Phase unwrapping in the presence of strong turbulence

Phase unwrapping in the presence of branch points using a least mean square error (LMSE) wave-front reconstructor requires the use of a Postprocessing Congruence Operation (PCO) to ensure the unwrapped output is congruent or modulo-2π-equivalent to the wrapped input. 2π discontinuities known as branch cuts in the unwrapped phase are altered by the addition of a constant parameter h to the rotational component when applying the PCO. Selecting a value of h which minimizes the proportion of irradiance in the pupil-plane adjacent to branch cuts is an effective method to maximize performance of adaptive optics (AO) systems in strong turbulence. The optimal value of h varies significantly in open-loop AO or while the loop is closing. Once the loop is closed, optimal values tend to occur near h = 0. This paper proposes two algorithms which utilize this behavior to optimize the PCO and compares them with other unwrappers in closed-loop AO simulations. When compared to other PCO unwrappers, both algorithms reduced the probability of low Strehl ratios, as well as the normalized variance of the Strehl ratio. The second algorithm reduced normalized variance by up to 33 percent. AO systems which depend on steady performance and Strehl ratio values above a minimum threshold serve to benefit from these algorithms when operating in the presence of branch points.