Skip to main content
Log in

Determination of the optical and microstructural characteristics of water droplet clouds in laser sensing taking into account multiple scattering

  • Equipment and Methods of Environmental Diagnostics
  • Published:
Atmospheric and Oceanic Optics Aims and scope Submit manuscript


We considered the inverse problem of retrieving the profiles of the extinction coefficient and effective cloud droplet size from lidar returns measured for different receiver field-of-view (FOV) angles. For the solution of the problem, we suggested a special mathematical formulation of the lidar equation, taking into account multiple scattering in the framework of the small-angle approximation of the transfer theory. In the multiply scattered signal, we separated the diffraction component which, for large FOVs, explicitly depends on the effective particle size. The sought characteristics are retrieved using a developed iteration algorithm of the solution of the system of lidar equations defined for two and more FOV angles. We presented the results of the algorithm testing in processing of the field data of laser sensing of stratocumulus clouds. The retrieved extinction coefficients and cloud particle sizes are found to agree well with the known published data.

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.

Similar content being viewed by others


  1. L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober and G. A. Isaac, “Multiple-Scattering Lidar Retrieval Method: Tests on Monte Carlo Simulations and Comparisons with in situ Measurements,” Appl. Opt. 41(30), 6307 (2002).

    Article  ADS  Google Scholar 

  2. L. R. Bissonnette, G. Roy and N. Roy, “Multiple-Scattering-Based Lidar Retrieval: Method and Results of Cloud Probings,” Appl. Opt. 44(26), 5565 (2005).

    Article  ADS  Google Scholar 

  3. A. V. Malinka and E. P. Zege, “Possibilities of Warm Cloud Microstructure Profiling with Multiple-Field-of-View Raman Lidar,” Appl. Opt. 46(35), 8419 (2007).

    Article  ADS  Google Scholar 

  4. I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy and L. Bissonnette, “Information Content of Data Measured with a Multiplefield-of-View Lidar,” Appl. Opt. 45(26), 6839 (2006).

    Article  ADS  Google Scholar 

  5. V. E. Zuev, V. V. Belov and V. V. Veretennikov, System Theory in Optics of Disperse Media (Spektr Publishing House, Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, 1997) [In Russian].

    Google Scholar 

  6. V. V. Veretennikov, Asymptotic Methods in the Theory of Lidar Sounding in the Small-Angle Multiple-Scattering Approximation, in Proceedings of MUSCLE 10 (Florence, 1999).

  7. V. V. Veretennikov, Determination of Particle Sizes from Lidar Signals Taking into Account the Multiple Scattering in Small-Angle Approximation, in Proceedings of Fourth Interrepublic Symposium “Atmospheric and Oceanic Optics” (Tomsk, 1997) [In Russian].

  8. V. V. Veretennikov, “Separation of Components in Asymptotic Estimates of Lidar Signals with Consideration of Multiple Scattering in the Small-Angle Approximation,” Proc. SPIE 4341, 264 (2000).

    Article  ADS  Google Scholar 

  9. B. V. Ermakov and Yu. A. Ilyinskii, “On Propagation of Light Pulses in a Scattering Medium,” Izv. Vyssh. Uchebn. Zaved. SSSR, Radiofis. 12 (5), 694 (1969).

    Google Scholar 

  10. L. S. Dolin and V. A. Savelyev, “On Backscattering Signal Characteristics during Pulsed Irradiation of Turbid Medium by a Narrow Directed Light Beam,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 7(5), 505 (1971) [In Russian].

    Google Scholar 

  11. K. S. Shifrin, Light Scattering in a Turbid Medium (Gostekhteorizdat, Moscow, 1951) [In Russian].

    Google Scholar 

  12. V. V. Veretennikov, “Lidar Return Structure at Multiple Scattering in the Small-Angle Approximation,” Optika Atmosfery i Okeana 12(5), 385 (1999) [Atm. Oceanic Opt. 12 (5), 369 (1999).

    Google Scholar 

  13. D. Deirmenjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

  14. V. V. Veretennikov, “The Method of Consequent Decomposition in the Theory of Lidar Sensing of Dense Media,” Optika Atmosfery i Okeana 20(11), 980 (2007) [Atm. Oceanic Opt. 20 (11), 894 (2007)]

    MathSciNet  Google Scholar 

  15. V.E. Zuev, G. M. Krekov and M. M. Krekova, Laser Sensing of Atmospheric Aerosol, Remote Sensing of the Atmosphere (Nauka, Novosibirsk, 1978) [In Russian].

    Google Scholar 

  16. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Mir, Moscow, 1975) [In Russian].

    Google Scholar 

  17. A. B. Bakushinskii and A. V. Goncharskii, Iterative Solution Methods for Ill-Posed Problems (Nauka, Moscow, 1989) [In Russian].

    Google Scholar 

  18. J.J. Moré, “The Levenberg-Marquardt Algorithm: Implementation and Theory, Numerical Analysis,” Ed. by G. A. Watson, Springer-Verlag, Lecture Notes in Mathematics 630, 105 (1978).

  19. Handbook of Clouds and Cloudy Atmosphere, Ed. By I.P. Mazin and A. Kh. Khrgian (Gidrometeoizdat, Leningrad, 1989) [In Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

Original Russian Text © V.V. Veretennikov, A.I. Abramochkin 2009, published in Optica Atmosfery i Okeana.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Veretennikov, V.V., Abramochkin, A.I. Determination of the optical and microstructural characteristics of water droplet clouds in laser sensing taking into account multiple scattering. Atmos Ocean Opt 22, 527–535 (2009).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: