Skip to main content
SpringerLink
Log in

On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: I–equations

  • Remote Sensing of Atmosphere, Hydrosphere, and Underlying Surface
  • Published:
Atmospheric and Oceanic Optics Aims and scope Submit manuscript

Abstract

Asymptotic solutions for the problem of retrieving the distribution of the structure characteristic of refractive index fluctuations from measurement data on the backscattering enhancement factor have been found. The solutions are written in terms of fractional derivatives of the enhancement factor in the case of receivers with a small aperture or via usual derivatives in the case of receivers with a large aperture. Properties of the kernel of the integral equation from which the asymptotic formulas follow have been studied in detail. Attention is paid to the fact that the kernel is oscillating in the general case. The kernel oscillations slightly affect the magnitude of the enhancement factor; however, their effect on derivatives of this factor can be significant.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. G. Vinogradov, Yu. A. Kravtsov, and V. I. Tatarskii, “The effect of intensification of back scattering by bodies that are situated in a medium having random inhomogeneities,” Radiophys. Quantum Electron. 16 (7), 818–823 (1973).

    Article  ADS  Google Scholar 

  2. A. G. Vinogradov, A. S. Gurvich, S. S. Kashkarov, Yu. A. Kravtsov, and V. I. Tatarskii, USSR Inventor’s Certificate no. 35, Byull. Izobret., No. 21 (1989).

    Google Scholar 

  3. V. A. Banakh, I. N. Smalikho, and Ch. Werner, “Numerical simulation of effect of refractive turbulence on the statistics of a coherent lidar return in the atmosphere,” Appl. Opt. 39 (33), 5403–5414 (2000).

    Article  ADS  Google Scholar 

  4. V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Ocean. Opt. 24 (5), 457–465 (2011).

    Article  Google Scholar 

  5. I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Ocean. Opt. 26 (2), 135–139 (2013).

    Article  Google Scholar 

  6. V. A. Banakh, “Enhancement of the laser return mean power at the strong optical scintillation regime in a turbulent atmosphere,” Atmos. Ocean. Opt. 26 (2), 90–95 (2013).

    Article  MathSciNet  Google Scholar 

  7. A. S. Gurvich, “Lidar sounding of turbulence based on the backscatter enhancement effect,” Izv., Atmos. Ocean. Phys. 48 (6), 585–594 (2012).

    Article  Google Scholar 

  8. A. S. Gurvich, “Lidar positioning of higher clear-air turbulence regions,” Izv., Atmos. Ocean. Phys. 50 (2), 143–151 (2014).

    Article  MathSciNet  Google Scholar 

  9. A. S. Gurvich and M. I. Fortus, “Lidar sounding of the optical parameter of atmospheric turbulence,” Izv., Atmos. Ocean. Phys. 52 (2), 165–175 (2016).

    Article  Google Scholar 

  10. V. A. Banakh, I. A. Razenkov, and I. N. Smalikho, “Aerosol lidar for study of the backscatter amplification in the atmosphere. Part I. Computer simulation,” Opt. Atmos. Okeana 28 (1), 5–11 (2015).

    Google Scholar 

  11. V. A. Banakh and I. A. Razenkov, “Aerosol lidar for study of the backscatter amplification in the atmosphere. Part II. Construction and experiment,” Opt. Atmos. Okeana 28 (2), 113–119 (2015).

    Google Scholar 

  12. V. A. Banakh and I. A. Razenkov, “Lidar measurements of atmospheric backscattering amplification,” Opt. Spectrosc. 120 (2), 326–334 (2016).

    Article  ADS  Google Scholar 

  13. V. V. Vorob’ev and A. G. Vinogradov, “Effect of background turbulence in lidar investigations of clear air turbulence,” Atmos. Oceanic Opt. 27 (2), 134–141 (2014).

    Article  Google Scholar 

  14. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Nauka, Moscow, 1967) [in Russian]; (Dover Publications, New York, 1967).

    Google Scholar 

  15. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Izd-vo Fiz. Mat. Lit., Moscow, 1963) [in Russian].

    Google Scholar 

  16. A. V. Manzhirov and A. D. Polyanin, Methods for Solution of Integral Equations: Handbook (Faktorial, Moscow, 1999) [in Russian].

    MATH  Google Scholar 

  17. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some Applications (Nauka i tekhnika, Minsk, 1987) [in Russian].

    MATH  Google Scholar 

  18. V. V. Vorob’ev, “On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: II–Results of numerical simulation,” Atmos. Ocean. Opt. 30 (2), 162–168 (2016).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, 119017, Russia

    V. V. Vorob’ev

Authors
  1. V. V. Vorob’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Vorob’ev.

Additional information

Original Russian Text © V.V. Vorob’ev, 2016, published in Optika Atmosfery i Okeana.

Deceased.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vorob’ev, V.V. On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: I–equations. Atmos Ocean Opt 30, 156–161 (2017). https://doi.org/10.1134/S1024856017020130

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1024856017020130

Keywords

Search

Navigation