OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 11 — Nov. 1, 1994
  • pp: 2871–2886

Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths

Brent L. Ellerbroek, Charles Van Loan, Nikos P. Pitsianis, and Robert J. Plemmons  »View Author Affiliations


JOSA A, Vol. 11, Issue 11, pp. 2871-2886 (1994)
http://dx.doi.org/10.1364/JOSAA.11.002871


View Full Text Article

Enhanced HTML    Acrobat PDF (1978 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The performance of a closed-loop adaptive-optics system may in principle be improved by selection of distinct and independently optimized control bandwidths for separate components, or modes, of the wave-front-distortion profile. We describe a method for synthesizing and optimizing a multiple-bandwidth adaptive-optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. The approach is applicable to adaptive-optics systems that use either one or several wave-front sensing beacons and also to systems that include multiple deformable mirrors for atmospheric-turbulence compensation across an extended field of view. Numerical results are presented for the case of an atmospheric-turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack–Hartmann wave-front sensor with from 8 to 16 subapertures across the aperture of the telescope, and a continuous-face-sheet deformable mirror with actuators conjugate to the corners of the wave-front-sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave-front-sensor noise level that is permitted for the adaptive-optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system that uses only two distinct bandwidths, one of which is the zero bandwidth.

© 1994 Optical Society of America

History
Original Manuscript: February 17, 1994
Revised Manuscript: June 24, 1994
Manuscript Accepted: June 24, 1994
Published: November 1, 1994

Citation
Brent L. Ellerbroek, Charles Van Loan, Robert J. Plemmons, and Nikos P. Pitsianis, "Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths," J. Opt. Soc. Am. A 11, 2871-2886 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-11-2871


Sort:  Author  |  Year  |  Journal  |  Reset  

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. 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]
  3. R. Q. Fugate, B. L. Ellerbroek, C. H. Higgins, M. P. Jelonek, W. J. Lange, A. C. Slavin, W. J. Wild, D. M. Winker, J. M. Wynia, J. M. Spinhirne, B. R. Boeke, R. E. Ruane, J. F. Moroney, M. D. Oliker, D. W. Swindle, R. A. Cleis, “Two generations of laser-guide-star adaptive-optics experiments at the Starfire Optical Range,” J. Opt. Soc. Am. A 11, 310–324 (1994). [CrossRef]
  4. V. E. Zuez, V. P. Lukin, “Dynamic characteristics of optical adaptive systems,” Appl. Opt. 26, 139–144 (1987). [CrossRef]
  5. C. Boyer, E. Gendron, P. Y. Madec, “Adaptive optics for high resolution imagery: control algorithms for optimized modal corrections,” in Lens and Optical Systems Design, H. Zuegge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1780, 943–957 (1992).
  6. E. Gendron, “Modal control optimization in an adaptive optics system,” presented at the International Commission for Optics–16 Satellite Conference, August 2–5, 1993, Garching, Germany.
  7. C. Schwartz, G. Baum, E. N. Ribak, “Turbulence-degraded wave fronts as fractal surfaces,” J. Opt. Soc. Am. A 11, 444–451 (1994). [CrossRef]
  8. G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Lena, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).
  9. G. Rousset, J. L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P. Y. Madec, P. Gigan, J. C. Richard, M. Vittot, J. P. Gaffard, F. Rigaut, P. Lena, “The Come-On-Plus adaptive optics system: results and performance,” presented at the International Commission for Optics–16 Satellite Conference, August 2–5, 1993, Garching, Germany.
  10. F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on the 3.6 m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).
  11. G. Rousset, J. Fontanella, P. Kern, P. J. Lena, P. Gigan, F. Rigaut, J. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 336–344, 1990. [CrossRef]
  12. E. Gendron, J. Cuby, F. Rigaut, P. J. Lena, J. Fontanella, G. Rousset, J. Gaffard, C. Boyer, J. Richard, M. Vittot, F. Merkle, N. Hubin, “Come-On-Plus project: an upgrade of the Come-On adaptive optics prototype system,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 297–307 (1991). [CrossRef]
  13. F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, D. Roddier, “One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation,” J. Opt. Soc. Am. A 10, 957–965 (1993). [CrossRef]
  14. R. R. Parenti, R. J. Sasiela, “Laser-guide-star systems for astronomical applications,” J. Opt. Soc. Am. A 11, 288–3091994. [CrossRef]
  15. 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]
  16. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,”J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  17. J. Herrmann, “Least-squares wave-front errors of minimum norm,”J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  18. D. P. Greenwood, D. L. Fried, “Power spectra requirements for wave-front compensation systems,”J. Opt. Soc. Am. 66, 193–206 (1976). [CrossRef]
  19. J. Y. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,”J. Opt. Soc. Am. 68, 78–87 (1978). [CrossRef]
  20. R. J. Noll, “Zernike polynomials and atmospheric turbulence,”J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  21. G. H. Golub, C. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins U. Press, Baltimore, Md., 1989).
  22. B. 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). [CrossRef]
  23. E. P. Wallner, “Optimal wave-front correction using slope measurements,”J. Opt. Soc. Am. 73, 1771–1776 (1983). [CrossRef]
  24. 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]
  25. R. C. Fisher, An Introduction to Linear Algebra (Dickenson, Encino, Calif., 1970).
  26. Equation (2.27) requires that the matrix Sbe positive definite. Sis positive semidefinite by construction, and any eigenvector of Swith a zero eigenvalue defines a wave-front-sensor measurement mode that must be identically zero. Such measurement modes, in the cases in which they exist at all, cannot contribute to the wave-front estimate. When necessary we may replace the measurement vector sby its projection onto the subspace orthogonal to all such modes and redefine Mand Gas their restrictions to this subspace.
  27. G. A. Tyler, “Turbulence-induced adaptive-optics performance evaluation: degradation in the time domain,” J. Opt. Soc. Am. A 1, 251–262 (1984). [CrossRef]
  28. The case of a fixed, known wind direction requires a slight modification to the formulas developed in Ref. 22 for the matrices Aand S. Ensemble averaging over the direction of the wind in Eq. (3.22) of Ref. 22 now has no effect, and the ray separation vector Δmust be replaced by Δ+ (τ1− τ2)vfor the remainder of the derivation. The velocity vof the random wind must also be set to zero. The resulting formula for a general element of the matrix Aor Sis identical to Eq. (3.27) of Ref. 22, except that the term f(2δv/D, 2Δ/D) is replaced by f(0, 2|δv+ Δ|/D). The function f(a, b) remains as defined by Eq. (3.28) of Ref. 22.

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