Adaptive optics is the technology of sensing, estimating, and correcting the distortions induced in beams of light as they propagate through turbulent media. Applications include ground-based astronomical imaging and spectroscopy, laser power beaming through the atmosphere, and imaging the retina of the human eye. The fundamental components of an adaptive optical (AO) system are a wavefront sensor to measure the distortions in the optical beam, a wavefront corrector to compensate these errors, and an estimation and control algorithm to derive the control signals from the distortion measurements. The current generation of AO systems for ground-based imaging apply corrections to a few hundred to about one thousand degrees of freedom at update rates between a few hundred and a few thousands samples/second, using linear control algorithms that are implemented as explicit matrix multiplies. Proposed future systems could increase the number of degrees of freedom by a factor between ten and one hundred, with additional complexities introduced via the use of multiple wavefront sensors and correctors. More efficient control algorithms must be developed for these larger and more sophisticated systems, together with the theory to evaluate and optimize their performance.
Encouraging initial results are now being obtained in a variety of computational experiments investigating the simpler problem of estimating the instantaneous value of the phase disturbance from a single wavefront sensor snapshot. Some of the estimation algorithms under investigation include spatial filtering via fast Fourier transforms, sparse matrix methods, conjugate gradients with multi-grid or circulant preconditioning, and “hybrid” combinations of these methods. These methods have computational complexity between O(n log n) and O(n 3/2), as opposed to O(n3) to compute, and O(n2) to apply, conventional matrix multiply algorithms. But more work is necessary to optimize, understand, extend, and eventually implement these new approaches. Some of this work includes:
We believe that this meeting can lead to a new synthesis of ideas and numerous valuable collaborations and initiatives, towards a goal of developing advanced control algorithms that will enable an entirely new generation of AO for future giant telescopes.
(National Optical Astronomical Observatory)
Donald Gavel (University of California at Santa Cruz, Astronomy)
Andrea M. Ghez (UCLA, Division of Astronomy and Astrophysics)
Mark Morris (UCLA, Physics & Astronomy)
Stanley Osher (IPAM, Mathematics)
Curt Vogel (Montana State University, Bozeman, Mathematical Sciences)