The results of testing the adaptive optics system with a correlation sensor at the Big Solar Vacuum Telescope at the Baikal Astrophysical Observatory are presented. Based on fast 12-bit DALSTAR DS-12-16K5H camera and an active mirror with a piezoelectric drive a system to correct for image jitter has been built, that shows good performance in the image patterns with 10 to 15% contrast. In tracking objects with a very noisy granulation image with 1 to 2% contrast, a modified correlation-tracking algorithm is proposed, which demonstrates a capability of using the correlation method in the case of low contrast objects.