OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 11 — Nov. 1, 2010
  • pp: A235–A245

Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

Rufus Fraanje, Justin Rice, Michel Verhaegen, and Niek Doelman  »View Author Affiliations

JOSA A, Vol. 27, Issue 11, pp. A235-A245 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (295 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order.

© 2010 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7060) Atmospheric and oceanic optics : Turbulence
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.1080) Imaging systems : Active or adaptive optics

Original Manuscript: April 1, 2010
Revised Manuscript: July 10, 2010
Manuscript Accepted: August 3, 2010
Published: September 27, 2010

Rufus Fraanje, Justin Rice, Michel Verhaegen, and Niek Doelman, "Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering," J. Opt. Soc. Am. A 27, A235-A245 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Morari and E. Zafiriou, Robust Process Control (Prentice Hall, 1989).
  2. C. Vogel, “Sparse matrix methods for wavefront reconstruction revisited,” Proc. SPIE 5490, 1327–1335 (2004). [CrossRef]
  3. M. Le Louarn, N. Hubin, M. Sarazin, and A. Tokovinin, “New challenges for adaptive optics: Extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000). [CrossRef]
  4. B. Ellerbroek, “Efficient computation of minimum variance wavefront reconstructors using sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002). [CrossRef]
  5. L. Gilles, C. Vogel, and B. Ellerbroek, “Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002). [CrossRef]
  6. L. Poyneer, D. Gavel, and J. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002). [CrossRef]
  7. M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Proceedings of Adaptive Optics: Analysis and Methods (2007), pp. 1–3.
  8. L. Lessard, M. West, D. MacMynowski, and S. Lall, “Warm-started wavefront reconstruction for adaptive optics,” J. Opt. Soc. Am. A 25, 1147–1155 (2008). [CrossRef]
  9. M. Jorgenson and G. Aitken, “Prediction of atmospherically induced wave-front degradations,” Opt. Lett. 17, 466–468 (1992). [CrossRef] [PubMed]
  10. C. Schwartz, G. Baum, and E. Ribak, “Turbulence-degraded wave fronts as fractal surfaces,” J. Opt. Soc. Am. A 11, 444–451 (1994). [CrossRef]
  11. D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890–901 (2003). [CrossRef]
  12. B. L. Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004). [CrossRef]
  13. K. Hinnen, M. Verhaegen, and N. Doelman, “Robust spectral factor approximation of discrete-time frequency domain power spectra,” Automatica 41, 1791–1798 (2005). [CrossRef]
  14. A. Beghi, A. Cenedese, and A. Madiero, “Atmospheric turbulence prediction: a PCA approach,” in Proceedings of the 46th IEEE Conference on Decision and Control (IEEE, 2007), pp. 566–571. [CrossRef]
  15. A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008). [CrossRef]
  16. K. Hinnen, M. Verhaegen, and N. Doelman, “Exploiting the spatiotemporal correlation in adaptive optics using data-driven H2-optimal control,” J. Opt. Soc. Am. A 24, 1714–1725 (2007). [CrossRef]
  17. N. Doelman, R. Fraanje, I. Houtzager, and M. Verhaegen, “Real-time optimal control for adaptive optics systems,” Eur. J. Control 15, 480–488 (2009). [CrossRef]
  18. L. Poyneer, B. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24, 2645–2660 (2007). [CrossRef]
  19. S. Chandrasekaran, P. Dewilde, M. Gu, T. Pals, and A.-J. van der Veen, “Fast stable solvers for sequentially semi-separable linear systems of equations,” in Lecture Notes in Computer Science (Springer Verlag, 2002), pp. 545–554. [CrossRef]
  20. J. Rice and M. Verhaegen, “Distributed control: A sequentially semi-separable approach for spatially heterogeneous linear systems,” IEEE Trans. Autom. Control 54, 1270–1283 (2009). [CrossRef]
  21. R. Conan, “Modélisation des effects de l’échelle externe de cohérence spatiale du front d’onde pour l’observation à haure résolution angulaire en astronomie,” Ph.D. dissertation (Université de Nice-Sophia Antipolis, 2000).
  22. J. Rice and M. Verhaegen, “Distributed control of spatially invariant systems in multiple dimensions: A structure preserving computational technique” (submitted for publication, http://www.dcsc.tudelft.nl/jrice/Publications.htm).
  23. T. Laakso, V. Välimäki, M. Karjalainen, and U. Laine, “Splitting the unit delay—tools for fractional delay filter design,” IEEE Signal Process. Mag. 13, 30–60 (1996). [CrossRef]
  24. P. Brockwell and R. Davies, Time Series: Theory and Methods (Springer, 1991). [CrossRef]
  25. M. Verhaegen and V. Verdult, Filtering and System Identification—A Least Squares Approach (Cambridge University Press, 2007). [CrossRef]
  26. P. Van Overschee and B. De Moor, “Subspace algorithms for the stochastic identification problem,” Automatica 29, 649–660 (1993). [CrossRef]
  27. B. Anderson and J. Moore, Optimal Filtering (Prentice-Hall, 1979).
  28. C. Vogel and Q. Yang, “Multigrid algorithm for least-squares wave-front reconstruction,” Appl. Opt. 45, 705–715 (2006). [CrossRef] [PubMed]

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