Fig. 1. Effect of atmospheric turbulence on vortex beams. (a) OAM spectrum broadening caused by atmospheric turbulence^[21]; (b) Intensity distributions, phase distributions and OAM spectra of LG beam and BG beam before and after propogating through atmospheric turbulence^[23]

Fig. 2. Distortion compensation for vortex beams. (a) Schemes of a probe Gaussian beam associated with wavefront sensor ^[34]; (b) Non-probe pre-compensation scheme based on GS algorithm^[40]; (c) SPGD algorithm scheme^[43]; (d) HIOA scheme^[58]

Fig. 3. Compensating distorted vortex beams through CNN. (a) CNN network based on Alexnet; (b) Adaptive optics system for distorted vortex beam^[93]

Fig. 4. Compensating distorted vectorial vortex beams through deep learning. (a) Special TACCNN network based on Alexnet. The input is a series of images with 224×224×3 pixel, and the output is 1×20 Zernike coefficients vector; (b) The intensities of mode purity without and with turbulence, as well as after compensation; (c) Detected mode purity before and after compensation in various turbulence atmospheres (D/r₀ within the scope of a value in 0-6.29). The blue bar and the pink bar represent mode purities before compensation and incremental mode purities after compensation, respectively^[94]

Fig. 5. Deep learning based atmospheric turbulence compensation. (a)CNN model for atmospheric turbulence compensation; (b) The mode purity of vortex beam (l=3) before and after compensation, under different strength of atmospheric turbulence^[96]