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The effect of atmosphere turbulence on light’s spatial structure compromises the information capacity of photons carrying the Orbital Angular Momentum (OAM) in free-space optical (FSO) communications. In this paper, we study two aberration correction methods to mitigate this effect. The first one is the Shack-Hartmann wavefront correction method, which is based on the Zernike polynomials, and the second is a phase correction method specific to OAM states. Our numerical results show that the phase correction method for OAM states outperforms the Shark-Hartmann wavefront correction method, although both methods improve significantly purity of a single OAM state and the channel capacities of FSO communication link. At the same time, our experimental results show that the values of participation functions go down at the phase correction method for OAM states, i.e., the correction method ameliorates …