Abstract

A fairly accurate analytical expression of the measured reflectance is established for the general case of a non-Lambertian and nonuniform ground by separating the atmospheric and surface effects. The signal is nearly linear in the function of intrinsic atmospheric reflectance, the actual target reflectance, and two average ground reflectances, angular and spatial, to be defined. Contrast reduction by the atmosphere, defined in the cases of Lambertian and directional ground reflectances, has been evaluated using this formulation.

© 1979 Optical Society of America

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  1. S. Q. Duntley, J. I. Gordon, J. H. Taylor, C. T. White, A. R. Boileau, J. E. Tyler, R. W. Austin, J. L. Harris, Appl. Opt. 3, 549 (1964).
    [CrossRef]
  2. R. S. Fraser, J. Opt. Soc. Am. 54, 289 (1964).
    [CrossRef]
  3. B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
    [CrossRef]
  4. S. Ueno, S. Mukai, in Proceedings of the IFAC Symposium on Environmental Systems Planning, Design, and Control, H. Akashi, Ed. (Pergamon, Oxford, 1977), pp. 423–428.
  5. H. R. Gordon, Appl. Opt. 17, 1631 (1978).
    [CrossRef] [PubMed]
  6. A. P. Odell, J. A. Weinman, J. Geophys. Res. 80, 5035 (1975).
    [CrossRef]
  7. Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.
  8. P. Koepke, K. T. Kriebel, Appl. Opt. 17, 260 (1978).
    [CrossRef] [PubMed]
  9. K. L. Coulson, E. L. Gray, G. M. Bouricius, “A Study of the Reflection and Polarization Characteristics of Selected Natural and Artificial Surfaces,” Technical Information Series, Report R65SD4, Space Sciences Laboratory, General Electric Co. (1965).
  10. K. L. Coulson, H. Jacobowitz, “Proposed Calibration Target for the Visible Channel of a Satellite Radiometer,” NOAA Technical Report NESS 62 (1972).
  11. S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).
  12. D. V. Hoyt, J. Appl. Meteorol. 16, 432 (1977).
    [CrossRef]
  13. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).
  14. D. Tanré, “Etude de l’influence des Aérosols sur le Rayonnement Terrestre Retrodiffusé,” Thèse de 3e Cycle, Université de’Lille (1977).
  15. K. T. Kriebel, Appl. Opt. 17, 253 (1978).
    [CrossRef] [PubMed]

1978 (3)

1977 (1)

D. V. Hoyt, J. Appl. Meteorol. 16, 432 (1977).
[CrossRef]

1975 (1)

A. P. Odell, J. A. Weinman, J. Geophys. Res. 80, 5035 (1975).
[CrossRef]

1971 (1)

B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
[CrossRef]

1964 (2)

Austin, R. W.

Boileau, A. R.

Bouricius, G. M.

K. L. Coulson, E. L. Gray, G. M. Bouricius, “A Study of the Reflection and Polarization Characteristics of Selected Natural and Artificial Surfaces,” Technical Information Series, Report R65SD4, Space Sciences Laboratory, General Electric Co. (1965).

Browing, S. R.

B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
[CrossRef]

Coulson, K. L.

K. L. Coulson, E. L. Gray, G. M. Bouricius, “A Study of the Reflection and Polarization Characteristics of Selected Natural and Artificial Surfaces,” Technical Information Series, Report R65SD4, Space Sciences Laboratory, General Electric Co. (1965).

K. L. Coulson, H. Jacobowitz, “Proposed Calibration Target for the Visible Channel of a Satellite Radiometer,” NOAA Technical Report NESS 62 (1972).

Curran, R. J.

B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
[CrossRef]

Duntley, S. Q.

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

Fraser, R. S.

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

Gordon, H. R.

Gordon, J. I.

Gray, E. L.

K. L. Coulson, E. L. Gray, G. M. Bouricius, “A Study of the Reflection and Polarization Characteristics of Selected Natural and Artificial Surfaces,” Technical Information Series, Report R65SD4, Space Sciences Laboratory, General Electric Co. (1965).

Haba, Y.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

Harris, J. L.

Herman, B. M.

B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
[CrossRef]

Hoyt, D. V.

D. V. Hoyt, J. Appl. Meteorol. 16, 432 (1977).
[CrossRef]

Jacobowitz, H.

K. L. Coulson, H. Jacobowitz, “Proposed Calibration Target for the Visible Channel of a Satellite Radiometer,” NOAA Technical Report NESS 62 (1972).

Kawata, Y.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

Koepke, P.

Kriebel, K. T.

Kusaka, T.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

Mukai, S.

S. Ueno, S. Mukai, in Proceedings of the IFAC Symposium on Environmental Systems Planning, Design, and Control, H. Akashi, Ed. (Pergamon, Oxford, 1977), pp. 423–428.

Odell, A. P.

A. P. Odell, J. A. Weinman, J. Geophys. Res. 80, 5035 (1975).
[CrossRef]

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

Tanré, D.

D. Tanré, “Etude de l’influence des Aérosols sur le Rayonnement Terrestre Retrodiffusé,” Thèse de 3e Cycle, Université de’Lille (1977).

Taylor, J. H.

Terashita, Y.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

Tyler, J. E.

Ueno, S.

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

S. Ueno, S. Mukai, in Proceedings of the IFAC Symposium on Environmental Systems Planning, Design, and Control, H. Akashi, Ed. (Pergamon, Oxford, 1977), pp. 423–428.

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Voltz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

Weinman, J. A.

A. P. Odell, J. A. Weinman, J. Geophys. Res. 80, 5035 (1975).
[CrossRef]

White, C. T.

Appl. Opt. (4)

J. Appl. Meteorol. (1)

D. V. Hoyt, J. Appl. Meteorol. 16, 432 (1977).
[CrossRef]

J. Atmos. Sci. (1)

B. M. Herman, S. R. Browing, R. J. Curran, J. Atmos. Sci. 28, 419 (1971).
[CrossRef]

J. Geophys. Res. (1)

A. P. Odell, J. A. Weinman, J. Geophys. Res. 80, 5035 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (7)

S. Ueno, S. Mukai, in Proceedings of the IFAC Symposium on Environmental Systems Planning, Design, and Control, H. Akashi, Ed. (Pergamon, Oxford, 1977), pp. 423–428.

K. L. Coulson, E. L. Gray, G. M. Bouricius, “A Study of the Reflection and Polarization Characteristics of Selected Natural and Artificial Surfaces,” Technical Information Series, Report R65SD4, Space Sciences Laboratory, General Electric Co. (1965).

K. L. Coulson, H. Jacobowitz, “Proposed Calibration Target for the Visible Channel of a Satellite Radiometer,” NOAA Technical Report NESS 62 (1972).

S. Ueno, Y. Haba, Y. Kawata, T. Kusaka, Y. Terashita, in Remote Sensing of the Atmosphere: Inversion Methods and Application, A. L. Fymat, V. E. Zuev, Eds. (Elsevier, New York, 1979).

Y. Kawata, Y. Haba, T. Kusaka, Y. Terashita, S. Ueno, in Proceedings of the Twelfth International Symposium on Remote Sensing of Environment, Ann Arbor (1978), pp. 1241–1257.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, J. S. Garing, “Optical Properties of the Atmosphere,” AFCRL 71-0279, Environmental Research Paper 354 (1971).

D. Tanré, “Etude de l’influence des Aérosols sur le Rayonnement Terrestre Retrodiffusé,” Thèse de 3e Cycle, Université de’Lille (1977).

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Figures (5)

Fig. 1
Fig. 1

Successive orders of radiation interactions in the ground–atmosphere system.

Fig. 2
Fig. 2

Relative contributions A, B, and C of reflectances ρ, ρ ¯, and 〈ρ〉 vs the zenithal solar angle, for a vertical observation (A is represented by a solid line, B is represented by a dashed line, and C is represented by a dotted line).

Fig. 3
Fig. 3

Angular average reflectance ρ ¯ for the incident diffuse radiation vs true reflectance for three atmosphere models at λ = 450 nm [Fig. 4(a)] and 850 nm [Fig. 4(b)]. Each point corresponds to different geometric conditions (solar incidence and observation angle).

Fig. 4
Fig. 4

Average reflectance of environment vs the distance between the target M and the separation of the two half planes (ρ0 = 0 and ρ1 = 1) for two of McClatchey’s models (V = 23 km and V = 5 km) at λ = 450 nm and λ = 850 nm.

Fig. 5
Fig. 5

Contrast reduction vs wavelength for three atmosphere models: (1) large Lambertian targets; (2) small Lambertian targets; (3) and (4) are the same as (1) and (2) but for the directional reflectance of the savannah, and (5) specular reflectance.

Tables (4)

Tables Icon

Table I Optical Thicknesses for Four Wavelengths and Four Visibilities

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Table II Function r for Four Wavelengths and for Three Atmosphere Models

Tables Icon

Table III Function E(μ) for Several Zenithal Angles (μ = cosΘ)

Tables Icon

Table IV Atmospheric Contribution ρa(μ,Φ,μ00) for Vertical Observation (μ = 1)

Equations (20)

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ρ = I μ 0 f ,
ρ ( M , S 0 , S ) = ρ a ( μ 0 , μ , ϕ ) + exp ( - τ / μ 0 ) ρ exp ( - τ / μ ) + E ( μ 0 ) ρ exp ( - τ / μ ) + [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] ρ E ( μ ) + { n = 1 [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] ( ρ r ) n } × ρ [ exp ( - τ / μ ) + E ( μ ) ] ,
ρ ( M , S 0 , S ) = ρ a ( μ 0 , μ , ϕ ) + ρ 1 - ρ r [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] [ exp ( - τ / μ ) + E ( μ ) ] .
E ( μ ) = E ( μ ) .
ρ ( M , S 0 , S ) = ρ a ( μ 0 , μ , ϕ ) + ρ 1 - ρ r [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] [ exp ( - τ / μ ) + E ( μ ) ] .
E ( μ 0 ) = 1 μ 0 f 0 2 π 0 - 1 I d - ( τ , μ 0 , μ , ϕ ) μ d μ d ϕ ,
r = 1 π 0 2 π 0 - 1 I - ( τ , μ ) μ d μ d ϕ ,
ρ ( M , μ 0 , μ , ϕ ) = ρ a ( μ 0 , μ , ϕ ) + ρ ( M , μ 0 , μ , ϕ ) exp ( - τ / μ 0 ) exp ( - τ / μ ) + ρ ¯ ( M , μ 0 , μ , ϕ ) exp ( - τ / μ ) E ( μ 0 ) + ρ ( M , μ 0 , μ , ϕ ) [ E ( μ 0 ) + exp ( - τ / μ 0 ) ] E ( μ ) + ρ ( M , μ 0 , μ , ϕ ) r [ ρ ¯ ( M , μ 0 μ , ϕ ) exp ( - τ / μ ) + ρ ( M , μ 0 , μ , ϕ ) E ( μ ) 1 - ρ ( M , μ 0 , μ , ϕ ) r ] [ E ( μ 0 ) + exp ( - τ / μ 0 ) ] .
ρ ¯ ( M , μ 0 , μ , ϕ ) = 1 μ 0 f E ( μ 0 ) 0 2 π 0 - 1 ρ ( M , μ , μ , ϕ - ϕ ) I d - ( τ , μ 0 , μ , ϕ ) μ d μ d ϕ .
ρ ( M , μ 0 , μ , ϕ ) = 1 E ( μ ) - + - + ρ ¯ ( M ) t ( μ , x , y ) d x d y ,
ρ ρ a + 1 1 - ρ r ( A ρ + B ρ ¯ + C ρ ) ,
r ( 0.92 τ r + α τ p ) exp [ - ( τ r + τ p ) ] ,
E ( μ ) exp ( - τ / μ ) { exp [ ( 0.52 τ r + β τ p ) / μ ] - 1 } ,
ρ ¯ = ρ ¯ 0 + a ρ ,
R = ρ 1 - ρ 2 ρ 1 - ρ 2 ,
R = A + B + C , R = [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] [ exp ( - τ / μ ) + E ( μ ) ] .
R = A + B , R = [ exp ( - τ / μ 0 ) + E ( μ 0 ) ] exp ( - τ / μ ) . } .
R = [ exp ( - τ / μ 0 ) + a E ( μ 0 ) ] [ exp ( - τ / μ ) + a E ( μ ) ] .
R = [ exp ( - τ / μ 0 ) + a E ( μ 0 ) ] exp ( - τ / μ 0 ) .
R = exp ( - τ / μ 0 ) exp ( - τ / μ ) .

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