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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 11 — Apr. 10, 2009
  • pp: 2105–2114

Interaction matrix uncertainty in active (and adaptive) optics

Douglas G. MacMynowski  »View Author Affiliations


Applied Optics, Vol. 48, Issue 11, pp. 2105-2114 (2009)
http://dx.doi.org/10.1364/AO.48.002105


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Abstract

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.

© 2009 Optical Society of America

OCIS Codes
(110.6770) Imaging systems : Telescopes
(220.1080) Optical design and fabrication : Active or adaptive optics

ToC Category:
Imaging Systems

History
Original Manuscript: December 10, 2008
Revised Manuscript: March 13, 2009
Manuscript Accepted: March 20, 2009
Published: April 3, 2009

Citation
Douglas G. MacMynowski, "Interaction matrix uncertainty in active (and adaptive) optics," Appl. Opt. 48, 2105-2114 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-11-2105


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References

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