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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 8 — Aug. 1, 2011
  • pp: 1732–1740

Wavefront propagation in turbulence: an unified approach to the derivation of angular correlation functions

Guillaume Molodij  »View Author Affiliations


JOSA A, Vol. 28, Issue 8, pp. 1732-1740 (2011)
http://dx.doi.org/10.1364/JOSAA.28.001732


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Abstract

A general expression of the spatial correlation functions of quantities related to the phase fluctuations of a wave that have propagated through the atmospheric turbulence are derived. A generalization of the method to integrand containing the product of an arbitrary number of hypergeometric functions is presented. The formalism is able to give the coefficients of phase-expansion functions orthogonal over an arbitrary circularly symmetric weighting function for an isotropic turbulence spectrum, as well as to describe the effect of the finite outer and inner scales of the turbulence and to describe the spherical propagation or to derive the effects of the analytical operators acting on the phase such as the derivatives of any order. The derivation of the generalized integrals with multiparameters is based on the Mellin transforms integration method.

© 2011 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(350.1270) Other areas of optics : Astronomy and astrophysics

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: March 16, 2011
Revised Manuscript: June 26, 2011
Manuscript Accepted: June 27, 2011
Published: July 28, 2011

Citation
Guillaume Molodij, "Wavefront propagation in turbulence: an unified approach to the derivation of angular correlation functions," J. Opt. Soc. Am. A 28, 1732-1740 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-8-1732


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References

  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium(Dover, 1961).
  2. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposure,” J. Opt. Soc. Am. 56, 1372–1379 (1966). [CrossRef]
  3. R. F. Lutomirski and H. Yura, “Wave structure function and mutual coherence function of an optical wave in a turbulent atmosphere,” J. Opt. Soc. Am. A 61, 482–487 (1971). [CrossRef]
  4. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975). [CrossRef]
  5. G. C. Valley, “Long and short term Strehl ratio for turbulence with finite inner and outer scales,” Appl. Opt. 18, 984–987(1979). [CrossRef] [PubMed]
  6. A. Consortini, L. Ronchi, and E. Moroder, “Role of the outer scale of turbulence in atmospheric degradation of optical images,” J. Opt. Soc. Am. 63, 1246–1248 (1973). [CrossRef]
  7. 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]
  8. M. Bertolotti, M. Carnevale, A. Consortini, and L. G. Ronchi, “Optical propagation—problems and trends,” Opt. Acta 26, 507–529 (1979). [CrossRef]
  9. R. G. Frehlich and G. R. Ochs, “Effects of saturation on the optical scintillometer,” Appl. Opt. 29, 548–553, (1990). [CrossRef] [PubMed]
  10. J. H. Churnside and S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 4, 1923–1930 (1987). [CrossRef]
  11. J. Borgnino, F. Martin, and A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992). [CrossRef]
  12. G. C. Valley and S. M. Wandzura, “Spatial correlation of phase expension coefficients for propagation through atmospheric turbulence,” J. Opt. Soc. Am. 69, 712–717 (1979). [CrossRef]
  13. F. Chassat, “Calcul du domaine d’isoplanetisme d’un systeme d’optique adaptative fonctionnant a travers la turbulence atmospherique,” J. Opt. 20, 13–23 (1989). [CrossRef]
  14. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  15. 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, 1978), pp. 9–43.
  16. G. Molodij and G. Rousset, “Angular correlation of Zernike polynomial coefficients using laser guide star in adaptive optics,” J. Opt. Soc. Am. A 14, 1949–1966 (1997). [CrossRef]
  17. R. J. Sasiela and J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of the outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A 10, 646–660 (1993). [CrossRef]
  18. R. E. Hufnagel, Optical Propagation Through Turbulence, OSA Technical Digest Series, (Optical Society of America, 1974), pp. WA1-1–WA1-4.
  19. D. J. Shelton and R. J. Sasiela, “Mellin transform methods applied to integral evaluation: Taylor series and asymptotic approximations,” J. Math. Phys. 34, 2572–2618 (1993). [CrossRef]
  20. G. A. Tyler, “Analysis of propagation through turbulence: evaluation of an integral involving the product of three Bessel fonctions,” J. Opt. Soc. Am. A 7, 1218–1223 (1990). [CrossRef]
  21. F. Roddier, “The effect of atmospheric turbulence in optical astromomy,” in Progress in Optics, E.Wolf, ed., (North Holland, 1981), Vol.  19, pp. 283–376. [CrossRef]
  22. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large reynolds,” Dokl. Akad. Nauk SSSR 30, 301–305 (1941).
  23. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225(1988). [CrossRef] [PubMed]
  24. G. Molodij and J. Rayrole, “Performance analysis for T.H.E.M.I.S(*) image stabilizer optical system. II. Anisoplanatism limitations (*) Telescope Heliographique pour l’Etude DU Magnetisme et des Instabilites de l’atmosphere Solaire,” Astron. Astrophys. Suppl. 128, 229–244 (1998). [CrossRef]
  25. G. Rousset, “Adaptative optics,” in Adaptive Optics for Astronomy, D.Alloin and J.M.Mariotti, ed., NATO Advanced Study Institute Series (Kluwer, 1994), pp. 115–137.
  26. E. Gendron and P. Lena, “Astronomical adaptive optics. I: Modal control optimization,” Astron. Astrophys. 291, 337–347(1994).
  27. R. Dautray and J. L. Lions, Transformations de Mellin Analyse Mathematique et Calcul Numerique (Masson, 1987), Vol.  3.
  28. S. Colombo, Les Transformations de Mellin et de Hankel (CNRS, 1959).
  29. J. M. Conan, P. Y. Madec, and G. Rousset, “Wavefront temporal spectra in high resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995). [CrossRef]
  30. F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “A grating scale monitor for atmospheric turbulence measurements. I,” Astron. Astrophys. Suppl. 108, 173–180(1994).
  31. A. Agabi, J. Borgnino, F. Martin, A. Tokovinin, and A. Ziad, “A grating scale monitor for atmospheric turbulence measurements. II,” Astron. Astrophys. Suppl. Ser. 109, 557–562(1995).
  32. J. Primot, G. Rousset, J. Fontanella, “Deconvolution from wave-front sensing—a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608(1990). [CrossRef]
  33. G. Molodij, J. Rayrole, P. Y. Madec, and F. Colson, “Performance analysis for T.H.E.M.I.S(*) image stabilizer optical system. I,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996). [CrossRef]
  34. R. J. Sasiela, “A unified approch to electromagnetic wave propagation in turbulence and evaluation of multiparameter integrals,” Tech. Rep. 807 (MIT Lincoln Laboratory, 1988).

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