Exact Wavefront Correction in Adaptive Optics

In this work we consider an adaptive optical system in which a deformable mirror is controlled to compensate for random wavefront disturbances. For most systems of this type, the shape of the mirror is taken as a linear function of the wavefront error, leading to satisfactory results in linear regimes. Here, the geometric shape of the mirror leading to a perfect correction of the wavefront is derived. Next, a control is designed to reach that geometric shape when the deformable mirror is a membrane mirror with electrostatic actuators. Numerical simulations illustrating the improvements supplied by the geometric approach are also reported here. Copyright c 2005 IFAC