OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 11 — Nov. 1, 2010
  • pp: A182–A200

Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics

Fernando Quirós-Pacheco, Jean-Marc Conan, and Cyril Petit  »View Author Affiliations


JOSA A, Vol. 27, Issue 11, pp. A182-A200 (2010)
http://dx.doi.org/10.1364/JOSAA.27.00A182


View Full Text Article

Enhanced HTML    Acrobat PDF (496 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.

© 2010 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(100.3190) Image processing : Inverse problems

History
Original Manuscript: April 9, 2010
Revised Manuscript: August 19, 2010
Manuscript Accepted: August 22, 2010
Published: September 22, 2010

Citation
Fernando Quirós-Pacheco, Jean-Marc Conan, and Cyril Petit, "Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics," J. Opt. Soc. Am. A 27, A182-A200 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-11-A182


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999). [CrossRef]
  2. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]
  3. C. Paterson, “Constraints of ground-based observations: The atmosphere,” in Optics in Astrophysics, NATO Science Series, R.Foy and F.Foy, eds. (Springer, 2005), pp. 1–10.
  4. S. Esposito, “Introduction to multi-conjugate adaptive optics systems,” C. R. Phys. 6, 1039–1048 (2005). [CrossRef]
  5. N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005). [CrossRef]
  6. E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005). [CrossRef]
  7. D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]
  8. B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994). [CrossRef]
  9. A. Tokovinin, M. Le Louarn, and M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000). [CrossRef]
  10. F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations and performance of multi-conjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000). [CrossRef]
  11. R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (2000). [CrossRef]
  12. A. Tokovinin and E. Viard, “Limiting precision of tomographic phase estimation,” J. Opt. Soc. Am. A 18, 873–882 (2001). [CrossRef]
  13. T. Fusco, J.-M. Conan, G. Rousset, L.-M. Mugnier, and V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001). [CrossRef]
  14. M. Lloyd-Hart and N. M. Milton, “Fundamental limits on isoplanatic correction with multiconjugate adaptive optics,” J. Opt. Soc. Am. A 20, 1949–1957 (2003). [CrossRef]
  15. J. Herrmann, “Cross coupling and aliasing in modal wave-front estimation,” J. Opt. Soc. Am. 71, 989–992 (1981). [CrossRef]
  16. W. H. Southwell, “What’s wrong with cross coupling in modal wave-front estimation?” Proc. SPIE 365, 97–104 (1982).
  17. E. Gendron, “Optimisation de la commande modale en optique adaptative: applications a l’astronomie,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1995).
  18. G. M. Dai, “Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loeve functions,” J. Opt. Soc. Am. A 13, 1218–1225 (1996). [CrossRef]
  19. J.-P. Véran, “Estimation de la reponse impulsionnelle et restauration d’image en optique adaptative,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1997).
  20. B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L.-M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004). [CrossRef]
  21. E. Gendron and P. Léna, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).
  22. R. Ragazzoni, E. Marchetti, and F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).
  23. M. Tallon and R. Foy, “Adaptive telescope with laser probe—Isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).
  24. G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt, 1988).
  25. M. Le Louarn and M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002). [CrossRef]
  26. T. Fusco, J.-M. Conan, V. Michau, L.-M. Mugnier, and G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999). [CrossRef]
  27. T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000). [CrossRef]
  28. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  29. We will denote the covariance matrices in the eigenspace with an MP, which stands for modes propres, or eigenmodes in French.
  30. J. M. Conan, “Etude de la Correction Partielle en Optique Adaptative,” Ph.D. dissertation (Université de Paris XI Orsay, 1994).
  31. F. Quirós-Pacheco, “Reconstruction and control laws for multi-conjugate adaptive optics in astronomy,” Ph.D. dissertation (Imperial College London, 2006).
  32. F. Rigaut and E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  33. C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).
  34. B. L. Ellerbroek, C. Vanloan, N. P. Pitsianis, and R. J. Plemmons, “Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths,” J. Opt. Soc. Am. A 11, 2871–2886 (1994). [CrossRef]
  35. G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003). [CrossRef]
  36. C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006). [CrossRef] [PubMed]
  37. C. Dessenne, “Commande modale et predictive en optique adaptative,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1998).
  38. T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004). [CrossRef]
  39. J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997). [CrossRef]
  40. J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995). [CrossRef]
  41. E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008). [CrossRef]
  42. H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008). [CrossRef]
  43. L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005). [CrossRef] [PubMed]
  44. C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009). [CrossRef]
  45. E. A. Laag, S. M. Ammons, D. T. Gavel, and R. Kupke, “Multiconjugate adaptive optics results from the laboratory for adaptive optics MCAO/MOAO testbed,” J. Opt. Soc. Am. A 25, 2114–2121 (2008). [CrossRef]
  46. A. Costille, C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited