Measurement accuracy in control of segmented-mirror telescopes

MacMartin, Douglas G.; Chanan, G. A.

doi:10.1364/ao.43.000608

Cited by 22 publications

(16 citation statements)

References 10 publications

(21 reference statements)

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“…The propagation of sensor noise is understood [3,10], and while this may limit the desired control bandwidths, it does not otherwise affect the feedback problem.…”

Section: A Segmented-mirror Controlmentioning

confidence: 99%

“…The next smallest nonzero singular values, corresponding to astigmatism, scale roughly as 2:5=N; these scalings can both be verified by construction using the formulas in [3]; the astigmatism scaling also follows from Eq. (6) in [10]. Even for the relatively large sensor moment arm at Keck of L eff ¼ 55 mm, focus mode will have the smaller sensitivity for any telescopes currently being designed.…”

Section: A Segmented-mirror Controlmentioning

confidence: 99%

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Interaction matrix uncertainty in active (and adaptive) optics

MacMynowski

2009

Appl. Opt.

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Uncertainty in the interaction matrix between sensors and actuators can lead to performance degradation or instability in control of segmented mirrors (typically the telescope primary). The interaction matrix is ill conditioned, and thus the position estimate required for control can be highly sensitive to small errors in knowledge of the matrix, due to uncertainty or temporal variations. The robustness to different types of uncertainty is bounded here using the small gain theorem and structured singular values. The control is quite robust to moderate uncertainty in actuator gain, sensor gain, or the ratio of sensor dihedral and height sensitivity. However, the control is extremely sensitive to small errors in geometry, with the maximum error that can be tolerated scaling inversely with the number of segments. The same tools can be applied to adaptive optics; however, the interaction matrix here is better conditioned and so uncertainty is less of an issue, with the tolerable error scaling inversely with the square root of the number of actuators.

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“…The propagation of sensor noise is understood [3,10], and while this may limit the desired control bandwidths, it does not otherwise affect the feedback problem.…”

Section: A Segmented-mirror Controlmentioning

confidence: 99%

Section: A Segmented-mirror Controlmentioning

confidence: 99%

Interaction matrix uncertainty in active (and adaptive) optics

MacMynowski

2009

Appl. Opt.

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“…We considered this question in detail elsewhere 19,20 and concluded that a supplementary wave-front sensor is not likely to be needed for stabilization purposes. Here we just summarize the argument.…”

Section: Error Multipliers From Singular-value Decompositionmentioning

confidence: 99%

Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation

Chanan¹,

MacMartin²,

Nelson³

et al. 2004

Appl. Opt.

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Starting from the successful Keck telescope design, we construct and analyze the control matrix for the active control system of the primary mirror of a generalized segmented-mirror telescope, with up to 1000 segments and including an alternative sensor geometry to the one used at Keck. In particular we examine the noise propagation of the matrix and its consequences for both seeing-limited and diffractionlimited observations. The associated problem of optical alignment of such a primary mirror is also analyzed in terms of the distinct but related matrices that govern this latter problem.

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“…For realistic choices of dihedral sensitivity, focus-mode remains the least-observable deflection pattern (smallest singular value) after global piston, tip, and tilt. The next least-observable modes (relatively large ratio of rms surface motion to resulting rms edge discontinuity [9]) are spatially smooth and similar to Zernike basis functions. The full interaction matrix relates all three displacements at the sensor location (height combined with dihedral, gap, and shear) to all six possible rigid-body deflections of each mirror segment.…”

Section: A Descriptionmentioning

confidence: 83%

In-plane effects on segmented-mirror control

et al. 2012

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Extremely large optical telescopes are being designed with primary mirrors composed of hundreds of segments. The "out-of-plane" piston, tip, and tilt degrees of freedom of each segment are actively controlled using feedback from relative height measurements between neighboring segments. The "in-plane" segment translations and clocking (rotation) are not actively controlled; however, in-plane motions affect the active control problem in several important ways, and thus need to be considered. We extend earlier analyses by constructing the "full" interaction matrix that relates the height, gap, and shear motion at sensor locations to all six degrees of freedom of segment motion, and use this to consider three effects. First, in-plane segment clocking results in height discontinuities between neighboring segments that can lead to a global control system response. Second, knowledge of the in-plane motion is required both to compensate for this effect and to compensate for sensor installation errors, and thus, we next consider the estimation of in-plane motion and the associated noise propagation characteristics. In-plane motion can be accurately estimated using measurements of the gap between segments, but with one unobservable mode in which every segment clocks by an equal amount. Finally, we examine whether in-plane measurements (gap and/or shear) can be used to estimate out-of-plane segment motion; these measurements can improve the noise multiplier for the "focus-mode" of the segmented-mirror array, which involves pure dihedral angle changes between segments and is not observable with only height measurements.

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Measurement accuracy in control of segmented-mirror telescopes

Cited by 22 publications

References 10 publications

Interaction matrix uncertainty in active (and adaptive) optics

Interaction matrix uncertainty in active (and adaptive) optics

Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation

In-plane effects on segmented-mirror control

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