Optimal sensor placement for modal based estimation of deformable mirror shape

We propose a mechanically motivated strategy for determining sensor locations for maximum observability of continuous faceplate deformable mirrors in adaptive optics systems. We introduce an observability measure based on the eigenvalues of the observability gramian, incorporating a penalty term for identically located sensors. It is shown that analytically derived eigenmodes of deformable mirrors can be used to determine optimal positions for a limited number of sensors using simulated annealing. The derived optimal sensor positions are valid for displacement and velocity measurements. The constructed observer is a Kalman-Filter designed for a reduced order modal model. Simulation results illustrate the feasibility of this method and a good estimation quality.