Effects of atmospheric turbulence, on long distance endo-atmospheric propagation (over a few miles), can be seriously detrimental to free-space optical communications (FSO). The field of the optical wave undergoes phase perturbations that modulate the received intensity. These perturbations can seriously afflict FSO reliability. Pre-compensation by adaptive optics (AO) has been proposed to mitigate these effects and enable the possibility to increase propagation distance and data throughput. The purpose of this thesis is to evaluate the performance and limitations, in terms of FSO effectiveness, of different AO correction methods and to study the possibility of more efficient concepts. We demonstrate that a phase and amplitude iterative correction approach - latter described as optimal correction - enables excellent performance, among the best so far proposed. The study of this theoretical approach enables us to set boundaries to the effectiveness of AO system. We showed that an efficient correction can be achieved greatly beyond the weak perturbation regime. In strong turbulence, it appears that classical approaches - AO by wavefront measurement, phase modulation or iterative phase correction (described as sub-optimal) - are limited. These limitations are due to scintillation, phase branch points and noise. We quantify the drop of performance relative to the optimal correction and propose a solution enabling the minimization of scintillation effects on phase measurements. We finally propose a method to pre-compensation for phase and amplitude and in particular for measurement and control, that should enable the implementation of the optimal correction.
