The wavefront sensor [WFS] is a key element of an Adaptive Optics [AO] system. It gives access to a direct
measurement of the turbulent phase, its curvature or its slope, from which the mirror voltages are computed. The
ability of the system to correct efficiently the atmospheric turbulence is strongly dependent on the performance
of the WFS in estimating the turbulent phase. The Shack-Hartmann [SH] WFS has been for a long time the
standard used in AO systems. In 1996, it has been proposed1 a new generation WFS, the pyramid WFS. It is a
focal plane WFS, based on the principle of a Foucault knife-edge. It has been demonstrated that it provides a
consistent gain with respect to the Shack-Hartmann.2,5-7 More recently, improvements were proposed to increase
the pyramid performance.3, 4 On the framework of the developpement of extremely large telescopes, the interest
of a pyramid wave front sensor appears clearly. But its behaviour with laser guide stars [LGS], most probably
necessary in any Extremely Large Telescope [ELT], is still relatively unknown. Some WFS dedicated to LGS
wave front sensing has already been proposed8,9 but a full study of the pyramid WFS behaviour is still necessary.
This work's aim is to bring answers to this topic.