Forward and inverse solution for the MEMS deformable mirrors in adaptive optics

Adaptive optics is used in modern telescope to compensate the wavefront aberrations introduced by the Earth´s atmosphere. A continuous facesheet MEMS deformable mirror owing to its advantages is gaining popularity in the area of adaptive optics. The mirror layer is influenced by a matrix of force actuators each applying a point force for generating a desired shape. For small deformations this layer is treated as a thin plate undergoing linear displacement. The resulting shape of deformed mirror due to the applied forces can be given by superposition of the independent Navier solution. In an adaptive optics system desired shape of mirror is known beforehand from the measured light wavefront and inverse problem is solved to obtain the force to be applied. We present the Tikhonov regularization technique for obtaining the inverse solution and compare it with the solution obtained using matrix inversion. The inverse solution obtained by regularization technique is stable even in presence of significant noise in the wavefront measurements.