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In this paper, we study the outage behavior of a decode-and-forward multi-hop free-space optical (FSO) system over a Poisson channel degraded by atmospheric turbulence. We assume that perfect channel side information (CSI) is available at the receiver side and consider both cases of perfect CSI and no CSI at the transmitter side. We solve the outage probability minimization problem subject to a peak power constraint as well as a short- or long-term average sum power constraint. As a result, optimal power control strategies are presented for different scenarios under consideration. A sub-optimal yet low-complexity solution is further proposed under the short-term power constraint. Our results demonstrate that multi-hop relaying yields significant performance improvements which are particularly important for long-range FSO links.