Optimal design of wavefront sensors for adaptive optical systems

Models of adaptive optical systems appropriate for the analysis of controllability and observability are developed. These models consist of mappings among three vector spaces: actuator command space, wavefront error space, and sensor output space. The condition numbers of these mappings are developed as a measure of combined controllability and observability. The sensitivity of the condition number to a variety of design parameters, including actuator stiffness, wavefront sensor subaperture diameter, and the number and location of wavefront sensor channels, is examined via simulation. This analysis shows that satisfactory controllability and observability properties are obtained when the wavefront sensor samples all degrees of freedom of the system above the Nyquist rate. The problem of determining sensor subaperture locations that maximize controllability and observability is examined and shown to be an intractable optimization problem. A practical algorithm, the sequential backward selection algorithm, is used to determine a suboptimal sensor configuration. Monte Carlo studies show that the algorithm determines a nearly optimal and entirely acceptable configuration in a reasonable time.