Decoupling control algorithm based on numerical orthogonal polynomials for a woofer-tweeter adaptive optics system.

To resolve cooperative control issues of dual wavefront correctors in generalized irregular pupil regions, we propose a decoupling control algorithm based on numerical orthogonal polynomials (NOP). The proposed algorithm firstly deduces NOP from Zernike polynomials in generalized irregular pupil regions. Then, according to wavefront restoration, different spatial frequency aberrations to different wavefront correctors are assigned precisely. Finally, the algorithm calculates and eliminates the cross-coupling between dual wavefront correctors. As observed in numerical simulations and experiments based on a typical woofer-tweeter (W-T) adaptive optics system, NOP decoupling control algorithm restrains the cross-coupling between woofer and tweeter in generalized irregular pupil regions. Moreover, there are obvious advantages over Zernike polynomials decoupling control algorithm in cross-coupling suppression for various scenarios in irregular pupil regions and restoration orders.