Decomposition of deformable-mirror shapes based on influence functions of stroke-saturation actuators

We describe a deformable-mirror control algorithm based on mirror-actuator influence functions. Since these influence functions are nonorthogonal, the voltages transmitted to the actuators are calculated using a least-squares technique. The resulting solution was then optimized to take into account the constraints on maximum permissible actuator voltages. A practical demonstration of this algorithm was performed in MATLAB, using the example of a deformable mirror with 49 actuators. We show that in certain cases, the root-mean-square deviation between the surface and the specified shape can be reduced by as much as 70% through additional optimization.