Reconstruction of phase of the wave propagating in atmosphere under conditions of strong optical turbulence

It is well known that on long propagation paths the intensity fluctuations of optical wave become strong, the intensity distribution in the plane transverse to propagation direction becomes speckled and includes areas where intensity is close to zero. In the areas where the optical intensity is much lower than the mean intensity, a phase function can be discontinued owing to the presence of branch points in the complex optical field. In this case the most widely used in phase reconstruction from measured phase gradients the least squares technique generates erroneous result that is missing the hidden phase. There are two approach for hidden phase reconstruction. One of them is associated with detection of branch points and consequent calculation of the hidden phase. The other is based on reconstruction of the hidden phase directly from the measured phase gradient. In the paper we compare both approach to the reconstruction of the phase of optical wave propagating in a turbulent atmosphere under conditions of strong scintillation.