Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics

Gilles, Luc

doi:10.1364/ao.44.000993

Cited by 52 publications

(34 citation statements)

References 10 publications

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“…This is also a requirement for closed-loop stability reasons. In the absence of measurement noise and systematic errors (WFS pupil distortion and misregistration/calibration errors), the poles of the closedloop transfer matrix are then equal to those of a conventional minimum-variance reconstructor with closed-loop constraints [11]. POL gradients represent an estimate of the open-loop gradients that would have been measured with ideal flat DMs and ideal fully linear WFSs.…”

Section: A Pseudo-open-loop Gradient Computationmentioning

confidence: 99%

Split atmospheric tomography using laser and natural guide stars

Gilles

Ellerbroek

2008

J. Opt. Soc. Am. A

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Laser guide star (LGS) atmospheric tomography is described in the literature as integrated minimum-variance tomographic wavefront reconstruction from a concatenated wavefront-sensor measurement vector consisting of many high-order, tip/tilt (TT)-removed LGS measurements, supplemented by a few low-order natural guide star (NGS) components essential to estimating the TT and tilt anisoplanatism (TA) modes undetectable by the TT-removed LGS wavefront sensors (WFSs). The practical integration of these NGS WFS measurements into the tomography problem is the main subject of this paper. A split control architecture implementing two separate control loops driven independently by closed-loop LGS and NGS measurements is proposed in this context. Its performance is evaluated in extensive wave optics Monte Carlo simulations for the Thirty Meter Telescope (TMT) LGS multiconjugate adaptive optics (MCAO) system, against the delivered performance of the integrated control architecture. Three iterative algorithms are analyzed for atmospheric tomography in both cases: a previously proposed Fourier domain preconditioned conjugate gradient (FDPCG) algorithm, a simple conjugate gradient (CG) algorithm without preconditioning, and a novel layer-oriented block Gauss-Seidel conjugate gradient algorithm (BGS-CG). Provided that enough iterations are performed, all three algorithms yield essentially identical closed-loop residual RMS wavefront errors for both control architectures, with the caveat that a somewhat smaller number of iterations are required by the CG and BGS-CG algorithms for the split approach. These results demonstrate that the split control approach benefits from (i) a simpler formulation of minimum-variance atmospheric tomography allowing for algorithms with reduced computational complexity and cost (processing requirements), (ii) a simpler, more flexible control of the NGS-controlled modes, and (iii) a reduced coupling between the LGS-and NGS-controlled modes. Computation and memory requirements for all three algorithms are also given for the split control approach for the TMT LGS AO system and appear feasible in relation to the performance specifications of current hardware technology.

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Section: A Pseudo-open-loop Gradient Computationmentioning

confidence: 99%

Split atmospheric tomography using laser and natural guide stars

Gilles

Ellerbroek

2008

J. Opt. Soc. Am. A

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“…Standard closed-loop techniques give rise to stability problems in MCAO [9,10]. We tried three different closedloop architectures in SCAO and found them all to be stable for every method tested.…”

Section: Introductionmentioning

confidence: 99%

Warm-started wavefront reconstruction for adaptive optics

et al. 2008

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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.

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“…Wavefront control is done by using a double-pole integrator with a gain of 0.5 operating in pseudo-open loop. 7 The error budget has been computed by subtracting in quadrature noise-free from noisy closed-loop Monte Carlo simulation results by using the same mean sodium profile as in Fig. 5.…”

Section: Simulation Resultsmentioning

confidence: 99%

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

Gilles

Ellerbroek

2006

Appl. Opt.

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We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noiseoptimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.

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Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics

Cited by 52 publications

References 10 publications

Split atmospheric tomography using laser and natural guide stars

Split atmospheric tomography using laser and natural guide stars

Warm-started wavefront reconstruction for adaptive optics

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

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