OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 44, Iss. 13 — May. 1, 2005
  • pp: 2626–2637

Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

Hongwu Ren, Richard Dekany, and Matthew Britton  »View Author Affiliations

Applied Optics, Vol. 44, Issue 13, pp. 2626-2637 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (2665 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system.

© 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

Original Manuscript: July 1, 2004
Revised Manuscript: December 11, 2004
Manuscript Accepted: December 14, 2004
Published: May 1, 2005

Hongwu Ren, Richard Dekany, and Matthew Britton, "Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm," Appl. Opt. 44, 2626-2637 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000). [CrossRef]
  2. K. R. Freischlad, C. L. Koliopoulos, “Modal estimation of a wave font from difference measurements using the discrete Fourier transform,” J. Opt. Soc. Am. A 3, 1852–1861 (1986). [CrossRef]
  3. L. A. Poyneer, D. T. Gavel, J. M. Base, “Fast wavefront reconstruction in large adaptive optics systems using the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002). [CrossRef]
  4. L. A. Poyneer, M. Troy, B. Macintosh, D. T. Gavel, “Experimental validation of Fourier-transform wavefront reconstruction at the Palomar Observatory,” Opt. Lett. 28, 798–800 (2003). [CrossRef] [PubMed]
  5. F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991). [CrossRef] [PubMed]
  6. R. J. Noll, “Phase estimates from slope-type wavefront sensors,” J. Opt. Soc. Am. 68, 139–140 (1978). [CrossRef]
  7. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  8. L. Gilles, C. R. Vogel, B. L. Ellerbroek, “A multigrid preconditioned conjugate gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002). [CrossRef]
  9. L. Gilles, “Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics,” Opt. Lett. 28, 1927–1929 (2003). [CrossRef] [PubMed]
  10. D. G. MacMartin, “Local, hierachic, and iterative reconstructors for adaptive optics,” J. Opt. Soc. Am. A 20, 1084–1093 (2003). [CrossRef]
  11. F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002). [CrossRef]
  12. D. C. Ghiglia, L. A. Romero, “Direct phase estimation from phase differences using fast elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989). [CrossRef] [PubMed]
  13. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  14. D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994). [CrossRef]
  15. H. Ren, R. Dekany, “Fast wavefront reconstruction by solving the Sylvester equation with the alternating direction implicit method,” Opt. Express 12, 3279–3296 (2004), http://www.opticsexpress.org . [CrossRef] [PubMed]
  16. R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. SPIE551, 170–176 (1985). [CrossRef]
  17. G. Rousset, “Wavefront sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, 1999). [CrossRef]
  18. B. L. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1802–1816 (2002). [CrossRef]
  19. D. S. Watkins, Fundamentals of Matrix Computations, 2nd ed. (Wiley, New York, 2002). [CrossRef]
  20. G. H. Golub, C. F. van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).
  21. K. R. Rao, P. Yip, Discrete Cosine Transform: Algorithm, Advantages, Applications (Academic, San Diego, Calif., 1990).
  22. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992). [CrossRef]
  23. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

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