It is commonly believed that the main obstacles in functioning of adaptive optical systems in the atmosphere under the conditions of strong turbulence are wave front dislocations (optical vortices). It is assumed in this case that wave front singularities connected with vortices disappear at disappearance (annihilation) of vortices, so it makes no problem to correct for the distorting effect of the atmosphere on the propagating laser beam using, for example, flexible mirrors. This paper is devoted to the study of properties of the wave front phase distribution at the stage following annihilation of optical vortices. It is established that the absolute values of the mean curvature and the Gaussian curvature of wave front parts increase greatly in the areas of vortex aftereffect. It is shown that the efficiency of an adaptive optical system reduces due to the increase of the error at the stage of retrieval of such phase distribution in the process of wave front sensing. This effect should be also taken into consideration when developing principles of construction of single-mirror and multiple-mirror adaptive optical systems operating by the phase conjugation method and intended for work under the conditions of strong atmospheric turbulence.