Fig. 1. Flow chart of the hybrid modal algorithm

Fig. 2. Correction results of different optimization algorithms. (a) SR varies; (b) RMS varies

Fig. 3. Histogram of Zernike coefficients between hybrid algorithm correction

Fig. 4. The wavefront sensorless adaptive optical system. (a) Schematic; (b) Experiment

Fig. 5. Captured intensity of the far-field spot. (a) Before corrected; (b) Corrected by the SPGD algorithm; (c) Corrected by the hybrid algorithm

Fig. 6. Fitted intensity of the far-field spot on the horizontal axis

Fig. 7. Improvement of normalized intensity for different algorithms

Fig. 8. Experiment of data transmission in atmospheric laser communications

Fig. 9. Waveform measured in atmospheric turbulence

Fig. 10. Variation curve of BER with modulation rate