Projection-based decoupling algorithm for a woofer–tweeter adaptive optics system

We propose a projection-based decoupling algorithm for a woofer–tweeter (W–T) adaptive optics system. This algorithm uses the response matrix of woofer deformable mirrors (DM) to construct a slope-based orthogonal basis, which can be used to distribute different spatial frequency aberrations to the dual DMs. At the same time, to restrain the cross coupling between the dual DMs, the command vector of the tweeter will be projected onto the slope-based orthogonal basis, and then the portion of the tweeter's command vector, which may generate opposite shape with the woofer can be calculated and eliminated accurately. Numerical simulation for this algorithm demonstrates that it can make the woofer and tweeter correct different spatial frequency aberrations simultaneously, and have more practical value compared with the traditional decoupling algorithm. Experimental results for this algorithm are consistent with the simulation results and proved that the cross coupling between the dual DMs can be restrained well for both static and dynamic aberrations.