An adaptive optics (AO) system with Stochastic Parallel Gradient Descent (SPGD) algorithm and a 61-element deformable mirror is simulated to restore the image of a turbulence-degraded extended object. SPGD is used to search the optimum voltages for the actuators of the deformable mirror. We try to find a convenient image performance metric, which is needed by SPGD, merely from a gray level distorted image and without any additional optics elements. Simulation results show the gray level variance function acts more promising than other metrics, such as metrics based on the gray level gradient of each pixel. The restoration capability of the AO system is investigated with different images and different turbulence strength wave-front aberrations using SPGD with the above resultant image quality criterion. Numerical simulation results verify the performance metric is effective and the AO system can restore those images degraded by different turbulence strengths successfully.