Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths

The performance of a closed-loop adaptive-optics system may in principle be improved by selection of distinct and independently optimized control bandwidths for separate components, or modes, of the wave-front-distortion profile. We describe a method for synthesizing and optimizing a multiple-bandwidth adaptive-optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. The approach is applicable to adaptive-optics systems that use either one or several wave-front sensing beacons and also to systems that include multiple deformable mirrors for atmospheric-turbulence compensation across an extended field of view. Numerical results are presented for the case of an atmospheric-turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack–Hartmann wave-front sensor with from 8 to 16 subapertures across the aperture of the telescope, and a continuous-face-sheet deformable mirror with actuators conjugate to the corners of the wave-front-sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave-front-sensor noise level that is permitted for the adaptive-optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system that uses only two distinct bandwidths, one of which is the zero bandwidth.