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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. 30, Iss. 5 — May. 1, 2013
  • pp: 859–870

Generalized orthogonal wavelet phase reconstruction

Travis W. Axtell and Roberto Cristi  »View Author Affiliations


JOSA A, Vol. 30, Issue 5, pp. 859-870 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000859


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Abstract

Phase reconstruction is used for feedback control in adaptive optics systems. To achieve performance metrics for high actuator density or with limited processing capabilities on spacecraft, a wavelet signal processing technique is advantageous. Previous derivations of this technique have been limited to the Haar wavelet. This paper derives the relationship and algorithms to reconstruct phase with O(n) computational complexity for wavelets with the orthogonal property. This has additional benefits for performance with noise in the measurements. We also provide details on how to handle the boundary condition for telescope apertures.

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.0100) Image processing : Image processing
(100.7410) Image processing : Wavelets

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: October 19, 2012
Revised Manuscript: March 13, 2013
Manuscript Accepted: March 13, 2013
Published: April 12, 2013

Citation
Travis W. Axtell and Roberto Cristi, "Generalized orthogonal wavelet phase reconstruction," J. Opt. Soc. Am. A 30, 859-870 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-859


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References

  1. F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
  2. P. Y. Bely, ed., The Design and Construction of Large Optical Telescopes (Springer, 2003).
  3. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  4. L. A. Poyneer, D. T. Gavel, and J. M. 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]
  5. D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  6. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  7. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  8. K. Freischlad, “Wavefront reconstruction from noisy slope or difference data using the discrete Fourier transform,” Proc. SPIE 551, 74–80 (1985). [CrossRef]
  9. L. Gilles, C. R. Vogel, and B. L. Ellerbroek, “Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002). [CrossRef]
  10. D. G. MacMartin, “Local, hierarchic, and iterative reconstructors for adaptive optics,” J. Opt. Soc. Am. A 20, 1084–1093 (2003). [CrossRef]
  11. L. Gilles, “Sparse minimum-variance open-loop reconstructors for extreme adaptive optics: order N multigrid versus preordered Cholesky factorization,” Proc. SPIE 5169, 201–205 (2003). [CrossRef]
  12. C. R. Vogel, “Sparse matrix methods for wavefront reconstruction, revisited,” Proc. SPIE 5490, 1327–1335 (2004). [CrossRef]
  13. C. R. Vogel and Q. Yang, “Multigrid algorithm for least-squares wavefront reconstruction,” Appl. Opt. 45, 705–715 (2006). [CrossRef]
  14. C. Béchet, M. Tallon, and E. Thiébaut, “FRIM: minimum-variance reconstructor with a fractal iterative method,” Proc. SPIE 6272, 62722U (2006). [CrossRef]
  15. E. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010). [CrossRef]
  16. J. Herrmann, “Phase variance and Strehl ratio in adaptive optics,” J. Opt. Soc. Am. A 9, 2257–2258 (1992). [CrossRef]
  17. M. Rosensteiner, “Cumulative reconstructor: fast wavefront reconstruction algorithm for extremely large telescopes,” J. Opt. Soc. Am. A 28, 2132–2138 (2011). [CrossRef]
  18. C. C. de Visser and M. Verhaegen, “Wavefront reconstruction in adaptive optics systems using nonlinear multivariate splines,” J. Opt. Soc. Am. A 30, 82–95 (2013). [CrossRef]
  19. F. U. Dowla, “Fast Fourier and wavelet transforms for wavefront reconstruction in adaptive optics,” Proc. SPIE 4124, 118–127 (2000). [CrossRef]
  20. P. J. Hampton, P. Agathoklis, and C. Bradley, “A new wave-front reconstruction method for adaptive optics systems using wavelets,” IEEE J. Sel. Top. Signal Process. 2, 781–792 (2008). [CrossRef]
  21. P. J. Hampton, “Robust order N wavelet filterbanks to perform 2-D numerical integration directly from partial difference or gradient measurements,” Ph.D. thesis (University of Victoria, 2009).
  22. P. J. Hampton, P. Agathoklis, R. Conan, and C. Bradley, “Closed-loop control of a woofer-tweeter adaptive optics system using wavelet-based phase reconstruction,” J. Opt. Soc. Am. A 27, A145–A156 (2010). [CrossRef]
  23. D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, 1984).
  24. W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial (SIAM, 2000).
  25. P. P. Vaidyanathan, Multirate Systems and Filter Banks(Prentice-Hall, 1993).
  26. C. Shannon, “The mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423, 623–656 (1948).
  27. A. Haar, “Zur Theorie der orthogonalen Funktionensysteme,” Ph.D. thesis (University of Göttingen, 1909).

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