OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 38, Iss. 18 — Jun. 20, 1999
  • pp: 3857–3868

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

Brent L. Ellerbroek and David W. Tyler  »View Author Affiliations

Applied Optics, Vol. 38, Issue 18, pp. 3857-3868 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (212 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF’s that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

© 1999 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(100.1830) Image processing : Deconvolution
(110.6150) Imaging systems : Speckle imaging
(110.6770) Imaging systems : Telescopes

Original Manuscript: October 7, 1998
Revised Manuscript: February 22, 1999
Published: June 20, 1999

Brent L. Ellerbroek and David W. Tyler, "Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems," Appl. Opt. 38, 3857-3868 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. M. Stepp, ed., Advanced Technology Optical Telescopes V, SPIE Proc.2199, (1994).
  2. M. A. Ealey, F. Merkle, eds., Adaptive Optics in Astronomy, SPIE Proc.2201, (1994).
  3. J. P. Veran, F. Rigaut, H. Maitre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997). [CrossRef]
  4. M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” J. Opt. Soc. Am. A 9, 1525–1535 (1992). [CrossRef]
  5. F. Rigaut, B. L. Ellerbroek, M. J. Northcott, “Comparison of adaptive-optics technologies for large astronomical telescopes,” Appl. Opt. 36, 2856–2864 (1997). [CrossRef] [PubMed]
  6. B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North Telescope,” Astron. Soc. Pac. 110, 165–185 (1998). [CrossRef]
  7. F. Rigaut, E. Gendron, “Dual adaptive optics, a solution to the tilt determination problem using laser guide star,” in Laser Guide Star Adaptive Optics Workshop, R. Fugate, ed. (Starfire Optical Range, Albuquerque, N.M., 1992), pp. 582–590.
  8. N. Hubin, B. Theodore, P. Petitjean, B. Delabre, “Adaptive optics system for the Very Large Telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 34–45 (1994). [CrossRef]
  9. D. W. Tyler, B. L. Ellerbroek, “Spectrometer slit-power-coupling calculations for natural and laser guide-star adaptive optics,” Appl. Opt. 37, 4569–4576 (1998). [CrossRef]
  10. J. W. Goodman, “Frequency analysis of optical imaging systems,” in Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 101–133.
  11. R. E. Hufnagel, N. R. Stanley, “Modulation transfer function associated with transmission through turbulent media,” J. Opt. Soc. Am. 54, 52–61 (1964). [CrossRef]
  12. M. Born, E. Wolf, “The diffraction theory of aberrations,” in Principles of Optics, 6 ed. (Pergamon, Sydney, Australia, 1989), pp. 459–490.
  13. V. N. Mahajan, “Random aberrations,” in Aberration Theory Made Simple, vol. TT6 of SPIE Tutorial Text Series (SPIE, Bellingham, Wash., 1991).
  14. T. Nakajima, C. A. Haniff, “Partial adaptive compensation and passive interferometry with large ground-based telescopes,” Astron. Soc. Pac. 105, 509–520 (1993). [CrossRef]
  15. 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]
  16. D. W. Tyler, B. L. Ellerbroek, “Sky coverage calculations for spectrometer slit power coupling with adaptive optics compensation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 201–209 (1998). [CrossRef]
  17. G. A. Tyler, D. L. Fried, “Image position error associated with a quadrant detector,” J. Opt. Soc. Am. 72, 804–808 (1982). [CrossRef]
  18. B. M. Welsh, B. L. Ellerbroek, M. C. Roggemann, T. L. Pennington, “Shot noise performance of Hartmann and shearing interferometer wave front sensors,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 277–288 (1995). [CrossRef]

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