Tomographic reconstruction for Wide Field Adaptive Optics systems: Fourier domain analysis and fundamental limitations

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.