Skip to main content
Log in

Estimation of the Atmospheric Turbulence Parameters Using the Angle-of-Arrival Covariance Function

  • ADAPTIVE AND INTEGRAL OPTICS
  • Published:
Atmospheric and Oceanic Optics Aims and scope Submit manuscript

Abstract

The Fried’s length r0, the outer scale L0, the isoplanatism θ0, the coherence time τ0, and the profile of the optical turbulence energy \(C_{n}^{2}(h)\) are parameters of the wavefront spatiotemporal coherence. Numerous optical methods are used to determine the images quality through the estimation of the parameters r0, L0, θ0, and τ0, where numerical simulations of the transversal and longitudinal covariance (as a function of the angle-of-arrival (AA)) play a significant role. In this work, we, first, perform the statistical analysis of the fluctuations of angle-of-arrival using theoretical models of the atmospheric turbulence, and second, the statistical analysis of the AA fluctuations in solar limb images. This analysis plays a significant role in the optimization of techniques, such as adaptive optics (OA) and in interferometry, in astronomical observations with high angular resolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.

Similar content being viewed by others

REFERENCES

  1. A. Y. Shikhovtsev, P. G. Kovadlo, A. V. Kiselev, D. Y. Kolobov, V. P. Lukin, I. V. Russkikh, and M. Y. Shikhovtsev, “Modified method to detect the turbulent layers in the atmospheric boundary layer for the large solar vacuum telescope,’’ Atmosphere 12, 156 (2021).

    Article  ADS  Google Scholar 

  2. J. Borgnino, PhD Thesis (Université de Nice, 1978).

  3. M. Xu, S. Shao, Q. Liu, G. Sun, Y. Han, and N. Weng, “Optical turbulence profile forecasting and verification in the offshore atmospheric boundary layer,” Appl. Sci. 11, 8523 (2021).

    Article  Google Scholar 

  4. T. Song, Z. Cai, Y. Liu, M. Zhao, Y. Fang, X. Zhang, J. Wang, X. Li, Q. Song, and Z. Du, “Daytime optical turbulence profiling with a profiler of the differential solar limb,” Mon. Not. R. Astron. Soc. 499 (2), 1909–1917 (2020).

    Article  ADS  Google Scholar 

  5. P.G. Kovadlo, A.Y. Shikhovtsev, and V.P. Lukin, “Development of the model of turbulent atmosphere at the Large Solar Vacuum Telescope site as applied to image adaptation,” Atmos. Ocean. Opt. 32 (2), 202–206 (2019).

    Article  Google Scholar 

  6. M. Xu, S. Shao, N. Weng, L. Zhou, Q. Liu, and Y. Zhao, “Atmospheric optical turbulence characteristics over the ocean relevant to astronomy and atmospheric physics,”. Appl. Sci. 11, 10548 (2021).

    Article  Google Scholar 

  7. R. Avila, A. Ziad, J. Borgnino, F. Martin, A. Agabi and A. Tokovinin, “Theoretical spatiotemporal analysis of angle of arrival induced by atmospheric turbulence as observed with the grating scale monitor experiment,” J. Opt. Soc. Am. A 14, 3070–3082 (1997).

    Article  ADS  Google Scholar 

  8. A. Berdja, A. Irbah and J. Borgnino, “Simulation of the anisoplanatic angle-of-arrival fluctuations measured on the solar edge images,” in EDPS Conference Series in Astronomy & Astrophysics, SF2A-2002: Semaine de l’Astrophysique Francaise, Paris, France, June 24–29, 2002, Ed by F. Combes and D. Barret (EdP-Sciences, 2002), p. 215.

  9. J. Borgnino and F. Martin, “Analyse statistique des déformations aléatoires d’une surface d’onde dues à la turbulence atmosphérique au voisinage du sol. I.—Exposé de la méthode, Premiers résultats,” J. Optics (Paris) 8, 319326 (1977).

    Google Scholar 

  10. T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data”, Mon. Not. R. Astron. Soc. 369, 835–845 (2006).

    Article  ADS  Google Scholar 

  11. R. Conan, PhD Thesis (Université de Nice-Sophia Antipolis, 2000).

  12. J. Maire, PhD Thesis (Université de Nice-Sophia Antipolis, 2007).

  13. S. L. Odintsov, V. A. Gladkikh, A. P. Kamardin, and I. V. Nevzorova, “Determination of the structural characteristic of the refractive index of optical waves in the atmospheric boundary layer with remote acoustic sounding facilities,” Atmosphere 10, 711 (2019).

    Article  ADS  Google Scholar 

  14. A. Y. Shikhovtsev, P. G. Kovadlo, and A. V. Kiselev “The method to restore the profiles of atmospheric turbulence from solar observations,” Proc. SPIE 112081E (2019). https://doi.org/10.1117/12.2540073

  15. A. Shikhovtsev, P. Kovadlo, V. Lukin, A. Kiselev, D. Kolobov, E. Kopylov, M. Shikhovtsev, and F. Avdeev, “Statistics of the optical turbulence from the micrometeorological measurements at the Baykal Astrophysical Observatory site”. Atmosphere 10, 661 (2019).

    Article  ADS  Google Scholar 

  16. A. Y. Shikhovtsev, A. V. Kiselev, P. G. Kovadlo, D. Y. Kolobov, V. P. Lukin, and V. E. Tomin, “Method for estimating the altitudes of atmospheric layers with strong turbulence,” Atmos. Ocean. Opt. 33, 295–301 (2020).

    Article  Google Scholar 

  17. J. Chabé, E. Aristidi, A. Ziad, Y. Fantéi-Caujolle, H. Lantéri, C. Giordano, J. Borgnino, and C. Renaud, “Monitoring the atmospheric turbulence profile with high vertical resolution with the PML instrument.” HAL Id: hal-03122656(2021).

  18. A. Ziad, E. Aristidi, J. Chabé, and J. Borgnino, “On the isoplanatic patch size in high-angular resolution technique,” MNRAS 487 (3), 3664–3671(2019).

    ADS  Google Scholar 

  19. C. Giordanoa, A. Ziada, E. Aristidia, J. Chabéb, Y. Fanteï-Caujollea, C. Renauda, and A. Rafalimanana, “CATS: Continuous turbulence characterization station for both optical link and astronomical support,” Proc. ICSO 11852, 118522D (2021). https://doi.org/10.1117/12.2599373

  20. S. Changdong, W. Xiaoqing, W. Su, Y. Qike, H. Yajuan, Q. Chun, L. Tao, and L. Yi, “In situ measurements and neural network analysis of the profiles of optical turbulence over the Tibetan Plateau,” MNRAS 506, 3430–3438 (2021).

    Article  Google Scholar 

  21. V. P. Lukin, “Outer scale of turbulence and its influence on fluctuations of optical waves,” Phys.-Usp. 64, 280(2021).

    Article  Google Scholar 

  22. V. P. Lukin, E. V. Nosov, and B. V. Fortes, “The efficient outer scale of atmospheric turbulence,” in Proc. of the ESO/OSA Topical Meeting “Astronomy with Adaptive Optics: Present Results and Future Programs,” Sonthofen, Germany, September 7–11, 1998, Ed. by Domenico Bonaccini (European Southern Observatory, Garching, Germany, 1999), p. 619.

  23. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2 (2), 164–168. https://doi.org/10.1090/qam/10666

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to F. Bennoui or D. Bahloul.

Ethics declarations

The author declares that he has no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bennoui, F., Bahloul, D. Estimation of the Atmospheric Turbulence Parameters Using the Angle-of-Arrival Covariance Function. Atmos Ocean Opt 36, 569–577 (2023). https://doi.org/10.1134/S1024856023050202

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1024856023050202

Keywords:

Navigation