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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 4 — Feb. 20, 2006
  • pp: 1339–1352

Wave front sensor-less adaptive optics: a model-based approach using sphere packings

Martin J. Booth  »View Author Affiliations


Optics Express, Vol. 14, Issue 4, pp. 1339-1352 (2006)
http://dx.doi.org/10.1364/OE.14.001339


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Abstract

Certain adaptive optics systems do not employ a wave front sensor but rather maximise a photodetector signal by appropriate control of an adaptive element. The maximisation procedure must be optimised if the system is to work efficiently. Such optimisation is often implemented empirically, but further insight can be obtained by using an appropriate mathematical model. In many practical systems aberrations can be accurately represented by a small number of modes of an orthogonal basis, such as the Zernike polynomials. By heuristic reasoning we develop a model for the operation of such systems and demonstrate a link with the geometrical problems of sphere packings and coverings. This approach aids the optimisation of control algorithms and is illustrated by application to direct search and hill climbing algorithms. We develop an efficient scheme using a direct maximisation calculation that permits the measurement of N Zernike modes with only N +1 intensity measurements.

© 2006 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

ToC Category:
Adaptive Optics

History
Original Manuscript: November 15, 2005
Revised Manuscript: January 20, 2006
Manuscript Accepted: February 13, 2006
Published: February 20, 2006

Virtual Issues
Vol. 1, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Martin Booth, "Wave front sensor-less adaptive optics: a model-based approach using sphere packings," Opt. Express 14, 1339-1352 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1339


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References

  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, 1998).
  2. M. J. Booth, M. A. A. Neil, R. Ju¡skaitis and T.Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Nat. Acad. Sci. 99, 5788-5792 (2002). [CrossRef] [PubMed]
  3. A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Technol. 67, 36-44 (2005). [CrossRef]
  4. L. Sherman, J. Y. Ye, O. Albert and T. B. Norris,"Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206, 65-71 (2002). [CrossRef] [PubMed]
  5. P. N. Marsh, D. Burns and J. M. Girkin, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express 11, 1123-1130 (2003). [CrossRef] [PubMed]
  6. O. Albert, L. Sherman, G. Mourou, T. B. Norris and G. Vdovin, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25, 52-54 (2000). [CrossRef]
  7. W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002). [PubMed]
  8. E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004). [CrossRef]
  9. A. C. F. Gonte and R. Dandliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002). [CrossRef]
  10. M. Vorontsov, "Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion," J. Opt. Soc. Am. A 19, 356-368 (2002). [CrossRef]
  11. M. J. Booth, T. Wilson, H.-B. Sun, T. Ota and S. Kawata, "Methods for the characterisation of deformable membrane mirrors," Appl. Opt. 44, 5131-5139 (2005). [CrossRef] [PubMed]
  12. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Academic Press, London, 1984).
  13. M. Born and E. Wolf, Principles of Optics, 6th Edition, (Pergamon Press, 1983).
  14. Z. Michalewicz and D. B. Fogel, How to Solve It: Modern Heuristics, (Springer, Berlin, 2000).
  15. J. H. Conway and N. J. A. Sloan, Sphere Packings, Lattices and Groups, 3rd Edition, (Springer-Verlag, 1998).
  16. T. C. Hales, "An overview of the Kepler conjecture," http://xxx.lanl.gov/ math.MG/9811071 (1999).
  17. R. Kershner, "The number of circles covering a set," Am. J. Math. 61, 665-671 (1939). [CrossRef]
  18. E. Vitterbo and J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. Inf. Theory 45, 1639-1642 (1999). [CrossRef]
  19. W. Press, S. Teukolsky, W. Vetterling and B. Flannery, Numerical Recipes in C, 2nd Edition, (Cambridge University Press, 1992).
  20. M. A. A. Neil, M. J. Booth and T. Wilson, "New modal wavefront sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000). [CrossRef]
  21. R. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-277 (1976). [CrossRef]

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