An experimental study on phase compensation for turbulent effects with a 37-element adaptive optics system is performed in both a simulated turbulence cell and in a real atmosphere. The experimental results demonstrate that the compensated Strehl ratio S 0, which is influenced mainly by the deformable-mirror fitting error, has a functional form S 0 =exp[-κ(d/ r 0)5/3], where r 0 is Fried’s coherence length and d is the average interval of the actuators on the deformable mirror. The fitting parameter κ is 0.45. Numerical simulations are also performed with the experimental parameters. The numerical results are in agreement with data obtained in the experiment, which shows that the direct-tilt phase-reconstruction method used in our four-dimensional simulation code is reasonable.
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