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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 31 — Nov. 1, 2010
  • pp: G105–G113

Force-optimized alignment for optical control of the Advanced Technology Solar Telescope

Robert Upton, Myung Cho, and Thomas Rimmele  »View Author Affiliations


Applied Optics, Vol. 49, Issue 31, pp. G105-G113 (2010)
http://dx.doi.org/10.1364/AO.49.00G105


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Abstract

We present formalism and analysis of three active alignment reconstruction techniques applied to the Advanced Technology Solar Telescope. The three reconstructors generate optical control signals that are a matrix product of a wavefront-sensing signal and the reconstructors themselves. The optical control signals are fed to the six rigid body degrees of freedom of the telescope secondary mirror and the eight bending modes of the primary mirror. The resulting aligned state is a least-squares alignment of the telescope subject to perturbations that result from thermal and gravitational flexures. Two of the reconstructors utilize a single guide object in the telescope field of view and the third reconstructor utilizes three guide objects. One of the single-guide-object reconstructors is developed with an explicit minimum force constraint that minimizes the actuator forces exerted on the telescope primary mirror during active alignment. The force optimized reconstructor also achieves close to the minimum residual wavefront error. Simulation results, optical control analysis, and a discussion of the reconstructor methods and properties are presented.

© 2010 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(110.6770) Imaging systems : Telescopes
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Wavefront Sensor Reconstruction

History
Original Manuscript: March 29, 2010
Revised Manuscript: June 1, 2010
Manuscript Accepted: June 23, 2010
Published: August 12, 2010

Citation
Robert Upton, Myung Cho, and Thomas Rimmele, "Force-optimized alignment for optical control of the Advanced Technology Solar Telescope," Appl. Opt. 49, G105-G113 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-31-G105


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References

  1. T. R. Rimmele, S. L. Keil, C. U. Keller, F. Hill, J. Briggs, N. E. Dalrymple, B. D. Goodrich, S. L. Hegwer, R. Hubbard, J. M. Oschmann, R. R. Radick, D. Ren, J. Wagner, S. Wampler, and M. Warner, “Technical challenges of the Advanced Technology Solar Telescope,” Proc. SPIE 4837, 94–109 (2003). [CrossRef]
  2. ATST project website, http://atst.nso.edu.
  3. F. Woeger and T. Rimmele, “Effect of anisoplanatism on the measurement accuracy of an extended-source Hartmann–Shack wavefront sensor,” Appl. Opt. 48, A35–A46 (2009). [CrossRef]
  4. Giant Magellan Telescope project website, http://www.gmto.org.
  5. J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M(2006). [CrossRef]
  6. R. Upton, “Optical control of the Advanced Technology Solar Telescope,” Appl. Opt. 45, 5881–5896 (2006). [CrossRef] [PubMed]
  7. C. R. Vogel, Computational Methods for Inverse Problems (SIAM2002). [CrossRef]
  8. R J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  9. The condition number is the ratio of the greatest to the least singular values of a positive semidefinite matrix, which are common in active optical control problems where the matrix is overdetermined. The condition number can also be used to quantify the degree of linear independence between the compensating DOFs that are encapsulated in the columns of Jacobian matrices such as HM2
  10. MATLAB is a licensed product of The Mathworks, http://www.mathworks.com.
  11. ZEMAX is a licensed product of the ZEMAX Development Corporation, http://www.zemax.com.

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