Abstract

Scattering from atmospheric aerosols causes blurring of satellite images. A study of this effect suggests that it might be possible to evaluate aerosol properties from these images. We consider an aerosol layer superimposed on a surface with a one-dimensional sinusoidal variation in reflectivity and with a half-plane reflectivity variation. A single scattering approximation is used to show that information about the aerosol layer height and optical depth can be extracted provided the variation in ground reflectivity is known.

© 1998 Optical Society of America

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References

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  1. A. P. Odell, J. A. Weinman, “The effect of atmospheric haze on images of the Earth’s surface,” J. Geophys. Res. 80, 5035–5040 (1975).
    [CrossRef]
  2. S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.
  3. R. E. Turner, “Elimination of atmospheric effects from remote sensor data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 783–793.
  4. Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.
  5. J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface nonhomogeneity,” Photogramm. Eng. Remote Sensing 46, 1173–1180 (1980).
  6. D. Tanre, M. Herman, P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981).
    [CrossRef] [PubMed]
  7. Y. J. Kaufman, “The atmospheric effect on the separability of field classes measured from satellite,” Remote Sensing Environ. 18, 21–34 (1985).
    [CrossRef]
  8. T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).
  9. Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
    [CrossRef]
  10. M. Griggs, “Determination of the aerosol content in the atmosphere from ERTS-1 data,” in Proceedings of the Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1974), pp. 471–481.
  11. D. H. Williams, J. L. Cogan, “Estimation of visibility from satellite imagery,” Appl. Opt. 30, 414–419 (1991).
    [CrossRef] [PubMed]
  12. D. J. Van Blerkom, “The effect of haze on the visibility of martian surface features,” Icarus 14, 235–244 (1971).
    [CrossRef]
  13. J. Otterman, R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979).
    [CrossRef] [PubMed]

1991 (1)

1988 (1)

Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
[CrossRef]

1985 (1)

Y. J. Kaufman, “The atmospheric effect on the separability of field classes measured from satellite,” Remote Sensing Environ. 18, 21–34 (1985).
[CrossRef]

1981 (1)

1980 (1)

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface nonhomogeneity,” Photogramm. Eng. Remote Sensing 46, 1173–1180 (1980).

1979 (1)

1975 (1)

A. P. Odell, J. A. Weinman, “The effect of atmospheric haze on images of the Earth’s surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

1971 (1)

D. J. Van Blerkom, “The effect of haze on the visibility of martian surface features,” Icarus 14, 235–244 (1971).
[CrossRef]

Cogan, J. L.

Dave, J. V.

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface nonhomogeneity,” Photogramm. Eng. Remote Sensing 46, 1173–1180 (1980).

Deschamps, P. Y.

Fraser, R. S.

Griggs, M.

M. Griggs, “Determination of the aerosol content in the atmosphere from ERTS-1 data,” in Proceedings of the Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1974), pp. 471–481.

Haba, Y.

T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

Herman, M.

Kaufman, Y. J.

Y. J. Kaufman, “The atmospheric effect on the separability of field classes measured from satellite,” Remote Sensing Environ. 18, 21–34 (1985).
[CrossRef]

Kawata, Y.

Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
[CrossRef]

T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

Kusaka, T.

Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
[CrossRef]

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

Odell, A. P.

A. P. Odell, J. A. Weinman, “The effect of atmospheric haze on images of the Earth’s surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Otterman, J.

Tanre, D.

Terashita, Y.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

Turner, R. E.

R. E. Turner, “Elimination of atmospheric effects from remote sensor data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 783–793.

Ueno, S.

Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
[CrossRef]

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).

Van Blerkom, D. J.

D. J. Van Blerkom, “The effect of haze on the visibility of martian surface features,” Icarus 14, 235–244 (1971).
[CrossRef]

Weinman, J. A.

A. P. Odell, J. A. Weinman, “The effect of atmospheric haze on images of the Earth’s surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Williams, D. H.

Appl. Opt. (3)

Icarus (1)

D. J. Van Blerkom, “The effect of haze on the visibility of martian surface features,” Icarus 14, 235–244 (1971).
[CrossRef]

Int. J. Remote Sensing (1)

Y. Kawata, S. Ueno, T. Kusaka, “Radiometric correction for atmospheric and topographic effects on Landsat MSS images,” Int. J. Remote Sensing 9, 729–748 (1988).
[CrossRef]

J. Geophys. Res. (1)

A. P. Odell, J. A. Weinman, “The effect of atmospheric haze on images of the Earth’s surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Photogramm. Eng. Remote Sensing (1)

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface nonhomogeneity,” Photogramm. Eng. Remote Sensing 46, 1173–1180 (1980).

Remote Sensing Environ. (1)

Y. J. Kaufman, “The atmospheric effect on the separability of field classes measured from satellite,” Remote Sensing Environ. 18, 21–34 (1985).
[CrossRef]

Other (5)

T. Kusaka, Y. Kawata, Y. Haba, S. Ueno, “Allowance of atmospheric effects on identification of ground objects in critical size,” in Proceedings of the Second Asian Conference on Remote Sensing (ACRS, Japan, 1981).

M. Griggs, “Determination of the aerosol content in the atmosphere from ERTS-1 data,” in Proceedings of the Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1974), pp. 471–481.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, “The atmospheric blurring effect on remotely sensed Earth imagery,” in Remote Sensing of the Environment: Inversion Methods and Applications, A. L. Fymat, V. E. Zuev, eds. (Elsevier, New York, 1978), p. 305.

R. E. Turner, “Elimination of atmospheric effects from remote sensor data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 783–793.

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, “Atmospheric effects and their correction in airborne sensor and Landsat MSS data,” in Proceedings of the Twelfth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1978), pp. 1241–1257.

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Figures (4)

Fig. 1
Fig. 1

Total radiance L s that reaches the sensor (dashed curve) and intrinsic ground radiance L i (solid curve), both normalized to the solar irradiance E 0 at the top of the atmosphere versus the dimensionless variable t = x/λ for a one-dimensional sinusoidal ground reflectivity variation with spatial frequency 1/λ. Results are shown for different values of the dimensionless parameter k = h/λ, (dτ = 0.1, b 0 = 1, ϑ0 = 30°).

Fig. 2
Fig. 2

Mean value s of the total radiance that reaches the sensor normalized to the solar irradiance E 0 at the top of the atmosphere versus the optical depth for a one-dimensional sinusoidal ground reflectivity variation with spatial frequency 1/λ (b 0 = 1, ϑ0 = 30°).

Fig. 3
Fig. 3

Amplitude ΔL s of the signal received by the sensor, normalized to the solar irradiance E 0 as a function of the dimensionless variable k = h/λ for a one-dimensional sinusoidal ground reflectivity variation with frequency 1/λ. Results are shown for different values of the aerosol layer optical depth (b 0 = 1, ϑ0 = 30°).

Fig. 4
Fig. 4

Total radiance L s that reaches the sensor normalized to the solar irradiance E 0 at the top of the atmosphere versus the distance y (m) perpendicular to the boundary between two half-planes of different reflectivity. Results are shown for different values of height h of the scattering layer ( = 0.1, a = 0.8, b = 0.01, ϑ0 = 30°).

Equations (12)

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L b x ,   y = d τ   E g π   h   - +     P φ b x ,   y h 2 + x - x 2 + y - y 2 3 / 2 d x d y ,
L b t = 1 2   b 0 d τ   E 0 π μ 0 exp - d τ 0 + d τ 2 × 1 + exp - 2 π k cos 2 π t ,
L i t = b 0 E 0 π μ 0 exp - d τ 0 + d τ 2 1 + cos 2 π t .
L S t = E 0 π b 0 μ 0 exp - d τ 0 + d τ 2 exp - d τ × 1 + cos 2 π t + d τ 2 1 + exp - 2 π k × cos 2 π t + d τ 4 .
L ¯ S = E 0 π b 0 μ 0 exp - d τ 0 + d τ 2 × exp - d τ + d τ 2 + d τ 4 ,
Δ L S = L S , max - L S , min = E 0 π   b 0 μ 0 exp - d τ 0 + d τ 2 × 2   exp - d τ + d τ   exp - 2 π k ,
b x ,   y = a , y < 0 b , y > 0
L b x ,   y = 1 2 π d τ   E 0 π μ 0 exp - d τ 0 + d τ 2 × π 2 a + b - a - b arctan y h .
L i x ,   y = a   E 0 π μ 0 exp - d τ 0 + d τ 2 , y < 0 b   E 0 π μ 0 exp - d τ 0 + d τ 2 , y > 0 ,
L S , y < 0 x ,   y = E 0 π μ 0 exp - d τ 0 + d τ 2 a   exp - d τ + d τ 2 π π 2 a + b - a - b arctan y h + d τ 4 , L S , y > 0 x ,   y = E 0 π μ 0 exp - d τ 0 + d τ 2 b   exp - d τ + d τ 2 π π 2 a + b - a - b arctan y h + d τ 4 .
L S , y < 0 - - L S , y > 0 + = a - b E 0 π μ 0 exp - d τ 0 + d τ 2 exp - d τ + d τ 2 .
- d 0   L S , y < 0 y d y = E 0 π μ 0 exp - d τ 0 + d τ 2 × ad   exp - d τ + d τ 2 π π 2   d a + b + b - a h 2 log 1 + d 2 h 2 + d   arctan - d h - d   d τ π ,

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