Probability density function models for adaptive optical systems operating in turbulence

This work deals with the effect of adaptive optics (AOs) configuration options, i.e., tip/tilt (N=3) and full AO (N=35) cases, on the intensity probability density functions (PDFs) associated with the turbulent channel. An ad hoc scintillation index model is proposed for the full AO options. This model is applicable for both power-in-the-bucket and power-in-the-fiber (PIF) signal receptions. The commonly used log-normal intensity PDF follows the no AO and tip/tilt experimental horizontal link data for two turbulence conditions but fails to accurately characterize the full AO option for those two cases, especially in depicting the perceived left skewness of the PDF in one case. The exponentiated Weibull distribution with the proposed full AO scintillation index model exhibits good agreement with the experimental data in the two cases and follows the strong left skewness in one case. These results also show that the median value for each PDF shifts to the right and the PDFs experience narrower shape changes, i.e., more received power, as AO Zernike modes are added. Finally, comparison of PIF PDF shifts with the estimated fiber coupling efficiencies is in reasonable agreement.