Abstract

We delimit a regime, valid for most ground-based lidar probings of cirrus clouds, in which the field-of-view dependence of multiple scattering reaches a plateau. In this regime and assuming the phase function to be constant around π, we formally demonstrate Platt’s modification of the single-scattering lidar equation, with a parameter ηP accounting for the reduction of the effective scattering coefficient defined so that (1 - ηP) is the amount of energy scattered in the forward peak. Then, to cope with nonconstant backscattering functions, we discuss the introduction of an effective backscattering coefficient that is an average of the scattering probabilities around π.

© 1997 Optical Society of America

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References

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  1. K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
    [CrossRef]
  2. S. K. Cox, “Cirrus clouds and the climate,” J. Atmos. Sci. 28, 1513–1515 (1971).
    [CrossRef]
  3. S. R. Pal, A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530–1535 (1973).
    [CrossRef] [PubMed]
  4. C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
    [CrossRef]
  5. C. M. R. Platt, “Remote sounding of high clouds. III: Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1980).
    [CrossRef]
  6. E. W. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisconsin, 1972).
  7. E. W. Eloranta, S. T. Shipley, “A solution for multiple scattering,” in Atmospheric Aerosols: Their Formation, Optical Properties and Effects, A. Deepak, ed. (Spectrum, Hampton, Va., 1982).
  8. L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
    [CrossRef]
  9. 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]
  10. L. R. Bissonnette, “Multiscattered model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2748–2484 (1988).
    [CrossRef]
  11. L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
    [CrossRef] [PubMed]
  12. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978).
  13. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  14. A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
    [CrossRef]
  15. D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
    [CrossRef]
  16. D. M. Winker, “Multiple scattering effects observed in LITE data: the good, the bad, and the ugly,” in Proceedings of the Eighth MUSCLE Workshop, Québec (1996).
  17. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 68–71 and 104–106.
  18. M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
    [CrossRef] [PubMed]
  19. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  20. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  21. E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
    [CrossRef]
  22. M. Wiegner, G. Echle, “Lidar multiple scattering: improvement of Bissonnette’s paraxial approximation,” Appl. Opt. 32, 6789–6803 (1993).
    [CrossRef] [PubMed]
  23. G. Zaccanti, P. Bruscaglioni, M. Dami, “Simple inexpensive method of measuring the temporal spreading of a light pulse propagating in a turbid medium,” Appl. Opt. 29, 3938–3944 (1990).
    [CrossRef] [PubMed]
  24. G. C. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, R. A. Krautwald, “Blue-green pulsed propagation through fog,” Appl. Opt. 18, 429–441 (1979).
    [CrossRef] [PubMed]
  25. J. S. Ryan, A. I. Carswell, “Laser beam broadening and depolarization in dense fogs,” J. Opt. Soc. Am. 68, 900–908 (1978).
    [CrossRef]
  26. I. L. Katsev, E. P. Zege, A. S. Prikhach, I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
    [CrossRef]
  27. H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
    [CrossRef]
  28. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [CrossRef] [PubMed]
  29. S. A. Young, “Analysis of lidar profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
    [CrossRef] [PubMed]

1997 (1)

1996 (2)

L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
[CrossRef] [PubMed]

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

1995 (3)

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, 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]

S. A. Young, “Analysis of lidar profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (2)

1990 (1)

1988 (1)

1986 (1)

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

1980 (1)

C. M. R. Platt, “Remote sounding of high clouds. III: Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1980).
[CrossRef]

1979 (1)

1978 (1)

1973 (2)

S. R. Pal, A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530–1535 (1973).
[CrossRef] [PubMed]

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

1971 (2)

S. K. Cox, “Cirrus clouds and the climate,” J. Atmos. Sci. 28, 1513–1515 (1971).
[CrossRef]

H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
[CrossRef]

Benayahu, Y.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
[CrossRef] [PubMed]

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

L. R. Bissonnette, “Multiscattered model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2748–2484 (1988).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Bruscaglioni, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

G. Zaccanti, P. Bruscaglioni, M. Dami, “Simple inexpensive method of measuring the temporal spreading of a light pulse propagating in a turbid medium,” Appl. Opt. 29, 3938–3944 (1990).
[CrossRef] [PubMed]

Cahalan, R.

A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
[CrossRef]

Carswell, A. I.

Cohen, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Cohen, L. D.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Couch, R. H.

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

Cox, S. K.

S. K. Cox, “Cirrus clouds and the climate,” J. Atmos. Sci. 28, 1513–1515 (1971).
[CrossRef]

Dami, M.

Davis, A.

A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 68–71 and 104–106.

Echle, G.

Eloranta, E. W.

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

E. W. Eloranta, S. T. Shipley, “A solution for multiple scattering,” in Atmospheric Aerosols: Their Formation, Optical Properties and Effects, A. Deepak, ed. (Spectrum, Hampton, Va., 1982).

Flesia, C.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Geller, M.

Harack, R. D.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Hess, M.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978).

Ismaelli, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Ivanov, A. P.

E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
[CrossRef]

Jacobowitz, H.

H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
[CrossRef]

Katsev, I. L.

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

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, 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, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
[CrossRef]

Krautwald, R. A.

Liou, K. N.

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Macke, A.

Marshak, A.

A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
[CrossRef]

McCormick, M. P.

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

Mooradian, G. C.

Oppel, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Pal, S. R.

Platt, C. M. R.

C. M. R. Platt, “Remote sounding of high clouds. III: Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1980).
[CrossRef]

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

Polonsky, I. N.

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

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, 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]

Prikhach, A. S.

Ryan, J. S.

Schwendimann, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Shipley, S. T.

E. W. Eloranta, S. T. Shipley, “A solution for multiple scattering,” in Atmospheric Aerosols: Their Formation, Optical Properties and Effects, A. Deepak, ed. (Spectrum, Hampton, Va., 1982).

Stephens, D. H.

Stotts, L. B.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wiegner, M.

Winkel, D. M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Winker, D. M.

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

D. M. Winker, “Multiple scattering effects observed in LITE data: the good, the bad, and the ugly,” in Proceedings of the Eighth MUSCLE Workshop, Québec (1996).

Wiscombe, W.

A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Young, S. A.

Zaccanti, G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, E. P. Zege, I. L. Katsev, I. N. Polonsky, “Lidar multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

G. Zaccanti, P. Bruscaglioni, M. Dami, “Simple inexpensive method of measuring the temporal spreading of a light pulse propagating in a turbid medium,” Appl. Opt. 29, 3938–3944 (1990).
[CrossRef] [PubMed]

Zege, E. P.

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

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, 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, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
[CrossRef]

Appl. Opt. (9)

Appl. Phys. B (2)

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, R. D. Harack, L. D. Cohen, C. Flesia, P. Schwendimann, M. Oppel, D. M. Winkel, 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]

J. Atmos. Sci. (3)

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

C. M. R. Platt, “Remote sounding of high clouds. III: Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1980).
[CrossRef]

S. K. Cox, “Cirrus clouds and the climate,” J. Atmos. Sci. 28, 1513–1515 (1971).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
[CrossRef]

Mon. Weather Rev. (1)

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Proc. IEEE (1)

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s Lidar In-Space Technology Experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

Other (10)

D. M. Winker, “Multiple scattering effects observed in LITE data: the good, the bad, and the ugly,” in Proceedings of the Eighth MUSCLE Workshop, Québec (1996).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 68–71 and 104–106.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
[CrossRef]

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

E. W. Eloranta, S. T. Shipley, “A solution for multiple scattering,” in Atmospheric Aerosols: Their Formation, Optical Properties and Effects, A. Deepak, ed. (Spectrum, Hampton, Va., 1982).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978).

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

A. Davis, A. Marshak, R. Cahalan, W. Wiscombe, “The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, implication for cloud remote sensing,” J. Atmos. Sci. (1997), in press.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Mie-calculated forward phase function and cumulative scattering probability [Eq. (2)] for a C1 cloud at a wavelength of 1.06 µm.

Fig. 2
Fig. 2

COP18 (cirrus optical properties): calculated forward phase function and cumulative scattering probability [Eq. (3)] for randomly oriented column crystals with lengths of the c axis equal to 130 µm and half-lengths of the a axis equal to 41 µm at a wavelength of 0.532 µm.

Fig. 3
Fig. 3

Definition of the configuration angle θ c: photons scattered at angles smaller than θ c remain within the FOV for one scattering mean-free path l s and are thus likely to contribute to the lidar signal.

Fig. 4
Fig. 4

Photon originating from the laser source and arriving at M′ corresponds to a photon originating from the virtual receiver source and arriving at M if the angle (OP 1, OP 1′) = (OM, OM′) is smaller than the FOV.

Fig. 5
Fig. 5

Integration domains for calculation of the lidar signal in the multiple-scattering plateau [Eq. (29)].

Equations (37)

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

l*=ls1-g,
Pθ=2π0θpθsin θdθ.
Pθ=2π0θ1-Rpθsin θdθ+R
θdλ/d,
θcL+lslsθFOV,
θcL+zzθFOV.
θc/θd1,
τs121-g.
Sz=Kct2Fz, r, nαszpz, n, n×Bz, r, n, θFOVdrdndn.
F0, r, ndrdn=F0,
Bˆz, r, -n, θFOV=Bz, r, n, θFOV,
Bˆ0, r, n, θFOVdrdn=AΩFOV,
Sz=Kct2Fz, r, nαszpbz, n, n×Bˆz, r, n, θFOVdrdndn.
Sz=Kct2βzz, rz, r, θFOVdr,
βz=αszpz, π
z, r=Fz, r, ndn,
z, r, θFOV=Bˆz, r, n, θFOVdn.
F0, r, n=F0δrδn,
z, r, θFOV=AF01L+z2r-rL+zθFOVz, rdr.
1-ηP=0.5ω+R,
Sz=KF0ct2AL+z2βzT2zexp-2ηPτsz.
Tz=exp-0L+zαax+αmxdx=exp-τazexp-τmz.
θl21+τsz θdlsL.
θcθg,
θFOVzz+Lθgθu.
θlθFOVθu,
Sz=Kct2βzz, rz, r, θFOVdr,
z, r, θFOV=AF01L+z2r-rL+zθFOVz, rdr.
Sz=Kct2βzAF01L+z2rL+zθFOV/2×z, rdrr-rL+zθFOVz, rdr.
rL+zθFOV/2z, rdr=r-rL+zθFOVz, rdr.
rL+zθFOV/2z, rdr=F0Tzexp-ηPτsz.
Sz=KF0ct2AL+z2βzexp-2ηzτsz,
βz=βzpθpπ,  π-1+τsz θdθπ,
Sz=KF0ct2AL+z2βzT2zexp-2ηPτsz.
τ=τa+τm+ηPτs.
l*=ls1-g,
lsn=0gn=ls1-g=l*.

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