Abstract

A new technique that efficiently simplifies the estimations of backscattered light power is presented. This technique allows one to consider real inhomogeneous scattering media with an underlying surface and to account for all the features both of media phase functions and of the reflection of underlying surfaces. It is assumed that the phase function has a sharp forward peak. Different sounding, vision, and location systems can be considered. The image transfer equation is derived for any observed object, including three-dimensional and non-Lambertian objects. A few examples of the successful use of the developed approach to solve various problems are given.

© 1997 Optical Society of America

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References

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  1. L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
    [CrossRef]
  2. P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
    [CrossRef]
  3. L. S. Dolin, V. A. Saveliev, “Backscattering signal characteristics at pulse narrow beam illumination of a turbid medium,” Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana 7, 505–510 (1971).
  4. E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
    [CrossRef]
  5. E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution of the lidar equation for cloud sounding taking into account multiple scattering,” in Fifteenth International Laser Radar Conference, Abstracts of Papers (Institute of Atmospheric Optics, Tomsk, USSR, 1990), Part I, pp. 333–337.
  6. V. V. Barun, “Visual perception of retroreflective objects through light-scattering media,” in Visual Data Exploration and Analysis II, G. G. Grinstein, R. F. Erbacher, eds. Proc. SPIE2410, 470–479 (1995).
    [CrossRef]
  7. B. Devison, Neutron Transfer Theory (Clarendon, Oxford, 1958).
  8. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Heidelberg, 1991).
  9. I. M. Levin, “Underwater television,” in Optics of Ocean, Vol. 2. Applied Optics of Ocean (Nauka, Moscow, 1983).
  10. B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar returns,” Appl. Opt. 21, 839–844 (1982).
    [CrossRef] [PubMed]
  11. J. F. Kusters, B. J. Rye, A. C. Walker, “Spatial weighting in laboratory incoherent light scattering experiments,” Appl. Opt. 28, 657–664 (1989).
    [CrossRef] [PubMed]
  12. E. P. Zege, I. L. Katsev, I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803–2812 (1993).
    [CrossRef] [PubMed]
  13. E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).
  14. E. M. Feigelson, L. D. Krasnokutskaja, Solar Radiation Fluxes and Clouds (Gidrometeoizdat, Moscow, 1978).
  15. T. Nakajima, M. D. King, “Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I. Theory,” J. Atmos. Sci. 47, 1878–1893 (1990).
    [CrossRef]
  16. N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).
  17. E. P. Zege, L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transf. 55, 19–31 (1996).
    [CrossRef]
  18. E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

1996 (1)

E. P. Zege, L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transf. 55, 19–31 (1996).
[CrossRef]

1995 (3)

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

1993 (1)

1990 (1)

T. Nakajima, M. D. King, “Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I. Theory,” J. Atmos. Sci. 47, 1878–1893 (1990).
[CrossRef]

1989 (1)

1988 (1)

E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).

1982 (1)

1971 (1)

L. S. Dolin, V. A. Saveliev, “Backscattering signal characteristics at pulse narrow beam illumination of a turbid medium,” Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana 7, 505–510 (1971).

Barun, V. V.

V. V. Barun, “Visual perception of retroreflective objects through light-scattering media,” in Visual Data Exploration and Analysis II, G. G. Grinstein, R. F. Erbacher, eds. Proc. SPIE2410, 470–479 (1995).
[CrossRef]

Benayahu, Y.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bissonette, L. R.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bruscaglioni, P.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

Chaikovskaya, L. I.

E. P. Zege, L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transf. 55, 19–31 (1996).
[CrossRef]

E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

Cohen, A.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Devison, B.

B. Devison, Neutron Transfer Theory (Clarendon, Oxford, 1958).

Dolin, L. S.

L. S. Dolin, V. A. Saveliev, “Backscattering signal characteristics at pulse narrow beam illumination of a turbid medium,” Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana 7, 505–510 (1971).

Egert, S.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Feigelson, E. M.

E. M. Feigelson, L. D. Krasnokutskaja, Solar Radiation Fluxes and Clouds (Gidrometeoizdat, Moscow, 1978).

Flesia, C.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Ismaelli, A.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Heidelberg, 1991).

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

Katsev, I. L.

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803–2812 (1993).
[CrossRef] [PubMed]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).

E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution of the lidar equation for cloud sounding taking into account multiple scattering,” in Fifteenth International Laser Radar Conference, Abstracts of Papers (Institute of Atmospheric Optics, Tomsk, USSR, 1990), Part I, pp. 333–337.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Heidelberg, 1991).

King, M. D.

T. Nakajima, M. D. King, “Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I. Theory,” J. Atmos. Sci. 47, 1878–1893 (1990).
[CrossRef]

Kleiman, M.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Krasnokutskaja, L. D.

E. M. Feigelson, L. D. Krasnokutskaja, Solar Radiation Fluxes and Clouds (Gidrometeoizdat, Moscow, 1978).

Kusters, J. F.

Levin, I. M.

I. M. Levin, “Underwater television,” in Optics of Ocean, Vol. 2. Applied Optics of Ocean (Nauka, Moscow, 1983).

Nakajima, T.

T. Nakajima, M. D. King, “Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I. Theory,” J. Atmos. Sci. 47, 1878–1893 (1990).
[CrossRef]

Noormohammadian, M.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Oppel, U. G.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Polonsky, I. N.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803–2812 (1993).
[CrossRef] [PubMed]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).

E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution of the lidar equation for cloud sounding taking into account multiple scattering,” in Fifteenth International Laser Radar Conference, Abstracts of Papers (Institute of Atmospheric Optics, Tomsk, USSR, 1990), Part I, pp. 333–337.

Rye, B. J.

Saveliev, V. A.

L. S. Dolin, V. A. Saveliev, “Backscattering signal characteristics at pulse narrow beam illumination of a turbid medium,” Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana 7, 505–510 (1971).

Schwendimann, P.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Starkov, A. V.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Walker, A. C.

Winkler, D. M.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Zaccanti, G.

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

Zege, E. P.

E. P. Zege, L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transf. 55, 19–31 (1996).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803–2812 (1993).
[CrossRef] [PubMed]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Heidelberg, 1991).

E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution of the lidar equation for cloud sounding taking into account multiple scattering,” in Fifteenth International Laser Radar Conference, Abstracts of Papers (Institute of Atmospheric Optics, Tomsk, USSR, 1990), Part I, pp. 333–337.

Appl. Opt. (3)

Appl. Phys. B (3)

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

L. R. Bissonette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winkler, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

Atmos. Opt. (1)

E. P. Zege, I. L. Katsev, I. N. Polonsky, “A modified small-angle diffusion approximation taking into account the specific form of the scattering phase function at small angles,” Atmos. Opt. 1, 19–27 (1988).

Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana (1)

L. S. Dolin, V. A. Saveliev, “Backscattering signal characteristics at pulse narrow beam illumination of a turbid medium,” Izv. Akad. Nauk SSSR Ser. Fiz. Atmos. Okeana 7, 505–510 (1971).

J. Atmos. Sci. (1)

T. Nakajima, M. D. King, “Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I. Theory,” J. Atmos. Sci. 47, 1878–1893 (1990).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

E. P. Zege, L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transf. 55, 19–31 (1996).
[CrossRef]

Other (8)

E. P. Zege, I. N. Polonsky, I. L. Katsev, L. I. Chaikovskaya, “Polarization of multiple scattered return signals from clouds,” in Proceedings of the 5th International Workshop on Multiple Scattering Lidar Experiment (Drexel U., Philadelphia, Pa., 1992), pp. 16–26.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

E. M. Feigelson, L. D. Krasnokutskaja, Solar Radiation Fluxes and Clouds (Gidrometeoizdat, Moscow, 1978).

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution of the lidar equation for cloud sounding taking into account multiple scattering,” in Fifteenth International Laser Radar Conference, Abstracts of Papers (Institute of Atmospheric Optics, Tomsk, USSR, 1990), Part I, pp. 333–337.

V. V. Barun, “Visual perception of retroreflective objects through light-scattering media,” in Visual Data Exploration and Analysis II, G. G. Grinstein, R. F. Erbacher, eds. Proc. SPIE2410, 470–479 (1995).
[CrossRef]

B. Devison, Neutron Transfer Theory (Clarendon, Oxford, 1958).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Heidelberg, 1991).

I. M. Levin, “Underwater television,” in Optics of Ocean, Vol. 2. Applied Optics of Ocean (Nauka, Moscow, 1983).

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Figures (4)

Fig. 1
Fig. 1

Power of the multiple-scattering contribution into lidar returning from a cloud (C1 model14) at σs=0.017 km-1 for H=1000 m at source FOV=0.0005 and receiver FOV =0.005 and for lidar in space (H=300 km) at source FOV =0.0002 and receiver FOV=0.00055. Solid curves, SAA; dashed curves, analytical solution with modified small-angle method; asterisks, Monte Carlo data.2

Fig. 2
Fig. 2

Phase function of Sargasso Sea (from Ref. 16).

Fig. 3
Fig. 3

Backscattering interference power in the wide–narrow pulse monostatic vision system as a function of depth z, where the BSI comes from the phase function depicted in Fig. 2 (curve 1), Peffb=P(π) (curve 2), and Peffb=Pb(n) (curve 3). Source FOV=0.2.

Fig. 4
Fig. 4

Power of backscattering interference at the driver's eye as a function of the driver's eye–headlight distance in fog with meteorological visibility ranges MVR=50 m (dashed curves) and 300 m (solid curves) for different angular emmitance patterns of headlights with 2γsrc=0.05 (curve 1), 0.1 (curve 2), and 0.2 (curve 3).

Equations (65)

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

F(Rsrc, Rrec)=dRΦrec(R, n)J(R, n)dn,
J(R, n)
=dRG(R, n; R, n)dnσs(R) P(R; n, n)4π×dndR0Φsrc(R0, n0)G(R, n; R0, n0)dn0,
G(R, n; R, n)=G(R,-n; R,-n).
F(Rsrc, Rrec)
=σs(R)dRdn P(R; -n, n)4πdn×dRΦsrcrec(R, n)G(R, n; R, n)dn×dR0Φsrc(R0, n0)G(R, n; R0, n0)dn0.
F(Rsrc, Rrec)=σs(R)dRdn P(R; -n, n)4π
×Jsrc(R, n)Jsrcrec(R, n)dn,
Jsrc(R, n)=dRΦsrc(R, n)G(R, n; R, n)dn,
Jsrcrec(R, n)=dRΦsrcrec(R, n)G(R, n; R, n)dn
σs(R)P(R; -n, n)/4π=σπ(R),
F(Rsrc, Rrec)=σπ(R)Esrc(R)Esrcrec(R)dR,
Esrc(R)=Jsrc(R, n)dn.
Ftot(Rsrc, Rrec)=F(Rsrc, Rrec)+Fbot(Rsrc, Rrec)+Fob(Rsrc, Rrec).
Fbot(Rsrc, Rrec)=dRdnAbot(R;-n, n)×Jsrc(R, n)Jsrcrec(R, n)dn,
Fob(Rsrc, Rrec)=dRdnAob(R; -n, n)×Jsrc(R, n)Jsrcrec(R, n)dn.
Fob(Rsrc, Rrec)=Aob(R)Esrc(R)Esrcrec(R)dR.
F(Rsrc, Rrec)=σs(z)dz Pb(z, |n|)4π H(z, n)dn,
H(z, n)=drJsrc(r, z, n)×Jsrcrec(r, z, n+n)dn,
Jsrc(q, z, p)=drJsrc(r, z, n)×exp(-iqr-ipn)dn,
Jsrcrec(q, z, p)=drJsrcrec(r, z, n)×exp(-iqr-ipn)dn,
H(z, p)=H(z, n)exp(-ipn)dn.
H(z, p)=1(2π)2Jsrc*(q, z, p)Jsrcrec(q, z, p)dq.
Φsrc(R, n)=ϕsrc(r, n),Φsrcrec(R, n)=ϕrec(r, n),
ϕsrc(r, n)drdn=F0;
ϕrec(r, n)drdn=ΣrecΩrec.
Jsrc*(q, z, p)=ϕsrc*(q, p+qz)I*(q, z, p),
Jsrcrec(q, z, p)=ϕrec(q, p+qz)I(q, z, p),
H(z, p)=1(2π)2ϕsrceff(q, p+qz)|I(q, z, p)|2dq,
ϕsrceff(q, p)=ϕsrc*(q, p)ϕrec(q, p);
ϕsrceff(r, n)=drϕsrc(r, n)×ϕrec(r+r, n+n)dn.
I(q, z, p)=exp-0zQ(z-ξ, p+qξ)dξ,
Q(z, p)=σe(z)-σs(z)P(p, z),
|I(q, z, p)|2=exp-20zQ(z-ξ, p+qξ)dξ.
Ieff(q, z, p)=|I(q, z, p)|2
σeeff(z)=2σe(z),σseff(z)=2σs(z),
Peff(z, |n|)=P(z, |n|).
H(z, p)=1(2π)2ϕsrceff(q, p+qz)Ieff(q, z, p)dq;
H(z, n)=Jsrceff(r=0, z, n),
F(Rsrc, Rrec)=σs(z)dz Pb(z, |n|)4π×Jsrceff(r=0, z, n)dn,
ϕsrc(r, n)=ϕsrc(n-ns).
ϕsrceff(r, n)=ϕsrc(n-ns)ϕrec(n+ns)dn,
ϕrec(n)=ϕrec(r, n)dr.
ϕsrc(n-ns)=E0δ(n-ns);
ϕsrceff(r, n)=E0ϕrec(n+ns).
ϕrec(n)ΣrecΩrecδ(n-nr),
ϕsrceff(r, n)=E0ΣrecΩrecδ[n-(nr-ns)].
ϕsrc(r, n)F0δ(r)ϕsrc(n),
ϕrec(r, n)Σrecδ(r)ϕrec(n),
ϕrec(n)dn=Ωrec.
ϕsrceff(r, n)=F0Σrecδ(r)ϕsrc(n)ϕrec(n+n)dn.
F(t)=σ(z)v2 Jsrceff(r=0, z, n) Pb(z, |n|)4π dn.
F(t)=σ(z)P(z, π)v8π Esrceff(r=0, z),
ϕsrc(r, n)=F0δ(r)δ(n-ns),
ϕrec(r, n)Σrecδ(r-rrec)ϕrec(n-nr).
ϕsrceff(r, n)=F0ΣrecΩrecδ(r-rrec)×ϕrec[n-(nr-ns)].
Esrceff(r=0, z)=F0ΣrecΩrec2πVreff exp-0zσaeff(l)dl
×exp-[rrec+(nr-ns)z]22Vreff.
σaeff(z)=σeeff(z)-σseff(z)
Vreff=Vr0+12 0zσseff(l)β2(l)(z-l)2dl=Vr0+0zσs(l)β2(l)(z-l)2dl.
β2(z)=P(β, z)β2βdβP(β, z)βdβ,
F(t)=F0ΣrecΩrecσ(z)P(z, π)v16π2Vreff exp-0zσaeff(l)dlexp(-rrec2/2Vreff).
F(t)=F0ΣrecΩrecσ(z)P(π, z)v16π2Vreff exp-0zσaeff(l)dl×exp-(nr-ns)2z22Vreff.
Vreff=γrec2 z2/2+σsβ2z3/3,
F(t)exp[-θ2z2/(γrec2 z2+2σsβ2z3/3)];

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