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Applied Optics

Applied Optics


  • Vol. 40, Iss. 9 — Mar. 20, 2001
  • pp: 1321–1328

Turbulence-induced edge image waviness: theory and experiment

Mikhail S. Belen’kii, John M. Stewart, and Patti Gillespie  »View Author Affiliations

Applied Optics, Vol. 40, Issue 9, pp. 1321-1328 (2001)

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A theoretical model for the edge image waviness effect is developed for the ground-to-ground imaging scheme and validated by use of IR imagery data collected at the White Sands Missile Range. It is shown that angle-of-arrival (AA) angular anisoplanatism causes the phenomenon of edge image waviness and that the AA correlation scale, not the isoplanatic angle, characterizes the edge image waviness scale. The latter scale is determined by the angular size of the imager and a normalized atmospheric outer scale, and it does not depend on the strength of turbulence along the path. Spherical divergence of the light waves increases the edge waviness scale. A procedure for estimating the atmospheric and camera-noise components of the edge image motion is developed and implemented. A technique for mitigation of the edge image waviness that relies on averaging the effects of AA anisoplanatism on the image is presented and validated. The edge waviness variance is reduced by a factor of 2–3. The time history and temporal power spectrum of the edge image motion are obtained. These data confirm that the observed edge image motion is caused by turbulence.

© 2001 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.7030) Atmospheric and oceanic optics : Troposphere
(100.2980) Image processing : Image enhancement

Original Manuscript: March 15, 2000
Revised Manuscript: December 19, 2000
Published: March 20, 2001

Mikhail S. Belen’kii, John M. Stewart, and Patti Gillespie, "Turbulence-induced edge image waviness: theory and experiment," Appl. Opt. 40, 1321-1328 (2001)

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  1. M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997). [CrossRef]
  2. A. Barducci, I. Pippi, “Object recognition by edge analysis: a case study,” Opt. Eng. 38, 284–294 (1999). [CrossRef]
  3. L. He, J. Wu, “Application of the staring-edge tracking in laser radar,” in Free-Space Laser Communication Technologies IX, G. S. Mecherle, ed., Proc. SPIE2990, 190–197 (1997). [CrossRef]
  4. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]
  5. D. L. Fried, “Varieties of anisoplanatism,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. SPIE75, 20–29 (1976). [CrossRef]
  6. V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, New York, 1961).
  7. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 63, 207–211 (1976). [CrossRef]
  8. J. Stone, P. H. Hu, S. P. Mills, S. Ma, “Anisoplanatic effects in finite-aperture optical systems,” J. Opt. Soc. Am. A 11, 347–357 (1994). [CrossRef]
  9. R. J. Sasiela, J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A 10, 646–660 (1993). [CrossRef]
  10. D. M. Winker, “Effect of finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A 8, 1568–1573 (1991). [CrossRef]
  11. 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]
  12. M. S. Belen’kii, “Principle of equivalency of the phase difference and off-axis tilt sensing technique with a laser guide star,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 280–292 (1996). [CrossRef]
  13. M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996). [CrossRef]
  14. B. L. Ellerbroek, “Including outer scale effects in zonal adaptive optics calculations,” Appl. Opt. 36, 9456–9467 (1997). [CrossRef]
  15. R. Avila, A. Ziad, J. Borgnino, F. Martin, A. Agabi, “Theoretical spatiotemporal analysis of angle of arrival induced by atmospheric turbulence as observed with a grating scale monitor experiment,” J. Opt. Soc. Am. A 14, 3070–3082 (1997). [CrossRef]
  16. M. R. Whiteley, B. M. Welsh, M. C. Roggemann, “Incorporating higher-order modal measurements in tilt estimation: natural and laser guide star applications,” Appl. Opt. 37, 8287–8296 (1998). [CrossRef]
  17. M. S. Belen’kii, “Full-aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagation and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995). [CrossRef]
  18. M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999). [CrossRef]
  19. S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 2. [CrossRef]
  20. I. Dror, N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995). [CrossRef]

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