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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 2 — Feb. 1, 2005
  • pp: 310–322

Linear systems modeling of adaptive optics in the spatial-frequency domain

Brent L. Ellerbroek  »View Author Affiliations

JOSA A, Vol. 22, Issue 2, pp. 310-322 (2005)

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Spatial-frequency domain techniques have traditionally been applied to obtain estimates for the independent effects of a variety of individual error sources in adaptive optics (AO). Overall system performance is sometimes estimated by introducing the approximation that these individual error terms are statistically independent, so that their magnitudes may be summed in quadrature. More accurate evaluation methods that account for the correlations between the individual error sources have required Monte Carlo simulations or large matrix calculations that can take much longer to compute, particularly as the order of the AO system increases beyond a few hundred degrees of freedom. We describe an approach to evaluating AO system performance in the spatial-frequency domain that is relatively computationally efficient but still accounts for many of the interactions between the fundamental error sources in AO. We exploit the fact that (in the limits of an infinite aperture and geometrical optics) all the basic wave-front propagation, sensing, and correction processes that describe the behavior of an AO system are spatial-filtering operations in the Fourier domain. Essentially all classical wave-front control algorithms and evaluation formulas are expressed in terms of these filters and may therefore be evaluated one spatial-frequency component at a time. Performance estimates for very-high-order AO systems may be obtained in 1 to 2 orders of magnitude less time than needed when detailed simulations or analytical models in the spatial domain are used, with a relative discrepancy of 5% to 10% for typical sample problems.

© 2005 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing

Brent L. Ellerbroek, "Linear systems modeling of adaptive optics in the spatial-frequency domain," J. Opt. Soc. Am. A 22, 310-322 (2005)

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  1. P. L. Wizinowich and D. Bonaccini, eds., Adaptive Optical System Technologies II , Proc. SPIE 4839 (2003).
  2. T. Andersen and A. Ardeberg, eds., Extremely Large Telescopes II , Proc. SPIE (to be published).
  3. B. L. Ellerbroek, L. Gilles, and C. R. Vogel, "Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes," Appl. Opt. 42, 4811-4818 (2003).
  4. L. Gilles, B. L. Ellerbroek, and C. R. Vogel, "Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics," Appl. Opt. 42, 5233-5250 (2003).
  5. B. L. Ellerbroek and C. R. Vogel, "Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 206-217 (2003).
  6. A. J. Ahmadia and B. L. Ellerbroek, "Parallelized simulation code for multiconjugate adaptive optics," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 218-227 (2003).
  7. C. Arcidiacono, E. Diolaiti, R. Ragazzoni, A. Baruffolo, A. Brindisi, J. Farinato, and E. Vernet-Viard, "Sky coverage and Strehl ratio uniformity in layer-oriented MCAO systems," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 169-180 (2003).
  8. D. L. Fried, "Anisoplanatism in adaptive optics," J. Opt. Soc. Am. 72, 52-61 (1982).
  9. D. P. Greenwood, "Bandwidth specification for adaptive optics systems," J. Opt. Soc. Am. 67, 390-392 (1977).
  10. G. A. Tyler, "Turbulence-induced adaptive-optics performance degradation: evaluation in the time domain," J. Opt. Soc. Am. A 1, 251-262 (1984).
  11. L. A. Poyneer and B. Macintosh, "Spatially filtered wave-front sensor for high-order adaptive optics," J. Opt. Soc. Am. A 21, 810-819 (2004).
  12. A. Tokovinin and M. Le Louarn, "Isoplanatism in a multiconjguate adaptive optics system," J. Opt. Soc. Am. A 17, 1819-1827 (2000).
  13. A. Tokovinin and E. Viard, "Limiting precision of tomographic phase estimation," J. Opt. Soc. Am. A 18, 873-8827 (2001).
  14. F. Rigaut, J.-P. Veran, and O. Lai, "Analytical model for Shack-Hartmann-based adaptive optics systems," in Adaptive Optical System Technologies, D. Bonaccini and R. K. Tyson, eds., Proc. SPIE 3353, 1038-1048 (1998).
  15. L. Jollisaint and J.-P. Veran, "Fast computation and morphologic interpretation of the adaptive optics point spread function," in Beyond Conventional Adaptive Optics , R. Ragazzoni, N. Hubin, S. Esposito, and E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002).
  16. E. P. Wallner, "Optimal wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 73, 1771-1776 (1983).
  17. B. M. Welsh and C. S. Gardner, "Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars," J. Opt. Soc. Am. A 8, 69-80 (1991).
  18. D. C. Johnston and B. M. Welsh, "Analysis of multiconjugate adaptive optics," J. Opt. Soc. Am. A 11, 394-408 (1994).
  19. 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).
  20. 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).
  21. W. H. Press, B. P. Flanner, S. A. Teukolosky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987).
  22. C. Boyer, E. Gendron, and P. Y. Madec, "Adaptive optics for high-resolution imagery: control algorithms for optimized modal corrections," in Lens and Optical Systems Design, H. Zuegge, ed., Proc. SPIE 1780, 943-957 (1992).
  23. B. L. Ellerbroek, "Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths," J. Opt. Soc. Am. A 11, 2871-2886 (1994).
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, Publications, New York, 1972), Eq. 4.3.133, p. 78.
  25. R. Hudgin, "Wave-front compensation error due to finite corrector-element size," J. Opt. Soc. Am. 67, 393-396 (1977).
  26. F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, and D. Roddier, "One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation," J. Opt. Soc. Am. A 10, 957-965 (1993).

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