Abstract
The dynamic model of a deformable adaptive mirror with actuators is presented. This model takes into account both properties of the deformable mirror itself and dynamic properties of each individual actuator. The set of equations describing dynamic behavior of such a complex system was derived. The approximate solution of this set was obtained by modal decomposition over the set of free deformable mirror spatial eigenfunctions. It was found that spatial mode frequency spectrum of dynamic system 'deformable mirror-actuators' is distorted with respect to the case of the free deformable mirror. Mode frequency dependence for each individual mode from the actuator's parameters was calculated. It was shown that the fundamental system frequency poses the largest frequency shift. The authors have also established the connection between some optical quality criteria (RMS wavefront deviation, aberration criterion etc.) and obtained modal decomposition. The control system for the adaptive deformable mirror was designed by treating the deformable mirror-actuators dynamic system as a multidimensional multicoupled automatic control system. It was shown it is possible to get a noticeable improvement in system dynamic behavior. The proposed dynamic model and its connection with optical quality criteria for a deformable mirror-actuator system can be used for adaptive optics systems design.
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