Optimal wave-front reconstruction strategies for multiconjugate adaptive optics

We propose an optimal approach for the phase reconstruction in a large fiel d of view (FOV) for multiconjugate adaptive optics. This optimal approach i s based on a minimum-mean-square-error estimator that minimizes the mean re sidual phase variance in the FOV of interest. It accounts for the C-n(2) pr ofile in order to optimally estimate the correction wave front to be applie d to each deformable mirror (DM). This optimal approach also accounts for t he fact that the number of DMs will always be smaller than the number of tu rbulent layers, since the C-n(2) profile is a continuous function of the al titude h. Links between this optimal approach and a tomographic reconstruct ion of the turbulence volume are established. In particular, it is shown th at the optimal approach consists of a fall tomographic reconstruction of th e turbulence volume followed by a projection onto the DMs accounting for th e considered FOV of interest. The case where the turbulent layers are assum ed to match the mirror positions [model-approximation (MA) approach], which might be a crude approximation, is also considered for comparison. This MA approach will rely on the notion of equivalent turbulent layers. A compari son between the optimal and MA approaches is proposed. It is shown that the optimal approach provides very good performance even with a small number o f DMs (typically, one or two). For instance, good Strehl ratios (greater th an 20%) are obtained for a 4-m telescope on a 150-arc see X 150-arc see FOV by using only three guide stars and two DMs. (C) 2001 Optical Society of A merica.