OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 5 — May. 1, 1994
  • pp: 1667–1673

Wave-front curvature sensing from a single defocused image

Paul Hickson  »View Author Affiliations

JOSA A, Vol. 11, Issue 5, pp. 1667-1673 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (844 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The possibility of sensing the curvature and the slope of a distorted wave front from a single defocused star image is investigated. The suggested technique is similar to the differential curvature-sensing method of Roddier [ R&D note 87-3 ( National Optical Astronomy Observatories, Tucson, Ariz., 1987)] but uses only a single sensor at a point either before or after the focus. The signal-to-noise ratio that is achievable with such a sensor is ultimately limited by atmospheric scintillation to a value of the order of Q r 0 2 / λ z 0, where r0 is Fried’s correlation scale, λ is the wavelength, and z0 is the root-mean-square distance through the atmosphere, weighted by the refractive-index structure constant Cn2. At the best astronomical sites, with an optimal adaptive-optics system, a value of Q 50 should be achievable. Adaptive-optics systems that use such a sensor should be capable of achieving an increase in the effective atmospheric correlation scale of a factor of Q 6 / 5; hence a single-image curvature sensor should be practical whenever D / r 0 Q 6 / 5. This condition is shown to hold at good astronomical sites even for telescopes as large as 8 m and wavelengths as short as 0.5 μm. In addition to optical and mechanical simplicity, the single-image sensor offers the advantage of reduced detector read noise and potentially higher efficiency compared with those from a differential system.

© 1994 Optical Society of America

Original Manuscript: December 7, 1992
Revised Manuscript: November 17, 1993
Manuscript Accepted: November 18, 1993
Published: May 1, 1994

Paul Hickson, "Wave-front curvature sensing from a single defocused image," J. Opt. Soc. Am. A 11, 1667-1673 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Roddier, “Curvature sensing: a diffraction theory,” R&D note 87-3 (National Optical Astronomy Observatories, Tucson, Ariz., 1987), pp. 1–5.
  2. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988). [CrossRef] [PubMed]
  3. F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wavefront sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988). [CrossRef]
  4. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966). [CrossRef]
  5. A. H. Mikesell, Publ. U.S. Naval Obs., Second Series 17, Part TV, 141 (1955).
  6. S. H. Reiger, “Starlight scintillation and atmospheric turbulence,” Astron. J. 68, 395–406 (1963). [CrossRef]
  7. A. T. Young, “Photometric error analysis. VIII. The temporal power spectrum of scintillation,” Appl. Opt. 8, 869–885 (1969). [CrossRef] [PubMed]
  8. T. Wang, J. Strohbehn, “Log-normal paradox in atmospheric scintillations,” J. Opt. Soc. Am. 64, 583–591 (1974). [CrossRef]
  9. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1691 (1975). [CrossRef]
  10. G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of laser light,” J. Opt. Soc. Am. 69, 796–798 (1979). [CrossRef]
  11. S. F. Clifford, R. J. Hill, “Relation between irradiance and log-amplitude variance for optical scintillation described by the K distribution,” J. Opt. Soc. Am. 71, 112–114 (1981). [CrossRef]
  12. M. Borne, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  13. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 8.
  14. F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990). [CrossRef]
  15. B. L. Ellerbroek, “Adaptive optics performance predictions for large telescope under good seeing conditions,” in Conference on Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 411–413.
  16. P. H. Hu, J. Stone, T. Stanley, “Application of Zernike polynomials to atmospheric propagation problems,” J. Opt. Soc. Am. A 6, 1595–1608 (1989). [CrossRef]
  17. F. Roddier, M. Northcott, J. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991). [CrossRef]
  18. R. E. Hufnagel, N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” J. Opt. Soc. Am. 54, 52–61 (1964). [CrossRef]
  19. G. Burley, Department of Geophysics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada (personal communication, 1993).

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.


Fig. 1

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited