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Applied Optics

Applied Optics


  • Vol. 41, Iss. 17 — Jun. 10, 2002
  • pp: 3385–3391

Effects of a finite outer scale on the measurement of atmospheric-turbulence statistics with a Hartmann wave-front sensor

Shen Feng and Jiang Wenhan  »View Author Affiliations

Applied Optics, Vol. 41, Issue 17, pp. 3385-3391 (2002)

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Phase-structure and aperture-averaged slope-correlated functions with a finite outer scale are derived based on the Taylor hypothesis and a generalized spectrum, such as the von Kármán modal. The effects of the finite outer scale on measuring and determining the character of atmospheric-turbulence statistics are shown especially for an approximately 4-m class telescope and subaperture. The phase structure function and atmospheric coherent length based on the Kolmogorov model are approximations of the formalism we have derived. The analysis shows that it cannot be determined whether the deviation from the power-law parameter of Kolmogorov turbulence is caused by real variations of the spectrum or by the effect of the finite outer scale.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.3920) Atmospheric and oceanic optics : Meteorology
(010.7350) Atmospheric and oceanic optics : Wave-front sensing

Original Manuscript: June 11, 2001
Revised Manuscript: December 6, 2001
Published: June 10, 2002

Shen Feng and Jiang Wenhan, "Effects of a finite outer scale on the measurement of atmospheric-turbulence statistics with a Hartmann wave-front sensor," Appl. Opt. 41, 3385-3391 (2002)

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  1. D. Dyton, B. Pierson, B. Spiebusch, J. Gonglewski, “Atmospheric structure function measurements with a Shack–Hartmann wave-front sensor,” Opt. Lett. 17, 1737–1739 (1992). [CrossRef]
  2. T. W. Nicholls, G. D. Boreman, J. C. Dainty, “Use of a Shack–Hartmann wave-front sensor to measure deviations from a Kolmogorov phase spectrum,” Opt. Lett. 20, 2460–2462 (1995). [CrossRef]
  3. E. E. Silbaugh, B. M. Welsh, M. C. Roggemann, “Characterization of atmospheric turbulence phase statistics using wave-front slope measurements,” J. Opt. Soc. Am. A 13, 2453–2460 (1996). [CrossRef]
  4. R. W.-H. Szeto, R. R. Butts, “Atmospheric characterization in the presence of strong additive measurement noise,” J. Opt. Soc. Am. A 15, 1698–1707 (1998). [CrossRef]
  5. D. L. Walters, D. L. Favier, J. R. Hines, “Vertical path atmospheric MTF measurements,” J. Opt. Soc. Am. 69, 828–837 (1979). [CrossRef]
  6. M. Sarazzin, F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).
  7. D. L. Fried, “Differential angle of arrival: theory, evaluation, and measurement feasibility,” Radio Sci. 10, 71–76 (1975). [CrossRef]
  8. B. L. Ellerbroek, D. J. Lee, J. D. Barchers, “Analysis of atmospheric turbulence measurements obtained with the Starfire Optical Range 3.5-m telescope adaptive optics system,” In Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 212–224 (1999). [CrossRef]
  9. B. L. Ellerbroek, “Including outer scale effects in zonal adaptive optics calculations,” Appl. Opt. 36, 9456–9467 (1997). [CrossRef]
  10. N. Takato, I. Yamaguchi, “Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale,” J. Opt. Soc. Am. A. 12, 958–963 (1995). [CrossRef]
  11. D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A. 8, 1568–1573 (1991). [CrossRef]
  12. 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]
  13. B. E. Stribling, B. M. Welsh, M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” in Atmospheric Propagation and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE, 2471, 181–196 (1995). [CrossRef]
  14. G. A. Tyler, “Bandwidth consideration for tracking through turbulence,” J. Opt. Soc. Am. A 11, 358–367 (1994). [CrossRef]
  15. E. P. Wallner, “Optimal wave front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983). [CrossRef]

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