OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 4 — Apr. 1, 2001
  • pp: 873–882

Limiting precision of tomographic phase estimation

Andrei Tokovinin and Elise Viard  »View Author Affiliations

JOSA A, Vol. 18, Issue 4, pp. 873-882 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (517 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In the context of multiconjugate adaptive optics, the optimum linear estimation of a wave-front phase for a target object using the phases of several surrounding natural guide stars (NGS’s) is studied. A Wiener-filter-type estimator is constructed. The minimum residual wave-front-phase (tomographic) error depends on the turbulence vertical profile, and for typical profiles it is almost insensitive to the presence of strong layers, contrary to current belief. Tomographic error is characterized by a new parameter δK, equivalent profile thickness, which depends on the NGS number K (typically δ5=0.5 km). The angular radius of the NGS configuration must not exceed r0/δK. Exact profile knowledge is not required. When the optimized filters are constructed from some model profile, the loss of the field size is within 10% with respect to exact profile knowledge. Moreover, a method to measure turbulence profile using wave-front-sensor data is outlined. Noise propagation in the restoration algorithm is significant, but not dramatic. Noise increases with increasing size of NGS constellation. Practically, guide stars for tomography should be at least as bright as those for classical adaptive optics.

© 2001 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

Original Manuscript: April 26, 2000
Revised Manuscript: September 11, 2000
Manuscript Accepted: November 2, 2000
Published: April 1, 2001

Andrei Tokovinin and Elise Viard, "Limiting precision of tomographic phase estimation," J. Opt. Soc. Am. A 18, 873-882 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975). [CrossRef]
  2. J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Proceedings of the ESO Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.
  3. M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549 (1990).
  4. D. C. Johnston, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]
  5. 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]
  6. T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999). [CrossRef]
  7. A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000). [CrossRef]
  8. R. Ragazzoni, E. Marchetti, G. Valente, “Adaptive-optics corrections available for the whole sky,” Nature 403, 54–56 (2000). [CrossRef] [PubMed]
  9. M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535 (2000). [CrossRef]
  10. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.
  11. F. Rigaut, J.-P. Véran, O. Lai, “An analytical model for Shack-Hartmann-based adaptive optics systems,” in Adap-tive Optical System Technologies, D. Bonaccini, ed., Proc. SPIE3353, 1038–1048 (1998). [CrossRef]
  12. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U., Cambridge, UK, 1992), Chap. 13.3.
  13. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]
  14. G. C. Valley, S. M. Wandzura, “Spatial correlation of phase-expansion coefficients for propagation through atmospheric turbulence,” J. Opt. Soc. Am. 69, 712–717 (1979). [CrossRef]
  15. A. Fuchs, J. Vernin, “Final report on PARSCA 1992 and 1993 campaigns,” (European Southern Observatory, Garching, Germany, 1996).
  16. M. Sarazin, in OSA/ESO Topical Meeting on Adaptive Optics, M. Cullum, ed. (European Southern Observatory, Garching, Germany, 1996), pp. 439–444.
  17. R. Avila, J. Vernin, E. Masciadri, “Whole atmosphere profiling with a generalized SCIDAR,” Appl. Opt. 36, 7898–7905 (1997). [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