Statistical Performance of Conjugate Gradient Method for Wave-Front Reconstruction in Adaptive Optics

We constructed a method both of wave-front reconstruction and phase unwrapping by introducing a technique to generate a set of unwrapped phase differences into a conventional version of the MAP estimation via the conjugate gradient method (CGM). Then, we investigated statistical performance of the present method for typical wave-fronts in synthetic aperture radar (SAR) interferometry. Using numerical simulations for several wave-fronts appearing in the SAR interferometry, we clarified that the MAP estimation via the CGM is completely successful in wave-front reconstruction using a set of observed phase differences, if optical measurement is perfectly carried out using the interferometer, and that the CGM is successful in reducing noises of the original wave-fronts by utilizing an appropriate model of the true prior, if aliasing does not occurs at every sampling point. On the other hand, we found that the MAP estimation via the CGM is successful in phase unwrapping by utilizing a set of unwrapped phase differences generated by the CGM using the model of true prior appropriately, even if aliasing occurs at several sampling points.