Wavefront estimation at low light levels

Law, Ngai-Fong; Lane, R. G.

doi:10.1016/0030-4018(96)00027-2

Cited by 27 publications

(11 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(Wallner 1983) developed an optimal reconstructor for zonal estimation. (Law and Lane 1996) developed a maximum a posteriori (MAP) modal reconstructor and showed that it was equivalent to Wallner's zonal reconstructor. (Kasper 2000) calculated the closed-loop MAP using an expression for the closed-loop modal variances presented in (Veran et.…”

Section: Modal Reconstructormentioning

confidence: 99%

“…Since the WFS measures either slopes or curvatures of the wavefront, the first step in the control algorithm is to reconstruct the wavefront from the WFS measurements (c.f., Wallner 1983;Lane and Law 1996;Kasper 2000). The reconstruction process requires a matrix multiplication of the WFS measurements to produce the reconstructed wavefront.…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Modal selection using genetic optimization

Looze¹,

Hippler²,

Feldt³

2004

Advancements in Adaptive Optics

View full text Add to dashboard Cite

The calibration process for an adaptive optics system using modal control computes the reconstructor matrix in terms of a matrix whose columns are the measurements from a wavefront sensor. Each column of wavefront sensor measurements corresponds to a mode that is applied to the mirror. Since the measured gradients are corrupted by errors, the accuracy of the computed reconstructor is degraded by large condition numbers of the gradient matrix. A common method used to limit the condition number of this matrix is to reject all higher order modes when the condition number reaches the maximum desired value. However, it is possible (even likely) that one or a few modes are responsible for much of the increase in the condition number. By rejecting only those modes, an increased number of modes could be controlled. Unfortunately, computing the condition number of the gradient matrix for all possible combinations of modes is prohibitive. This paper uses a genetic optimization algorithm to increase the number of modes that are retained for control. The genetic algorithm maximizes the number of modes retained. A bound on the condition number of the gradient matrix is imposed. The paper applies this method to both the ALFA adaptive optics system on Calar Alto (with 37 subapertures), and a proposed CHEOPS adaptive optics system with 1652 subapertures. IntroductionThe function of the control algorithm in an adaptive optics (AO) system is to compute the drive signal of a deformable mirror (DM) based on the measurements by a wavefront sensor (WFS) of the error in the phase wavefront. Since the WFS measures either slopes or curvatures of the wavefront, the first step in the control algorithm is to reconstruct the wavefront from the WFS measurements (c.f., Wallner 1983;Lane and Law 1996;Kasper 2000). The reconstruction process requires a matrix multiplication of the WFS measurements to produce the reconstructed wavefront. This matrix (the reconstructor) is usually computed by a calibration procedure that applies a sequence of known patterns to the DM and measures the resulting wavefront. In a modal control algorithm, the reconstruction process produces an estimate of the modal coefficient of the modal decomposition of the measured wavefront. The calibration process computes the reconstructor in terms of the interaction matrix. The columns of the interaction matrix are obtained from the WFS measurements of the resulting wavefront when the corresponding mode is applied by the DM. Since the measured gradients are corrupted by errors, the accuracy of the computed reconstructor is degraded by large condition numbers of the gradient matrix. A common method used to limit the condition number of this matrix is to reject all higher order modes when the condition number reaches the maximum desired value. However, it is possible (even likely) that one or a few modes are responsible for much of the increase in the condition number. By rejecting only those modes, an increased number of modes could be controlled. Unfortunately, computing the co...

show abstract

Section: Modal Reconstructormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Modal selection using genetic optimization

Looze¹,

Hippler²,

Feldt³

2004

Advancements in Adaptive Optics

View full text Add to dashboard Cite

show abstract

“…Both maximum likelihood and maximum a posteriori techniques have been used to improve the estimate by incorporating prior knowledge on the second order statistics of the spatial distribution of the wavefront [4], [7]. The modified statistics due to closed-loop operation, are often neglected.…”

Section: Introductionmentioning

confidence: 99%

A Data-Driven ${\cal H}_{2}$-Optimal Control Approach for Adaptive Optics

Hinnen

Verhaegen

Doelman

2008

IEEE Trans. Contr. Syst. Technol.

View full text Add to dashboard Cite

Adaptive optics (AO) is used in ground-based astronomical telescopes to improve the resolution by counteracting the effects of atmospheric turbulence. Most AO systems are based on a simple control law that neglects the temporal evolution of the distortions introduced by the atmosphere. This paper presents a datadriven control design approach that is able to exploit the spatiotemporal correlation in the wavefront, without assuming any form of decoupling. The approach consists of a dedicated subspace-identification algorithm to identify an atmospheric disturbance model from open-loop wavefront sensor data, followed by 2 -optimal control design. It is shown that in the case that the deformable mirror and wavefront sensor dynamics can be represented by a delay and a two taps impulse response, it is possible to derive an analytical expression for the 2 -optimal controller. Numerical simulations on AO test bench data demonstrate a performance improvement with respect to the common AO control approach.

show abstract

“…To improve the accuracy, both maximum-likelihood and maximum a posteriori techniques have been used to include prior knowledge of the spatial correlation of the wavefront. 3,4 Prior knowledge of the temporal evolution of the wavefront is usually not included in the control design. Each of the parallel feedback loops typically consists of a first-order lag filter or proportional-integral controller of which the parameters are tuned to make a trade-off among disturbance rejection, noise propagation, and closed-loop stability.…”

Section: Introductionmentioning

confidence: 99%

Exploiting the spatiotemporal correlation in adaptive optics using data-driven H_2-optimal control

Hinnen

Verhaegen

Doelman³

2007

J. Opt. Soc. Am. A

View full text Add to dashboard Cite

A recently proposed data-driven H 2 -optimal control approach is demonstrated on a laboratory setup. Most adaptive optics (AO) systems are based on a control law that neglects the temporal evolution of the wavefront. The proposed control approach is able to exploit the spatiotemporal correlation in the wavefront without assuming any form of decoupling. By analyzing the dynamic behavior of the wavefront sensor (WFS), it is shown that if the wavefront correction device can be considered static, the transfer function from control input to WFS output reduces to a two-tap impulse response and an integer number of samples delay. Considering this model structure, a data-driven identification procedure is developed to estimate the relevant parameters from measurement data. The specific structure allows for an analytical expression of the optimal controller in terms of the system matrices of the minimum-phase spectral factor of the atmospheric disturbance model. The performance of the optimal controller is compared with that of the standard AO control law. An analysis of the dominant error sources shows that optimal control may reduce the temporal error.

show abstract

Wavefront estimation at low light levels

Cited by 27 publications

References 18 publications

Modal selection using genetic optimization

Modal selection using genetic optimization

A Data-Driven ${\cal H}_{2}$-Optimal Control Approach for Adaptive Optics

Exploiting the spatiotemporal correlation in adaptive optics using data-driven H_2-optimal control

Contact Info

Product

Resources

About