Modeling electrostrictive deformable mirrors in adaptive optics systems

Adaptive optics correct light wavefront distortion caused by atmospheric turbulence or internal heating of optical components. This distortion often limits performance in ground-based astronomy, space-based earth observation and high energy laser applications. The heart of the adaptive optics system is the deformable mirror. In this study, an electromechanical model of a deformable mirror was developed as a design tool. The model consisted of a continuous, mirrored face sheet driven with multilayered, electrostrictive actuators. A fully coupled constitutive law simulated the nonlinear, electromechanical behavior of the actuators, while finite element computations determined the mirror's mechanical stiffness observed by the array. Static analysis of the mirror/actuator system related different electrical inputs to the array with the deformation of the mirrored surface. The model also examined the nonlinear influence of internal stresses on the active array's electromechanical performance and quantified crosstalk between neighboring elements. The numerical predictions of the static version of the model agreed well with experimental measurements made on an actual mirror system. The model was also used to simulate the systems level performance of a deformable mirror correcting a thermally bloomed laser beam. The nonlinear analysis determined the commanded actuator voltages required for the phase compensation and the resulting wavefront error.