A feasibility study and the mission definition for a Quantum Key Distribution from a geostationary satellite have been successfully completed by a Spanish consortium led by HISPASAT under ARTES ESA funding. The system will be a hosted payload of a regular communication satellite mission. In this work, the conceptual optical design of the payload is presented. It includes the trade-off between an on-axis telescope with central obscuration and an off-axis unobscured telescope. Besides, the optical design of the transmission (i.e.: quantum signal and downlink beacon) and reception channels (i.e.: uplink beacon) are described and the critical subsystems identified. A polarization control system based on liquid-crystals, which avoids mechanisms, is used to correct the errors due to instrumental residual polarization, reference system rotation or long-term instability of the QKD source during operation.
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