Hierarchical wave-front sensing

We present a new wave-front sensing technique for adaptive optics based on use of several wave-front sensors dedicated to the sensing of a different range of spatial frequencies. We call it a hierarchical wave-front sensor. We present the concept of a hierarchical wave-front sensor and apply it to the Shack-Hartmann sensor. We show the gain that is expected with two Shack-Hartmann sensors. We obtain a gain that increases with the size of the largest sensor, and we detail the application of hierarchical wave-front sensing to extreme adaptive optics and extremely large telescopes.