Probabilistic inference to the problem of atmospheric compensation in adaptive optics

On the basis of statistical mechanics of the Q-Ising model on the square lattice, we apply the maximizer of the posterior marginal (MPM) estimate to the problem of phase retrieval in adaptive optics. Then, using the Markov-chain Monte Carlo simulation, we estimate the performance of the MPM estimate for a typical wave-front in adaptive optics. Our method is divided into two kinds in accordance with the sensitivity of measurement by optical instruments using the shearing interferometer. The Monte Carlo simulation shows the result that the MPM estimate works effectively if we selectively choose the model of the true prior according to the sensitivity of measurement.