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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

  • Vol. 11, Iss. 2 — Feb. 1, 1994
  • pp: 783–805

First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes

Brent L. Ellerbroek  »View Author Affiliations


JOSA A, Vol. 11, Issue 2, pp. 783-805 (1994)
http://dx.doi.org/10.1364/JOSAA.11.000783


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Abstract

An approach is presented for evaluating the performance achieved by a closed-loop adaptive-optics system that is employed with an astronomical telescope. This method applies to systems incorporating one or several guide stars, a wave-front reconstruction algorithm that is equivalent to a matrix multiply, and one or several deformable mirrors that are optically conjugate to different ranges. System performance is evaluated in terms of residual mean-square phase distortion and the associated optical transfer function. This evaluation accounts for the effects of the atmospheric turbulence Cn2(h) and wind profiles, the wave-front sensor and deformable-mirror fitting error, the sensor noise, the control-system bandwidth, and the net anisoplanatism for a given constellation of natural and/or laser guide stars. Optimal wave-front reconstruction algorithms are derived that minimize the telescope’s field-of-view-averaged residual mean-square phase distortion. Numerical results are presented for adaptive-optics configurations incorporating a single guide star and a single deformable mirror, multiple guide stars and a single deformable mirror, or multiple guide stars and two deformable mirrors.

© 1994 Optical Society of America

History
Original Manuscript: August 7, 1992
Revised Manuscript: January 19, 1993
Manuscript Accepted: December 14, 1992
Published: February 1, 1994

Citation
Brent 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-2-783


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References

  1. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991). [CrossRef]
  2. C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991). [CrossRef]
  3. J. F. Belsher, D. L. Fried, “Expected antenna gain when correcting tilt-free wavefronts,” (Optical Sciences Company, Placentia, Calif., 1984).
  4. M. Welsh, “Imaging performance analysis of adaptive telescopes using laser guide stars,” Appl. Opt. 30, 5021–5030 (1991). [CrossRef] [PubMed]
  5. D. L. Fried, “Anisoplanatism in adaptive optics,”J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]
  6. R. Foy, A. Labeyrie, “Feasibility of adaptive telescopes using laser probe,” Astron. Astrophys. 152, 129–131 (1985).
  7. B. M. Welsh, 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). [CrossRef]
  8. J. M. Beckers, “Increasing the size of the isoplanatic patch within multiconjugate adaptive optics,” in Proceedings of European Southern Observatory Conference and Workshop on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed., Vol. 30 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.
  9. D. Johnston, B. Welsh, “Estimating contributions of turbulence layers to total wave-front phase aberration,” in Atmospheric Propagation and Remote Sensing, A. Kohnle, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1688, 510–521 (1992). [CrossRef]
  10. F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991). [CrossRef]
  11. R. Hudgin, “Wave-front compensation error due to finite corrector-element size,”J. Opt. Soc. Am. 67, 393–396 (1977). [CrossRef]
  12. E. P. Wallner, “Optimal wave-front correction using slope measurement,”J. Opt. Soc. Am. 73, 1771–1776 (1983). [CrossRef]
  13. 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]
  14. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,”J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  15. J. Herrmann, “Least-squares wave-front errors of minimum norm,”J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  16. D. P. Greenwood, D. L. Fried, “Power spectra requirements for wave-front compensation systems,”J. Opt. Soc. Am. 66, 193–206 (1976). [CrossRef]
  17. G. A. Tyler, “Turbulence-induced adaptive-optics performance evaluation: degradation in the time domain,” J. Opt. Soc. Am. A 1, 251–262 (1984). [CrossRef]
  18. Equations (2.1) and (2.2) imply that all modes of the wave-front-distortion profile must be compensated at the same control bandwidth. This simplification corresponds to the limitations of the existing closed-loop adaptive-optics systems with which we are familiar (see Ref. 1). More general approaches are possible but are not considered here.
  19. This objective represents a departure from previous studies of reconstruction algorithms for multiconjugate systems (see Ref. 9), which have instead developed reconstructors to estimate the contributions of individual atmospheric-turbulence layers to the total wave-front-distortion profile.
  20. Associated solutions for Λ and γare Λ = RQ(I− R−1AS−1G) (GTs−1G)−1and γ= A. These solutions are not unique, since the matrix (QT− I) is singular.
  21. The square root R1/2of a symmetric, positive-definite matrix Ris the quantity OTΛ1/2O, where the rows of the unitary matrix Oare the eigenvectors of Rand Λ is a diagonal matrix formed from the corresponding (positive) eigenvalues.
  22. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978). [CrossRef]
  23. R. J. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multi-parameter integrals,” (Massachusetts Institute of Technology, Cambridge, Mass., 1988).
  24. B. M. Welsh, C. S. Gardner, “Performance analysis of adaptive-optics systems using slope sensors,” J. Opt. Soc. Am. A 6, 1913–1923 (1989). [CrossRef]
  25. F. Olver, “Bessel functions of integer order,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, eds. (Dover, New York, 1973), pp. 358–389.
  26. D. L. Fried, “Limited resolution looking down through the atmosphere,”J. Opt. Soc. Am. 56, 1380–1384 (1966). [CrossRef]
  27. R. R. Beland, J. H. Brown, R. E. Good, E. A. Murphy, “Optical turbulence characterization of AMOS,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).
  28. D. P. Greenwood, “Bandwidth specifications for adaptive optics systems,”J. Opt. Soc. Am. 67, 390–392 (1977). [CrossRef]
  29. J. Bahcall, R. Soniera, Astrophys. J. Suppl. 47, 357 (1981). [CrossRef]
  30. Y. Luke, “Integrals of Bessel functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, eds. (Dover, New York, 1973), pp. 479–494.
  31. F. Oberhettinger, “Hypergeometric functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, eds. (Dover, New York, 1973), pp. 555–566.
  32. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1987).

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