Hidden-phase compensation in extended-beacon adaptive optics

In this paper, we use wave-optics simulations to explore the benefits of hidden-phase compensation for laser systems that employ extended-beacon adaptive optics. Specifically, we create a trade space, where we vary the strength of the scintillation as well as the size of the beacon, and score laser-system performance in terms of no phase compensation, perfect least-squares compensation, and perfect full-phase compensation. Here, "full phase" refers to the least-squares and hidden-phase components of the pupil-plane phase function. The results of this trade space lead to three main conclusions. (1) If the scintillation is weak and we have either a point-source beacon or a very small extended-source beacon, then we see similar performance with perfect least-squares and full-phase compensation; however, both significantly improve performance compared to the no compensation case. On the other hand, if the scintillation is strong and we have either a point-source beacon or a very small extended-source beacon, then we get a significant improvement in performance using perfect full-phase compensation compared to perfect least-squares compensation. (2) If the scintillation is strong, then there will be a large number of turbulence-induced branch points and branch cuts in the hidden-phase component of the pupil-plane phase function. These branch points and cuts will result in a major reduction in performance if left uncompensated. (3) If the extended-source beacon is large, then the associated rough-surface scattering and resultant speckle will corrupt the perfect least-squares and full-phase compensation to the point where performance is on par with or worse than the no compensation case. At large, (1)-(3) will inform the development of future laser systems that need to mitigate the effects of scintillation and speckle to perform extended-beacon adaptive optics.