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The ability to encode information on a single photon in the form of orbital angular momentum (OAM) has lead to recent research in the field of free space communication and quantum information processing. Whilst, in principle, one has access to an infinite number of OAM states, the influence of atmospheric turbulence on the light's spatial structure compromises the information capacity of photons carrying OAM. We present numerical analysis of the effect of atmospheric turbulence on single-photon communication systems based on orbital angular momentum states, and correct the aberrations by Shark-Hartmann algorithm. The results show the beam will be corrupted even in weak atmospheric turbulence, and Shack-Hartmann reconstruction algorithm could mitigate this effect, regain the information that lost in the aberration regime.