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Adaptive optics applies advanced sensing and control to improve the ability of optical systems to collect images through a turbulent atmosphere. The results of this research e ort demonstrate that the combination of two recent approaches improves the performance of adaptive optics in directed energy and laser communication scenarios. The rst approach is adaptive control, which o ers improved performance over xed-gain controllers in the presence of rapidly changing turbulence. The second approach incorporated into the study is a dual-mirror system. The two mirrors are a high-bandwidth, low-actuator-stroke (tweeter) mirror and a low-bandwidth, large-actuator-stroke (woofer) mirror. The woofer-tweeter combination allows for better compensation of the large-variance, high-spatial-frequency phase distortion generated by strong turbulence. Two di erent adaptive controllers are presented.