Abstract

An analytical approach to modeling Raman lidar return with multiple scattering is presented. This approach is based on a small-angle quasi-single-scattering approximation developed earlier for elastic lidar sounding. An approximation of isotropic backscattering for the Raman-scattering case is proposed and tested. The computed results are presented and compared with known data. The approximation was found to be quite simple and provided a high accuracy of Raman lidar return calculations.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
    [CrossRef]
  2. J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 5, 1457–1465 (1996).
    [CrossRef]
  3. V. Sherlock, A. Garnier, A. Hauchecorne, P. Keckhut, “Implementation and validation of a Raman lidar measurement of middle and upper tropospheric water vapor,” Appl. Opt. 38, 5838–5850 (1999).
    [CrossRef]
  4. V. Sherlock, A. Hauchecorne, J. Lenoble, “Methodology for the independent calibration of Raman backscatter water-vapor lidar systems,” Appl. Opt. 38, 5816–5837 (1999).
    [CrossRef]
  5. A. Ansmann, M. Reibesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with Raman lidar,” Opt. Lett. 15, 746–748 (1990).
    [CrossRef] [PubMed]
  6. S. Shipley, D. Tracy, E. Eloranta, J. Trauger, J. Sroga, F. Roesler, J. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1. Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
    [CrossRef] [PubMed]
  7. U. Wandinger, A. Ansmann, J. Reichardt, T. Deshler, “Determination of stratospheric-aerosol microphysical properties from independent extinction and backscattering measurements with Raman lidar,” Appl. Opt. 34, 8315–8329 (1995).
    [CrossRef] [PubMed]
  8. D. N. Klyshko, V. V. Fadeev, “Remote detecting the water impurity by means of laser spectroscopy calibrated by Raman scattering,” Rep. Acad. Sci. USSR 238, 320–323 (1978) (in Russian).
  9. A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
    [CrossRef] [PubMed]
  10. J. Reichardt, M. Hess, A. Macke, “Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions,” Appl. Opt. 39, 1895–1910 (2000).
    [CrossRef]
  11. D. Whiteman, S. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. D 134, 31411–31419 (1999).
    [CrossRef]
  12. C. Grund, E. Eloranta, “University of Wisconsin high spectral resolution lidar,” Opt. Eng. 30, 6–12 (1991).
    [CrossRef]
  13. P. Piironen, E. Eloranta, “Demonstration of a high-spectral-resolution lidar based on an iodine absorption filter,” Opt. Lett. 19, 234–236 (1994).
    [CrossRef] [PubMed]
  14. A. Cohen, M. Kleiman, J. Cooney, “Lidar measurements of rotational Raman and double scattering,” Appl. Opt. 17, 1905–1910 (1978).
    [CrossRef] [PubMed]
  15. S. Egert, A. Cohen, M. Kleiman, N. Ben-Yosef, “Instantaneous integrated Raman scattering,” Appl. Opt. 22, 1592–1597 (1983).
    [CrossRef] [PubMed]
  16. P. Bruscaglioni, M. Gai, A. Ismaelli, “Molecular lidar and Mie multiple scattering,” in Proceedings of MUSCLE 10 (International Workshop on Multiple Scattering Lidar Experiments), Florence, Italy, 19–22 April 1999 (University of Florence, Florence, Italy, 1999), p. 206.
  17. J. Weinman, S. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
    [CrossRef]
  18. U. Wandinger, “Multiple-scattering influence on extinction and backscatter-coefficient measurement with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998).
    [CrossRef]
  19. I. Katsev, E. Zege, A. Prikhach, I. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
    [CrossRef]
  20. E. Zege, I. Katsev, I. Polonsky, “Analytical solution to LIDAR return signals from clouds with regards to multiple scattering,” Appl. Phys. B 60, 345–354 (1995).
    [CrossRef]
  21. C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7503 (1993).
    [CrossRef] [PubMed]
  22. G. Boynton, H. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
    [CrossRef]
  23. J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
    [CrossRef]
  24. E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.
  25. E. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisconsin, 1972).
  26. V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).
  27. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.
  28. E. Zege, A. Ivanov, I. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), p. 85.

2000 (2)

1999 (3)

1998 (2)

1997 (1)

1996 (1)

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 5, 1457–1465 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (1)

1992 (2)

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

1991 (1)

C. Grund, E. Eloranta, “University of Wisconsin high spectral resolution lidar,” Opt. Eng. 30, 6–12 (1991).
[CrossRef]

1990 (1)

1983 (2)

1978 (2)

D. N. Klyshko, V. V. Fadeev, “Remote detecting the water impurity by means of laser spectroscopy calibrated by Raman scattering,” Rep. Acad. Sci. USSR 238, 320–323 (1978) (in Russian).

A. Cohen, M. Kleiman, J. Cooney, “Lidar measurements of rotational Raman and double scattering,” Appl. Opt. 17, 1905–1910 (1978).
[CrossRef] [PubMed]

1972 (1)

J. Weinman, S. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

Ansmann, A.

Belov, M. L.

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

Ben-Yosef, N.

Boynton, G.

Bruscaglioni, P.

P. Bruscaglioni, M. Gai, A. Ismaelli, “Molecular lidar and Mie multiple scattering,” in Proceedings of MUSCLE 10 (International Workshop on Multiple Scattering Lidar Experiments), Florence, Italy, 19–22 April 1999 (University of Florence, Florence, Italy, 1999), p. 206.

Cohen, A.

Cooney, J.

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.

Deshler, T.

Egert, S.

Eloranta, E.

Fadeev, V. V.

D. N. Klyshko, V. V. Fadeev, “Remote detecting the water impurity by means of laser spectroscopy calibrated by Raman scattering,” Rep. Acad. Sci. USSR 238, 320–323 (1978) (in Russian).

Freeman, J. D.

Gai, M.

P. Bruscaglioni, M. Gai, A. Ismaelli, “Molecular lidar and Mie multiple scattering,” in Proceedings of MUSCLE 10 (International Workshop on Multiple Scattering Lidar Experiments), Florence, Italy, 19–22 April 1999 (University of Florence, Florence, Italy, 1999), p. 206.

Garnier, A.

Gentili, B.

Gordon, H.

Grund, C.

C. Grund, E. Eloranta, “University of Wisconsin high spectral resolution lidar,” Opt. Eng. 30, 6–12 (1991).
[CrossRef]

Hauchecorne, A.

Hess, M.

Ismaelli, A.

P. Bruscaglioni, M. Gai, A. Ismaelli, “Molecular lidar and Mie multiple scattering,” in Proceedings of MUSCLE 10 (International Workshop on Multiple Scattering Lidar Experiments), Florence, Italy, 19–22 April 1999 (University of Florence, Florence, Italy, 1999), p. 206.

Ivanov, A.

E. Zege, A. Ivanov, I. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), p. 85.

Jin, Z.

Katsev, I.

I. Katsev, E. Zege, A. Prikhach, I. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. Zege, I. Katsev, I. Polonsky, “Analytical solution to LIDAR return signals from clouds with regards to multiple scattering,” Appl. Phys. B 60, 345–354 (1995).
[CrossRef]

E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.

E. Zege, A. Ivanov, I. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), p. 85.

Kattawar, G.

Keckhut, P.

Kleiman, M.

Klyshko, D. N.

D. N. Klyshko, V. V. Fadeev, “Remote detecting the water impurity by means of laser spectroscopy calibrated by Raman scattering,” Rep. Acad. Sci. USSR 238, 320–323 (1978) (in Russian).

Kogevnikov, A. N.

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

Lahmann, W.

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

Lenoble, J.

Ludbrook, G.

E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.

Macke, A.

Matvienko, G. G.

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

McLean, J. W.

Melfi, S.

D. Whiteman, S. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. D 134, 31411–31419 (1999).
[CrossRef]

Michaelis, W.

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

Mobley, C.

Morel, A.

Orlov, V. M.

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

Piironen, P.

Polonsky, I.

I. Katsev, E. Zege, A. Prikhach, I. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. Zege, I. Katsev, I. Polonsky, “Analytical solution to LIDAR return signals from clouds with regards to multiple scattering,” Appl. Phys. B 60, 345–354 (1995).
[CrossRef]

Prikhach, A.

I. Katsev, E. Zege, A. Prikhach, I. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.

Reibesell, M.

Reichardt, J.

Reinersman, P.

Riebesell, M.

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

Roesler, F.

Samohvalov, I. V.

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

Serwazi, M.

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 5, 1457–1465 (1996).
[CrossRef]

Sherlock, V.

Shipley, S.

Sroga, J.

Stamnes, K.

Stavn, R.

Tracy, D.

Trauger, J.

Voss, E.

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

Walker, R. E.

Wandinger, U.

Weinman, J.

Weitkamp, C.

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 5, 1457–1465 (1996).
[CrossRef]

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

A. Ansmann, M. Reibesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with Raman lidar,” Opt. Lett. 15, 746–748 (1990).
[CrossRef] [PubMed]

Whiteman, D.

D. Whiteman, S. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. D 134, 31411–31419 (1999).
[CrossRef]

Zege, E.

I. Katsev, E. Zege, A. Prikhach, I. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. Zege, I. Katsev, I. Polonsky, “Analytical solution to LIDAR return signals from clouds with regards to multiple scattering,” Appl. Phys. B 60, 345–354 (1995).
[CrossRef]

E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.

E. Zege, A. Ivanov, I. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), p. 85.

Appl. Opt. (12)

V. Sherlock, A. Garnier, A. Hauchecorne, P. Keckhut, “Implementation and validation of a Raman lidar measurement of middle and upper tropospheric water vapor,” Appl. Opt. 38, 5838–5850 (1999).
[CrossRef]

V. Sherlock, A. Hauchecorne, J. Lenoble, “Methodology for the independent calibration of Raman backscatter water-vapor lidar systems,” Appl. Opt. 38, 5816–5837 (1999).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

J. Reichardt, M. Hess, A. Macke, “Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions,” Appl. Opt. 39, 1895–1910 (2000).
[CrossRef]

S. Shipley, D. Tracy, E. Eloranta, J. Trauger, J. Sroga, F. Roesler, J. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1. Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
[CrossRef] [PubMed]

U. Wandinger, A. Ansmann, J. Reichardt, T. Deshler, “Determination of stratospheric-aerosol microphysical properties from independent extinction and backscattering measurements with Raman lidar,” Appl. Opt. 34, 8315–8329 (1995).
[CrossRef] [PubMed]

A. Cohen, M. Kleiman, J. Cooney, “Lidar measurements of rotational Raman and double scattering,” Appl. Opt. 17, 1905–1910 (1978).
[CrossRef] [PubMed]

S. Egert, A. Cohen, M. Kleiman, N. Ben-Yosef, “Instantaneous integrated Raman scattering,” Appl. Opt. 22, 1592–1597 (1983).
[CrossRef] [PubMed]

U. Wandinger, “Multiple-scattering influence on extinction and backscatter-coefficient measurement with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998).
[CrossRef]

C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7503 (1993).
[CrossRef] [PubMed]

G. Boynton, H. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
[CrossRef]

J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
[CrossRef]

Appl. Phys. B (2)

E. Zege, I. Katsev, I. Polonsky, “Analytical solution to LIDAR return signals from clouds with regards to multiple scattering,” Appl. Phys. B 60, 345–354 (1995).
[CrossRef]

A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, “Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio,” Appl. Phys. B 55, 18–28 (1992).
[CrossRef]

J. Geophys. Res. (1)

J. Weinman, S. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

J. Geophys. Res. D (1)

D. Whiteman, S. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. D 134, 31411–31419 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

C. Grund, E. Eloranta, “University of Wisconsin high spectral resolution lidar,” Opt. Eng. 30, 6–12 (1991).
[CrossRef]

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 5, 1457–1465 (1996).
[CrossRef]

Opt. Lett. (2)

Rep. Acad. Sci. USSR (1)

D. N. Klyshko, V. V. Fadeev, “Remote detecting the water impurity by means of laser spectroscopy calibrated by Raman scattering,” Rep. Acad. Sci. USSR 238, 320–323 (1978) (in Russian).

Other (6)

P. Bruscaglioni, M. Gai, A. Ismaelli, “Molecular lidar and Mie multiple scattering,” in Proceedings of MUSCLE 10 (International Workshop on Multiple Scattering Lidar Experiments), Florence, Italy, 19–22 April 1999 (University of Florence, Florence, Italy, 1999), p. 206.

E. Zege, I. Katsev, A. Prikhach, G. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic lidar return,” in Proceedings of the International Conference Current Problems in Optics of Natural Waters, St. Petersburg, Russia, 25–29 September 2001, (D. S. Rozhdestvensky Optical Society, St. Petersburg, Russia, 2001), p. 255.

E. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisconsin, 1972).

V. M. Orlov, I. V. Samohvalov, G. G. Matvienko, M. L. Belov, A. N. Kogevnikov, The Elements of Light Scattering Theory and Optical Sensing, (The Science, Novosibirsk, Russia1982) (in Russian).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.

E. Zege, A. Ivanov, I. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), p. 85.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Relative error of isotropic backscattering approximation.

Fig. 2
Fig. 2

(a) The total signal and (b) multiple-to-single scattering ratio for the cloud C.1 with an extinction coefficient of 0.01 m-1, a lidar-cloud distance of 5000 m, a source divergence of 0.1 mrad, and a receiver’s field-of-view of 0.4 mrad (full angles). Data is from Ref. 18 (open circles), Eq. (34) within the isotropic backscattering approximation with approximate forward-scattering phase function given by Eq. (38) (solid curve), and the same solution, but with the forward-scattering phase function calculated under Mie theory (dashed curve).

Tables (1)

Tables Icon

Table 1 Parameters Used in Eq. (38). Angles Are Given in Degrees and Are to Be Converted to Radians.

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

 φsrcr, ndrdn=1,
 φrecr, ndrdn=SrecΩrec,
120π Pθsinθdθ=1.
λR=11/λ0-δν˜.
Fz=W0σλ, z4πV2  drdndnIsrcz, r, n×Pbz, |n-n|Irecz, r, n,
t=2H/c+2z/V,
F2zF1z=σλz+HPπ×γrec0π/2 PγPπ-γdγ.
F2zF1z=z+HPRπ γrecσλR, z0π/2 PRγPπ-γdγ+σλ0, z0π/2 PγPRπ-γdγ.
PRbθ=341+3ρ1+2ρ1+1-ρ1+3ρcos2θ,
Fz=W0σR4πV2  drdndn Iscrλ0, z, r, n×PRb|n-n|IrecλR, z, r, n.
Ieffz, r, n= drdnIsrcλ0, z, r, n×IrecλR, z, r+r, n+n.
Fz=W0σR4πV2  dnPRb|n|Ieffz, r=0, n.
Ieffz, v, p= drdnIeffz, r, n×exp-iv · r-ip · n,
Pbp=120 PRbθJ0pθθdθ,
Fz=W0σRV2  dvdp2π4 PbpIeffz, v, p,
Ieffz, v, p=Isrc*λ0, z, v, pIrecλR, z, v, p.
Iz, v, p=φv, p+vz+H ×exp-0zεξ-σξPf|p+vz-ξ|dξ,
Pfp=120 PfθJ0pθθdθ.
Fz=W0σRV2  dvdp2π4 Pbpφeffv, p+vz+H×exp-0zεeffξ-σeffξ×Pefff|p+vz-ξ|dξ,
φeffv, p=φsrc*v, pφrecv, p,
εeffz=ελ0, z+ελR, z,
σeffz=σλ0, z+σλR, z,
Pefffz, θ=σλ0, zPfλ0, z, θ+σλR, zPfλR, z, θσλ0, z+σλR, z.
φeffr, n= drdnφsrcr, nφrecr+r, n+n
PRbθPRb01-1-ρ1+ρθ22.
1-ρ1+ρ dnn22 Ieffz, r=0, n dnIeffz, r=0, n.
1-ρ1+ρ Vθ.
1-ρ1+ρ Vθ  1.
Vθ  1.
Fz=W0σRπV2  dnIeffz, r=0, n,
σRπ=σRPRb04π.
Fz=W0σRπV2  dv2π2 Ieffz, v, p=0.
φjr, n=φjspace|r-rj0|φjang|n-nj0|, j=scr, rec,
φeffv, p=φscrspacevφscrangpφrecspacevφrecangp×exp-iv · R-ip · Ω,
φjangp=2π 0 φjangθJ0pθθdθ, φjspacev=2π 0 φjspacerJ0vrrdr j=scr, rec.
Fz=W0σRπV2  vdv2π J0v|R+z+HΩ|×Ieffz, v, p=0.
Ieffz, v, p=0=φv, vz+H×exp-0zεeff×ξ-σeffξPefffvz-ξdξ,
φv, p=φscrspacevφscrangpφrecspacevφrecangp.
NH=p0 exp-H/hkBT0-βH,
Pfθ=j=15ajπθj2exp-θ/θj2,

Metrics