Warm-started wavefront reconstruction for adaptive optics

Abstract

Future extreme adaptive optics (ExAO) systems have been suggested with up to 10 5 sensors and actuators. We analyze the computational speed of iterative reconstruction algorithms for such large systems. We compare a total of 15 different scalable methods, including multigrid, preconditioned conjugate-gradient, and several new variants of these. Simulations on a 128ϫ 128 square sensor/actuator geometry using Taylor frozen-flow dynamics are carried out using both open-loop and closed-loop measurements, and algorithms are compared on a basis of the mean squared error and floating-point multiplications required. We also investigate the use of warm starting, where the most recent estimate is used to initialize the iterative scheme. In open-loop estimation or pseudo-open-loop control, warm starting provides a significant computational speedup; almost every algorithm tested converges in one iteration. In a standard closed-loop implementation, using a single iteration per time step, most algorithms give the minimum error even in cold start, and every algorithm gives the minimum error if warm started. The best algorithm is therefore the one with the smallest computational cost per iteration, not necessarily the one with the best quasi-static performance.

Control of a Hypersegmented Space Telescope

“…However, while the transformation from motion to sensor response is sparse, the inverse is in general fully populated; that is, the estimation of segment motion requires global knowledge. For ground-based segmented mirrors, where the actuators influence the absolute motion of the segments, the inverse transformation has been shown to require attention to robustness (which is challenging [21]) and to computation (which is solvable [22,23]). With actuation that influences only relative motion between segments, there is a related problem of finding the set of actuator commands that produces a desired segment motion.…”

Experimental validation of single-iteration multigrid wavefront reconstruction at the Palomar Observatory

“…SIMG provides a dramatic reduction in computational cost when compared to vector-matrix multiplication and can be implemented in parallel, making it the obvious choice for reconstruction in future large-scale adaptive optics systems. [6]. In this Letter, we detail the experimental validation of this work on a real SCAO system.…”

“…These methods are O͑n log n͒. The SIMG is O͑n͒ and shows no performance degradation when compared to the leastsquares reconstructor.A good model for the wavefront sensor (WFS) is [6,8] where x is the wavefront phase, y are the measurements, v is white noise, and G is a sparse influence matrix. The least-squares reconstruction matrix is found by taking the pseudoinverse.…”

“…Examples include the conjugate-gradient (CG) [1], Fourier-domain (FD) [2], blended FD-CG [3], and sparse methods [4]. Recently, it was shown through simulation that a single-iteration multigrid (SIMG) method is as effective as CG methods for both multiconjugate [5] and single-conjugate adaptive optics (MCAO and SCAO, respectively) [6]. In this Letter, we detail the experimental validation of this work on a real SCAO system.…”

“…This ensures that unobservable modes such as piston and waffle are zeroed out. The SIMG method [6] uses a single multigrid sweep with an initial guess of 0 to obtain an approximate solution to the equation…”