To effectively mitigate the influence of atmospheric turbulence, a novel discrete-time analog transmission free-space optical (DTAT-FSO) communication scheme is proposed. It directly maps information sources to discrete-time analog symbols via joint source-channel coding and modulation. Differently from traditional digital free space optical (TD-FSO) schemes, the proposed DTAT-FSO approach can automatically adapt to the variation of the channel state, with no need to adjust the specific modulation and coding scheme. The performance of the DTAT-FSO system was evaluated in both intensity modulation/direct detection (IM/DD) and coherent FSO systems for high-resolution image transmission. The results show that the DTAT-FSO reliably transmits images at low received optical powers (ROPs) and automatically enhances quality at high ROPs, while the TD-FSO experiences cliff and leveling effects when the channel state varies. With respect to the TD-FSO scheme, the DTAT-FSO scheme improved receiver sensitivity by 2.5 dB in the IM/DD FSO system and 0.8 dB in the coherent FSO system, and it achieved superior image fidelity under the same ROP. The automatic adaptation feature and improved performance of the DTAT-FSO suggest its potential for terrestrial, airborne, and satellite optical networks, addressing challenges posed by atmospheric turbulence.