Abstract

A new technique for modeling image transfer through cirrus clouds is presented. The technique uses a ray trace to model beam propagation through a three-dimensional volume of polydisperse, hexagonal ice crystals. Beyond the cloud, the technique makes use of standard Huygens–Fresnel propagation methods. At the air–cloud interface, each wave front is resolved into a ray distribution for input to the ray trace software. Similarly, a wave front is reconstructed from the output ray distribution at the cloud–air interface. Simulation output from the ray trace program is presented and the modulation transfer function for stars imaged through cirrus clouds of varying depths is discussed.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  2. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
    [CrossRef]
  3. K. Sassen, K. N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,” J. Atmos. Sci. 36, 852–861 (1979).
    [CrossRef]
  4. K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Bull. Am. Meteorol. Soc. 114, 1167–1199 (1986).
  5. G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
    [CrossRef]
  6. L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
    [CrossRef]
  7. D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).
  8. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  9. K. M. Yoo, Q. Xing, R. R. Alfano, “Imaging objects hidden in highly scattering media using femtosecond second-harmonic-generation cross-correlation time gating,” Opt. Lett. 16, 1019–1021 (1991).
    [CrossRef] [PubMed]
  10. A. Sappey, “Optical imaging through turbid media with a degenerate four-wave mixing correlation time gate,” Appl. Opt. 33, 8346–8354 (1994).
    [CrossRef] [PubMed]
  11. O. Emile, F. Bretenaker, A. Le Floch, “Rotating polarization imaging in turbid media,” Opt. Lett. 21, 1706–1708 (1996).
    [CrossRef] [PubMed]
  12. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteor. Soc. Jpn. 58, 289–300 (1983).
  13. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
    [CrossRef]
  14. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).
  15. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, Vol. 38 of Pure and Applied Physics (Academic, New York, 1972).
  16. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
    [CrossRef]
  17. P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [CrossRef] [PubMed]
  18. K. Muinonen, K. Lumme, J. Peltoniemi, W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989).
    [CrossRef] [PubMed]
  19. Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
    [CrossRef] [PubMed]
  20. K. N. Liou, Q. Cai, P. W. Barber, S. C. Hill, “Scattering phase matrix comparison for randomly hexagonal cylinders and spheroids,” Appl. Opt. 22, 1684–1687 (1983).
    [CrossRef] [PubMed]
  21. K. N. Liou, Q. Cai, J. B. Pollack, J. N. Cuzzi, “Light scattering by randomly oriented cubes and parallelepipeds,” Appl. Opt. 22, 3001–3008 (1983).
    [CrossRef] [PubMed]
  22. Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
    [CrossRef] [PubMed]
  23. P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
    [CrossRef] [PubMed]
  24. M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
    [CrossRef] [PubMed]
  25. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [CrossRef] [PubMed]
  26. J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
    [CrossRef]
  27. H. Pruppacher, J. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
    [CrossRef]
  28. D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.
  29. F. G. Smith, ed., Atmospheric Propagation of Radiation, Vol. 2 of The Infrared and Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), p. 112.
  30. E. Hecht, A. Zajac, Optics, Addison-Wesley Series in Physics (Addison-Wesley, Reading, Mass., 1974).
  31. H. F. Davis, A. D. Snider, Introduction to Vector Analysis (Allyn and Bacon, Boston, 1979).
  32. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).
  33. A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
    [CrossRef] [PubMed]
  34. M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
    [CrossRef]
  35. A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
    [CrossRef]
  36. P. M. Duffieux, L’Integral de Fourier et ses Applications a l’Optique (Faculté des Sciences, Besançon, France, 1946).
  37. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
    [CrossRef]
  38. M. Roggeman, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  39. D. G. Voelz, J. D. Gonglewski, P. Idell, “SCIP computer simulation and laboratory verification,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc SPIE2029, 169–176 (1993).
  40. K. Sassen, “Cirrus clouds and halos: a closer look,” Opt. Photon. News 10, 39–42 (1999).
    [CrossRef]
  41. W. Tape, Atmospheric Halos, Vol. 64 of the Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  42. F. Pattloch, E. Trankle, “Monte carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. 1, 520–526 (1984).
    [CrossRef]

1999 (1)

K. Sassen, “Cirrus clouds and halos: a closer look,” Opt. Photon. News 10, 39–42 (1999).
[CrossRef]

1998 (1)

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

1996 (3)

1995 (4)

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

1994 (2)

1993 (1)

1992 (2)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

1991 (1)

1990 (1)

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

1989 (3)

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

K. Muinonen, K. Lumme, J. Peltoniemi, W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989).
[CrossRef] [PubMed]

1986 (1)

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Bull. Am. Meteorol. Soc. 114, 1167–1199 (1986).

1985 (1)

1984 (1)

F. Pattloch, E. Trankle, “Monte carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. 1, 520–526 (1984).
[CrossRef]

1983 (3)

1982 (1)

1979 (2)

K. Sassen, K. N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
[CrossRef] [PubMed]

1978 (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Alfano, R. R.

Asano, S.

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteor. Soc. Jpn. 58, 289–300 (1983).

Barber, P. W.

Bastiaans, M. J.

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Benayahu, Y.

L. R. Bissonnette, 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. Winker, 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, 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. Winker, 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, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Bretenaker, F.

Bruscaglioni, P.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Cai, Q.

Carlson, B. E.

Cohen, A.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Cuzzi, J. N.

Davis, H. F.

H. F. Davis, A. D. Snider, Introduction to Vector Analysis (Allyn and Bacon, Boston, 1979).

Dolash, T. M.

D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.

Duffieux, P. M.

P. M. Duffieux, L’Integral de Fourier et ses Applications a l’Optique (Faculté des Sciences, Besançon, France, 1946).

Egert, S.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Eloranta, E.

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

Emile, O.

Flatau, P. J.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Flesia, C.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Gonglewski, J. D.

D. G. Voelz, J. D. Gonglewski, P. Idell, “SCIP computer simulation and laboratory verification,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc SPIE2029, 169–176 (1993).

Hecht, E.

E. Hecht, A. Zajac, Optics, Addison-Wesley Series in Physics (Addison-Wesley, Reading, Mass., 1974).

Hess, M.

Hill, S. C.

Iaquinta, J.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

Idell, P.

D. G. Voelz, J. D. Gonglewski, P. Idell, “SCIP computer simulation and laboratory verification,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc SPIE2029, 169–176 (1993).

Irvine, W. M.

Isaka, H.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).

Ismaelli, A.

L. R. Bissonnette, 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. Winker, 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, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Jayaweera, K.

Katsev, I. L.

L. R. Bissonnette, 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. Winker, 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, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Kleiman, M.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Klett, J.

H. Pruppacher, J. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

Le Floch, A.

Leonelli, J.

D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.

Liou, K. N.

P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Bull. Am. Meteorol. Soc. 114, 1167–1199 (1986).

K. N. Liou, Q. Cai, J. B. Pollack, J. N. Cuzzi, “Light scattering by randomly oriented cubes and parallelepipeds,” Appl. Opt. 22, 3001–3008 (1983).
[CrossRef] [PubMed]

K. N. Liou, Q. Cai, P. W. Barber, S. C. Hill, “Scattering phase matrix comparison for randomly hexagonal cylinders and spheroids,” Appl. Opt. 22, 1684–1687 (1983).
[CrossRef] [PubMed]

Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
[CrossRef] [PubMed]

K. Sassen, K. N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

Lumme, K.

Macke, A.

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

Mishchenko, M. I.

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

Mueller, J.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Muinonen, K.

Noormohammadian, M.

L. R. Bissonnette, 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. Winker, 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. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Pattloch, F.

F. Pattloch, E. Trankle, “Monte carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. 1, 520–526 (1984).
[CrossRef]

Peltoniemi, J.

Personne, P.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

Piironen, P.

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

Pollack, J. B.

Polonsky, I. N.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Pruppacher, H.

H. Pruppacher, J. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

Raschke, E.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Roggeman, M.

M. Roggeman, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Rose, R. L.

D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.

Rusk, D. J.

D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.

Sappey, A.

Sassen, K.

K. Sassen, “Cirrus clouds and halos: a closer look,” Opt. Photon. News 10, 39–42 (1999).
[CrossRef]

K. Sassen, K. N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

Schwendimann, P.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Snider, A. D.

H. F. Davis, A. D. Snider, Introduction to Vector Analysis (Allyn and Bacon, Boston, 1979).

Stackhouse, P. W.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Starkov, A. V.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, Vol. 38 of Pure and Applied Physics (Academic, New York, 1972).

Stephens, G. L.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Takano, Y.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
[CrossRef] [PubMed]

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteor. Soc. Jpn. 58, 289–300 (1983).

Tape, W.

W. Tape, Atmospheric Halos, Vol. 64 of the Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

Trankle, E.

F. Pattloch, E. Trankle, “Monte carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. 1, 520–526 (1984).
[CrossRef]

Tsay, S. C.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Voelz, D. G.

D. G. Voelz, J. D. Gonglewski, P. Idell, “SCIP computer simulation and laboratory verification,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc SPIE2029, 169–176 (1993).

Weickmann, H. K.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

Welsh, B.

M. Roggeman, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Wendling, P.

Wendling, R.

Wiegner, M.

Winker, D. M.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Wolf, W.

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

Wylie, D.

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

Xing, Q.

Yang, P.

Yoo, K. M.

Zaccanti, G.

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Zajac, A.

E. Hecht, A. Zajac, Optics, Addison-Wesley Series in Physics (Addison-Wesley, Reading, Mass., 1974).

Zege, E. P.

L. R. Bissonnette, 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. Winker, 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, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Appl. Opt. (10)

P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
[CrossRef] [PubMed]

Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
[CrossRef] [PubMed]

K. N. Liou, Q. Cai, P. W. Barber, S. C. Hill, “Scattering phase matrix comparison for randomly hexagonal cylinders and spheroids,” Appl. Opt. 22, 1684–1687 (1983).
[CrossRef] [PubMed]

K. N. Liou, Q. Cai, J. B. Pollack, J. N. Cuzzi, “Light scattering by randomly oriented cubes and parallelepipeds,” Appl. Opt. 22, 3001–3008 (1983).
[CrossRef] [PubMed]

Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
[CrossRef] [PubMed]

K. Muinonen, K. Lumme, J. Peltoniemi, W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989).
[CrossRef] [PubMed]

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

A. Sappey, “Optical imaging through turbid media with a degenerate four-wave mixing correlation time gate,” Appl. Opt. 33, 8346–8354 (1994).
[CrossRef] [PubMed]

P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

Appl. Phys. B (1)

L. R. Bissonnette, 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. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bull. Am. Meteorol. Soc. (2)

D. Wylie, P. Piironen, W. Wolf, E. Eloranta, “Understanding satellite cirrus cloud climatologies with calibrated Lidar optical depths,” Bull. Am. Meteorol. Soc. 52, 4327–4343 (1995).

K. N. Liou, “Review: influence of cirrus clouds on weather and climate processes: a global perspective,” Bull. Am. Meteorol. Soc. 114, 1167–1199 (1986).

J. Atmos. Sci. (6)

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

K. Sassen, K. N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

J. Geophys. Res. (1)

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving d-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

J. Meteor. Soc. Jpn. (1)

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteor. Soc. Jpn. 58, 289–300 (1983).

J. Opt. Soc. Am. (1)

F. Pattloch, E. Trankle, “Monte carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. 1, 520–526 (1984).
[CrossRef]

Opt. Commun. (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Opt. Eng. (2)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

K. Sassen, “Cirrus clouds and halos: a closer look,” Opt. Photon. News 10, 39–42 (1999).
[CrossRef]

Other (13)

W. Tape, Atmospheric Halos, Vol. 64 of the Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

M. Roggeman, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

D. G. Voelz, J. D. Gonglewski, P. Idell, “SCIP computer simulation and laboratory verification,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc SPIE2029, 169–176 (1993).

P. M. Duffieux, L’Integral de Fourier et ses Applications a l’Optique (Faculté des Sciences, Besançon, France, 1946).

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, Vol. 38 of Pure and Applied Physics (Academic, New York, 1972).

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

H. Pruppacher, J. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

D. J. Rusk, R. L. Rose, T. M. Dolash, J. Leonelli, “Observations of high altitude tropical cirrus with an airborne LIDAR,” in Sixth Conference on Aviation Weather Systems (American Meteorological Society, Boston, 1995), pp. 320–324.

F. G. Smith, ed., Atmospheric Propagation of Radiation, Vol. 2 of The Infrared and Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), p. 112.

E. Hecht, A. Zajac, Optics, Addison-Wesley Series in Physics (Addison-Wesley, Reading, Mass., 1974).

H. F. Davis, A. D. Snider, Introduction to Vector Analysis (Allyn and Bacon, Boston, 1979).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).

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 (17)

Fig. 1
Fig. 1

Wire-frame models of columns and plates used in ray trace software.

Fig. 2
Fig. 2

Bullets and some bullet rosette combinations.

Fig. 3
Fig. 3

Sample particle size distribution with shape distribution, shown for the top and the bottom of the cloud.

Fig. 4
Fig. 4

One 0.125-cm3 element with not-to-scale crystal within three-dimensional space.

Fig. 5
Fig. 5

Ray distributions for uplink and downlink beams.

Fig. 6
Fig. 6

Phase function geometry for an in situ cloud.

Fig. 7
Fig. 7

Histogram of input rays from the ±3-mrad array used in phase functions.

Fig. 8
Fig. 8

Phase function for an in situ cloud whose particles have a random orientation. The solid curve was generated by a forward-scattered ray distribution from a downlink beam. The dotted curve was generated by a backscattered ray distribution from the same beam.

Fig. 9
Fig. 9

Phase function for an in situ cloud whose particles have a horizontal preference. The solid curve was generated by a forward-scattered ray distribution from a downlink beam. The dotted curve was generated by a backscattered ray distribution from the same beam.

Fig. 10
Fig. 10

Expanded phase functions for each of the three input beams from the cloud with horizontal-preference particles. The input beams are (a) ±3 mrad; (b) ±5 mrad, and (c) ±7 mrad.

Fig. 11
Fig. 11

General imaging model for image transfer through cirrus clouds.

Fig. 12
Fig. 12

Downlink forward-scattered ray distribution produced by starlight mapped onto a two-dimensional grid.

Fig. 13
Fig. 13

Binning of output ray distribution into individual pixels.

Fig. 14
Fig. 14

Model for the calculation of a MTF for the cloud and receiver combination.

Fig. 15
Fig. 15

MTF for diffraction-limited pupil compared with the cloud–receiver combination for three different cloud densities. The curves represent (a) diffraction-limited pupil, (b) τ = 1.8, (c) τ = 2.5, and (d) τ = 4.125.

Fig. 16
Fig. 16

Compressed star images as seen through cirrus clouds with (a) τ = 1.8, (b) τ = 2.5, and (c) τ = 4.125.

Fig. 17
Fig. 17

Cross-sectional plots of each of the star images shown in Fig. 16 with (a) τ = 1.8, (b) τ = 2.5, and (c) τ = 4.125.

Equations (8)

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

Pout=Pin exp-αt,
|Ei,j|=n=1N |Ei,jn|,
ki,j=n=1N |Ei,jn|ki,jnn=1N |Ei,jn|,
li,jn=q nqlq,
li,j=n=1N |Ei,jn|li,jnn=1N |Ei,jn|.
Wi,j=|Ei,j| expi 2πλli,j+ki,j·ri,j,
ξ, η=F-1|Fpx, y|2Σ |Fpx, y|2dΣ,
ξ, η=|ξ, η|.

Metrics