Fig. 1. Principle of MCAO system based on sodium LGSs. (a) Schematic diagram for two-layer turbulent tomography by MCAO system with three sodium LGSs constellation; (b) transformation of coordinates between footprint and meta-pupil, where xoy is for meta-pupil coordinates and x'o'y' is for footprint coordinates

Fig. 2. Gray map of projection matrix for three sodium LGSs constellation

Fig. 3. Simulated results of wavefront reconstruction with two layers of atmospheric turbulence and three sodium LGSs through tomography. Upper row for ground layer turbulence and lower row for high layer turbulence. (a), (d) Initial distorted wavefront; (b), (e) reconstructed wavefront through tomography; (c), (f) residual error

Fig. 4. SR map obtained by MCAO system with three sodium LGSs, with yellow pentagrams representing sodium LGSs

Fig. 5. Performance evolution of 500 frames for MCAO system with three sodium LGSs during 1 s

Fig. 6. Constellations of sodium LGSs with different numbers and located at different positions. (a) 3+1; (b) 4; (c) 4+1; (d) 5; (e) 5+1; (f) 6

Fig. 7. SR maps obtained by MCAO systems for sodium LGS constellations with different numbers and configurations, with yellow pentagrams representing sodium LGSs. (a) 3+1; (b) 4; (c) 4+1; (d) 5; (e) 5+1; (f) 6

Fig. 8. Mean values of SR and STD obtained by MCAO systems for sodium LGS constellations with different numbers and configurations

Fig. 9. Influence of zenith angle of sodium LGSs on performance of MCAO system

Fig. 10. Influence of zenith angle of sodium LGSs on uniformity of MCAO system

Table 1. Main parameters for simulation