Abstract

A hybrid technique to simulate the imaging of space-based objects through cirrus clouds is presented. The method makes use of standard Huygens–Fresnel propagation beyond the cloud boundary and a novel vector trace approach within the cloud. At the top of the cloud, the wave front is divided into an array of input gradient vectors, which are in turn transmitted through the cloud model by use of the Coherent Illumination Ray Trace and Imaging Software for Cirrus. At the bottom of the cloud, the output vector distribution is used to reconstruct a wave front that continues propagating to the ground receiver. Images of the object as seen through cirrus clouds with different optical depths are compared with a diffraction-limited image. Turbulence effects from the atmospheric propagation are not included.

© 2002 Optical Society of America

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References

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  1. B. T. Landesman, P. Kindilien, C. L. Matson, “Image transfer through cirrus cloud. I. Ray trace analysis and wave-front reconstruction,” Appl. Opt. 39, 5465–5476 (2000).
    [CrossRef]
  2. 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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 1995), pp. 320–324.
  3. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 58, 289–300 (1983).
  4. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
    [CrossRef]
  5. 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]
  6. K. Muinonen, K. Lumme, J. Peltoniemi, W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989).
    [CrossRef] [PubMed]
  7. Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
    [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
    [CrossRef] [PubMed]
  11. P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 271.
  14. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [CrossRef] [PubMed]
  15. 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., Vol. 10 of the SPIE Press Monograph Series (SPIE, Bellingham, Wash., 1993), p. 112.
  16. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]

2000 (1)

1996 (1)

1993 (1)

1992 (1)

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

1989 (1)

1985 (1)

1984 (1)

1983 (3)

1982 (1)

1979 (1)

Asano, S.

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

Barber, P. W.

Bissonnette, L. R.

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

Cai, Q.

Cuzzi, J. N.

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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 1995), pp. 320–324.

Hill, S. C.

Irvine, W. M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 271.

Jayaweera, K.

Kindilien, P.

Landesman, B. T.

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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 1995), pp. 320–324.

Liou, K. N.

Lumme, K.

Macke, A.

Matson, C. L.

Muinonen, K.

Peltoniemi, J.

Pollack, J. B.

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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 1995), pp. 320–324.

Takano, Y.

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. Meteorol. Soc. Jpn. 58, 289–300 (1983).

Warren, S. G.

Weickmann, H. K.

Wendling, P.

Wendling, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

Yang, P.

Appl. Opt. (10)

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]

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

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

B. T. Landesman, P. Kindilien, C. L. Matson, “Image transfer through cirrus cloud. I. Ray trace analysis and wave-front reconstruction,” Appl. Opt. 39, 5465–5476 (2000).
[CrossRef]

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

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

J. Meteorol. Soc. Jpn. (1)

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

Opt. Eng. (1)

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

Other (4)

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, P. Anderson, ed. (American Meteorological Society, Boston, Mass., 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., Vol. 10 of the SPIE Press Monograph Series (SPIE, Bellingham, Wash., 1993), p. 112.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 271.

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Figures (13)

Fig. 1
Fig. 1

General model for imaging through cirrus clouds.

Fig. 2
Fig. 2

Conceptual model for wave-front to normal conversion. The object is propagated to the far field with a fast Fourier-transform (FFT) routine, and the resultant real and imaginary components are treated separately.

Fig. 3
Fig. 3

Creation of the wave-front normals. (a) Demonstrates the creation of a normal vector N from three points. (b) Illustrates how five adjacent pixels are used to calculate the normals. The center pixel will contain four normals, as denoted by the stars, created from the field component values in three pixels: the center pixel and the two pixels adjacent to it, denoted by the triangles.

Fig. 4
Fig. 4

Downlink vector distributions for real and imaginary arrays.

Fig. 5
Fig. 5

Binning of output ray distributions into individual pixels. Any given pixel [i, j] will contain a number of wave vectors k, each with its associated orthogonal E field vector.

Fig. 6
Fig. 6

Conceptual model to test wave-front conversion. As in Fig. 2, the object is propagated to the far field with a fast Fourier-transform (FFT) routine, and the resultant real and imaginary components are treated separately.

Fig. 7
Fig. 7

Wave-front conversion test: nonspeckled target where (a) is the original object and (b) is the reconstructed object, obtained by reconstruction of Eq. (8).

Fig. 8
Fig. 8

Wave-front conversion test: speckled target where (a) is the target object and (b) is the reconstructed object, obtained by reconstruction of Eq. (8).

Fig. 9
Fig. 9

Schematic for wave-front conversion and propagation test where (a) is the diffraction-limited imaging and (b) is the imaging obtained with the wave-front conversion process with no transmission through a cloud.

Fig. 10
Fig. 10

Results of wave-front conversion and propagation test where (a) is the diffraction-limited image and (b) is the image obtained by the wave-front conversion process with no cloud.

Fig. 11
Fig. 11

End–end simulation schematic.

Fig. 12
Fig. 12

End–end imaging results for nonspeckled target with (a) τ = 0.5, (b) τ = 1.0, (c) τ = 1.5, (d) τ = 2.0.

Fig. 13
Fig. 13

End–end imaging results for speckled target, ten-frame average with (a) τ = 0.5, (b) τ = 1.0, (c) τ = 1.5, (d) τ = 2.0.

Equations (10)

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

Wi,j=Rei,j+i Imi,j,
Wi,j=Mi,j expikϕi,j,
ϕi,j=1ktan-1Imi,jRei,j.
ki,jq=n=1NEi,jnqki,jnqn=1NEi,jnq,
li,jnq=snsls,
li,jq=n=1NEi,jnqli,jnqn=1NEi,jnq.
Wi,jq=n=1NEi,jnq expi2πλli,jnq-ki,jnq · ri,jnq,
Wi,j=ReWi,j1+i ReWi,j2.
Pout=Pin expαt,
n=1.3117+i2.93×10-9.

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