Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

2008 (1)

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]

2007 (2)

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]

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]

2006 (1)

2004 (2)

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

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]

1999 (1)

C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[CrossRef]

1997 (1)

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]

1994 (1)

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]

1992 (1)

S. Sekulic and B. R. Kowalski, “MARS: a tutorial,” J. Chemometr. 6(4), 199–216 (1992).
[CrossRef]

1991 (1)

J. Friedman, “Multivariate adaptive regression splines,” Ann. Stat. 19(1), 1–67 (1991).
[CrossRef]

1979 (1)

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).

Assémat, F.

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]

Bierden, P.

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

Bifano, T.

Carlin, M.

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]

Coomans, D.

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]

Cornelissen, S.

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

Craven, P.

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).

Daeyaert, F.

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]

Daszykowski, M.

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]

de Jonge, M. R.

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]

Dean, P.

C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[CrossRef]

Deconinck, E.

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]

Dekany, R.

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]

Dillon, D.

Diouf, A.

Dubus, E.

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]

Ealey, M.

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]

Evans, J. W.

Friedman, J.

J. Friedman, “Multivariate adaptive regression splines,” Ann. Stat. 19(1), 1–67 (1991).
[CrossRef]

Gavel, D.

Gendron, E.

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]

Hammer, F.

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]

Heeres, J.

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]

Hom, C.

C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[CrossRef]

Ijjaali, I.

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]

Janssen, P. A.

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]

Kavli, T.

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]

Kim, J.

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

Kowalski, B. R.

S. Sekulic and B. R. Kowalski, “MARS: a tutorial,” J. Chemometr. 6(4), 199–216 (1992).
[CrossRef]

Koymans, L. M. H.

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]

Lewi, P. J.

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]

Lillekjendlie, B.

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]

Macintosh, B.

Massart, D. L.

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]

Morzinski, K.

Oppenheimer, B. R.

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]

Palmer, D.

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]

Petitet, F.

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]

Poyneer, L.

Price, T.

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]

Reza, L.

Sekulic, S.

S. Sekulic and B. R. Kowalski, “MARS: a tutorial,” J. Chemometr. 6(4), 199–216 (1992).
[CrossRef]

Severson, S.

Sivaramakrishnan, A.

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]

Stewart, J.

Vander Heyden, Y.

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]

Vinkers, H. M.

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]

Wahba, G.

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).

Walczak, B.

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]

Winzer, S.

C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[CrossRef]

Xu, Q.-S.

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]

Zhang, M. H.

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]

Zhou, Y.

Zhu, H.

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

Anal. Chim. Acta (1)

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]

Ann. Stat. (1)

J. Friedman, “Multivariate adaptive regression splines,” Ann. Stat. 19(1), 1–67 (1991).
[CrossRef]

Chemom. Intell. Lab. Syst. (2)

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]

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]

J. Chemometr. (1)

S. Sekulic and B. R. Kowalski, “MARS: a tutorial,” J. Chemometr. 6(4), 199–216 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

Mon. Not. R. Astron. Soc. (1)

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]

Numer. Math. (1)

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).

Opt. Express (1)

Proc. SPIE (2)

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]

T. Bifano, P. Bierden, H. Zhu, S. Cornelissen, and J. Kim, “Megapixel wavefront correctors,” Proc. SPIE 5490, 1472–1481 (2004).
[CrossRef]

Smart Mater. Struct. (1)

C. Hom, P. Dean, and S. Winzer, “Simulating electrostrictive DM: I nonlinear static analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[CrossRef]

Other (10)

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).

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.

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).

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).

J. Hardy, “Wavefront Correctors” in Adaptive Optics for Astronomical Telescopes (Oxford 1998), pp. 176–212.

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)

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

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).

L. Breiman, J. H. Friedman, R. A. Olshen, and C. G. Stone, Classification and Regression Trees., Wadsworth International Group, Belmont, CA (1984)

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).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

A graphical representation of a spline basis function. The left spline (x<t, −(x−t)) is shown as a dashed line; the right spline (x>t, +(x−t)) as a solid line.

Fig. 2
Fig. 2

non-linear behavior of DM actuators, in a 9 x 5 actuators example. Top-left panel: sum of individual actuators, poked to +12v (for an explanation for the tilted surrounding, please see section 5). Top-right panel: combined effect when poking all actuators together to +12v. The Z coordinate in the top panels is in nanometers. Bottom-left panel: difference between top panels, with residual RMS for the area being poked. Bottom-right panel: slice of the bottom-right panel along the central column, showing individual actuators, the sum of them and the joint poke.

Fig. 3
Fig. 3

Left panel: correlation coefficients matrix R; central panel: correlation coefficients for the central actuator, taken from matrix R.; right panel: comparison between a traditional influence function and the correlation coefficients

Fig. 4
Fig. 4

the 11 x 5 actuators area being modeled by our MARS model: The 55 actuator positions found are presented here with black crosses, and the surrounding area, sampled at 6 positions and presented with blue Xs, are used to fit a plane to account for tilt drifts throughout the runs. The DM is shown with a typical random deformation spanning a few micrometers in the Z coordinate

Fig. 5
Fig. 5

voltage/stroke plot for a central actuator

Fig. 6
Fig. 6

First 9 random pokes of one of the runs with our Xinetics DM. Z coordinate (color bar) is in nanometers

Fig. 7
Fig. 7

qualitative results, using various Zernike polynomials. The left panels are theoretical Zernike polynomials; the central panels are the output of the DM for the 11 x 5 actuators being modeled. The right panels present a slice in Y from the central panels, to appreciate the differences between theoretical and experimental polynomials (red plot: Zernike polynomial; blue plot: DM surface). The color map for the left and central panels is common, but it has not been included in order to simplify the figure

Fig. 8
Fig. 8

maxima and minima of each run. The residual error is presented for completeness. For more details on the latter, see Fig. 9

Fig. 9
Fig. 9

GoTo error: the top-panel presents the residual error in Nanometer. The bottom-panel presents the residual error as a fraction of the full-range of actuators excursion

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

y = f ( X ) + e
[ ( x t ) ] + q = { ( t x ) q i f     x < t 0 o t h e r w i s e
[ + ( x t ) ] + q = { ( t x ) q i f     x > t 0 o t h e r w i s e
y ^ = f ^ M ( x ) = c 0 + m = 1 M c m B m ( x )
G C V ( M ) = 1 n m = 1 n ( y i f M ( x i ) ) 2 ( 1 C ( M ) / n ) 2
C ( M ) = M + d M
f ^ ( x ) = c 0 + f i ( x i ) + f i j ( x i , x j ) + f i j k ( x i , x j , x k )
I f i j ( x i , x j ) = f i ( x i ) + f j ( x j ) + f i j ( x i , x j )
R M S E C V = i = 1 n ( y i y ^ i ) 2 n
q 2 = 1 i = 1 n ( y i y ^ i ) 2 i = 1 n ( y i y ¯ ) 2
R i , j = C i , j C i , i C j , j

Metrics