  Several Wide Field of view Adaptive Optics (WFAO) concepts like
Multi-Conjugate AO (MCAO), Multi-Object AO (MOAO) or Ground-Layer AO (GLAO) are
currently studied for the next generation of Extremely Large Telescopes (ELTs).
All these concepts will use atmospheric tomography to reconstruct the turbulent
phase volume. In this paper, we explore different reconstruction algorithms and
their fundamental limitations. We conduct this analysis in the Fourier domain.
This approach allows us to derive simple analytical formulations for the
different configurations, and brings a comprehensive view of WFAO limitations.
We then investigate model and statistical errors and their impact on the phase
reconstruction. Finally, we show some examples of different WFAO systems and
their expected performance on a 42m telescope case.
