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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 6492–6505

Deformable mirror model for open-loop adaptive optics using multivariate adaptive regression splines

Dani Guzmán, Francisco Javier de Cos Juez, Fernando Sánchez Lasheras, Richard Myers, and Laura Young  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6492-6505 (2010)

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Open-loop adaptive optics is a technique in which the turbulent wavefront is measured before it hits the deformable mirror for correction. We present a technique to model a deformable mirror working in open-loop based on multivariate adaptive regression splines (MARS), a non-parametric regression technique. The model’s input is the wavefront correction to apply to the mirror and its output is the set of voltages to shape the mirror. We performed experiments with an electrostrictive deformable mirror, achieving positioning errors of the order of 1.2% RMS of the peak-to-peak wavefront excursion. The technique does not depend on the physical parameters of the device; therefore it may be included in the control scheme of any type of deformable mirror.

© 2010 OSA

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.1285) Atmospheric and oceanic optics : Atmospheric correction

ToC Category:
Adaptive Optics

Original Manuscript: January 11, 2010
Revised Manuscript: February 19, 2010
Manuscript Accepted: February 22, 2010
Published: March 15, 2010

Dani Guzmán, Francisco Javier de Cos Juez, Fernando Sánchez Lasheras, Richard Myers, and Laura Young, "Deformable mirror model for open-loop adaptive optics using multivariate adaptive regression splines," Opt. Express 18, 6492-6505 (2010)

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  1. F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J. M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lancon, G. Monnet, M. Mouhcine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON Concept: Multi-Object Spectroscopy Combined with MCAO in Near-IR,” Proc. ESO Workshop (2002).
  2. F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy - principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376(1), 287–312 (2007). [CrossRef]
  3. D. Guzmán, A. Guesalaga, R. Myers, R. Sharples, T. Morris, A. Basden, C. Saunter, N. Dipper, L. Young, L. Rodríguez, M. Reyes, and Y. Martin, “Deformable mirror controller for open-loop adaptive optics” Proc. SPIE 7015, 70153X–70153X–12 (2008).
  4. J. Friedman, “Multivariate adaptive regression splines,” Ann. Stat. 19(1), 1–67 (1991). [CrossRef]
  5. C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999). [CrossRef]
  6. D. Andersen, M. Fischer, R. Conan, M. Fletcher, and J. P. Veran, “VOLT: the Victoria Open Loop Testbed” Proc. SPIE 7015, 7015OH-7015OH-11 (2008).
  7. E. Laag, D. Gavel, and M. Ammons, “Open-loop woofer-tweeter control on the LAO multi-conjugate adaptive optics testbed” in Adaptive optics for industry and medicine, C. Dainty. (Imperial College Press, 2008), pp. 143–148.
  8. T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004). [CrossRef]
  9. C. Blain, O. Guyon, R. Conan, and C. Bradley, “Simple iterative method for open-loop control of MEMS deformable mirrors”, Proc. SPIE 7015, 701534–701534–8 (2008).
  10. K. Morzinski, K. Harpsoe, D. Gavel, and M. Ammons, “The open-loop control of MEMS: modeling and experimental results”, Proc. SPIE 6467, 6467OG-6467OG-10 (2007).
  11. J. Stewart, A. Diouf, Y. Zhou, and T. Bifano, “Open-loop control of a MEMS deformable mirror for large-amplitude wavefront control,” J. Opt. Soc. Am. A 24(12), 3827–3833 (2007). [CrossRef]
  12. J. Hardy, “Wavefront Correctors” in Adaptive Optics for Astronomical Telescopes (Oxford 1998), pp. 176–212.
  13. S. Sekulic and B. R. Kowalski, “MARS: a tutorial,” J. Chemometr. 6(4), 199–216 (1992). [CrossRef]
  14. L. Breiman, J. H. Friedman, R. A. Olshen, and C. G. Stone, Classification and Regression Trees., Wadsworth International Group, Belmont, CA (1984)
  15. Q.-S. Xu, M. Daszykowski, B. Walczak, F. Daeyaert, M. R. de Jonge, J. Heeres, L. M. H. Koymans, P. J. Lewi, H. M. Vinkers, P. A. Janssen, and D. L. Massart, “Multivariate adaptive regression splines - studies of HIV reverse transcriptase inhibitors,” Chemom. Intell. Lab. Syst. 72(1), 27–34 (2004). [CrossRef]
  16. P. Craven and G. Wahba, “Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation,” Numer. Math. 31, 317–403 (1979).
  17. D. L. Massart, B. Vandeginste, L. Buydens, S. De Jong, P. Lewi, and J. Smeyers-Verbeke, In: “Handbook of Chemometrics and Qualimetrics” vol. 20 A., Elsevier, Amsterdam (1997)
  18. J. W. Evans, B. Macintosh, L. Poyneer, K. Morzinski, S. Severson, D. Dillon, D. Gavel, and L. Reza, “Demonstrating sub-nm closed loop MEMS flattening,” Opt. Express 14(12), 5558–5570 (2006). [CrossRef] [PubMed]
  19. Y.F. Li, S.H. Ng, M. Xie, T.N. Goh. “A systematic comparison of metamodeling techniques for simulation optimization in Decision Support Systems”. Applied Soft Computing, In Press, Corrected Proof, Available online 24 December 2009. doi:10.1016/j.asoc.2009.11.034
  20. M. Carlin, T. Kavli, and B. Lillekjendlie, “A comparison of four methods for non-linear data modelling,” Chemom. Intell. Lab. Syst. 23(1), 163–177 (1994). [CrossRef]
  21. E. Deconinck, M. H. Zhang, F. Petitet, E. Dubus, I. Ijjaali, D. Coomans, and Y. Vander Heyden, “Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood–brain barrier passage: A case study,” Anal. Chim. Acta 609(1), 13–23 (2008). [CrossRef] [PubMed]
  22. B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, and T. Price, “Investigating a Xinetics Inc. deformable mirror,” Proc. SPIE 3126, 569–579 (1997). [CrossRef]

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