optimizing the optical phase at the launching telescope by use of the stochastic parallel gradient descent algorithm. For a 10 km vertical uplink transmission, power coupling efficiencies of the system are 63.10%, 87.82%, and 97.80% corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. For a 30 km vertical uplink transmission, power coupling efficiencies of the system are 22.35%, 82.66%, and 91.91%, corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. The results show that power coupling efficiency of the two-Cassegrain-telescope system is significantly improved.