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[-kappa(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 kappa 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. (C) 1998 Optical Society of America.