Optical EngineeringOptimal design of wavefront sensors for adaptive optical systems: part 1, controllability and observability analysis
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Experience with adaptive optical systems has highlighted the fact that these systems are often designed without adequate attention to the wavefront control system. One example is the ‘‘mode visibility’’ problem, in which the wavefront sensor design results in aberrations that can be introduced into the optical system by the actuators but cannot be sensed adequately by the wavefront sensor and therefore cannot be corrected by the closed-loop wavefront control system. To prevent such problems, the overall system design must include control system issues at an appropriate level. For purposes of control system design, an adaptive optical system can be modeled as mappings among three vector spaces: the space containing the actuator command, the space containing the wavefront error of the system, and the space containing the wavefront sensor output. The singular value decompositions of these mappings enable analysis of the controllability and observability properties of the system. In particular, the condition number of the mapping from actuator space to sensor space is a measure of the combined controllability and observability of the system, and the minimization of this condition number results in a system with good controllability and observability properties.