Abstract

One of the assumptions made in calculating the horizontal visibility of black targets is that every volume element of the atmosphere or medium is illuminated by the same amount of light. This assumption has always been interpreted as a homogeneous illumination, without considering the importance of the reflectance properties of the ground extending between observer and horizon along the path of sight. This paper is a theoretical and experimental study of the effect of ground, with varying reflectance properties, on the horizontal visibility. The laboratory simulation shows that, if that part of the ground extending between observer and target has a higher reflectance than the one extending between target and horizon, the visibility may decrease by up to 15%. In the opposite case, the visibility increases.

© 1983 Optical Society of America

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References

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  1. H. Koschmieder, Beitr. Phys. Freien Atmos. 12, 33, 171 (1924).
  2. W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952, 1963).
  3. H. Horvath, Atmos. Environ. 15, 1785 (1980).
  4. 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, 556 (1964).
    [CrossRef]
  5. F. E. Nicodemus, Appl. Opt. 4, 767 (1965).
    [CrossRef]
  6. D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Proceedings, Institute of Environmental Sciences (1963).
  7. J. Overington, Vision and Acquisition (Pentech, London, 1976).
  8. K. L. Coulson, Appl. Opt. 5, 905 (1966).
    [CrossRef] [PubMed]
  9. W. E. K. Middleton, A. G. Mungall, J. Opt. Soc. Am. 42, 572 (1952).
    [CrossRef]
  10. A. G. Crowther, “A Note of Comparative Measurement of the Bidirectional Reflectance of Black Nylon Velvet and Matt Black Paint,” BAC (GW) Tech. Memo. 7, Ref. L50/249 (1971).
  11. A. R. Boileau, J. I. Gordon, Appl. Opt. 5, 803 (1966).
    [CrossRef] [PubMed]
  12. K. Kondratyev, “Actinometry,” NASA TTF-9712 (U.S. GPO, Washington, D.C., 1965).
  13. A. G. Crowther, “Polar Luminance and Contrast,” Annex A, Final Report, Third Visual Studies Contrast, BAC (GW), Ref. L50/196/1535 (1972).
  14. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  15. S. Q. Duntley, A. R. Boileau, R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
    [CrossRef]
  16. H. Horvath, Atmos. Environ. 4, 177 (1971).
  17. R. Penndorf, “The Vertical Distribution of Mie Particles in the Atmosphere,” Geophysical Research Paper 20 (AFCRL, Bedford, Mass., 1954).
  18. L. Eltermann, Appl. Opt. 9, 1804 (1970).
    [CrossRef]

1980 (1)

H. Horvath, Atmos. Environ. 15, 1785 (1980).

1971 (1)

H. Horvath, Atmos. Environ. 4, 177 (1971).

1970 (1)

1966 (2)

1965 (1)

1964 (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, 556 (1964).
[CrossRef]

1963 (1)

D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Proceedings, Institute of Environmental Sciences (1963).

1957 (1)

1952 (1)

1924 (1)

H. Koschmieder, Beitr. Phys. Freien Atmos. 12, 33, 171 (1924).

Austin, R. W.

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, 556 (1964).
[CrossRef]

Boileau, A. R.

A. R. Boileau, J. I. Gordon, Appl. Opt. 5, 803 (1966).
[CrossRef] [PubMed]

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, 556 (1964).
[CrossRef]

S. Q. Duntley, A. R. Boileau, R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Coulson, K. L.

Crowther, A. G.

A. G. Crowther, “Polar Luminance and Contrast,” Annex A, Final Report, Third Visual Studies Contrast, BAC (GW), Ref. L50/196/1535 (1972).

A. G. Crowther, “A Note of Comparative Measurement of the Bidirectional Reflectance of Black Nylon Velvet and Matt Black Paint,” BAC (GW) Tech. Memo. 7, Ref. L50/249 (1971).

Duntley, S. Q.

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, 556 (1964).
[CrossRef]

S. Q. Duntley, A. R. Boileau, R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
[CrossRef]

Edwards, D. K.

D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Proceedings, Institute of Environmental Sciences (1963).

Eltermann, L.

Gordon, J. I.

A. R. Boileau, J. I. Gordon, Appl. Opt. 5, 803 (1966).
[CrossRef] [PubMed]

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, 556 (1964).
[CrossRef]

Harris, J. L.

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, 556 (1964).
[CrossRef]

Horvath, H.

H. Horvath, Atmos. Environ. 15, 1785 (1980).

H. Horvath, Atmos. Environ. 4, 177 (1971).

Kondratyev, K.

K. Kondratyev, “Actinometry,” NASA TTF-9712 (U.S. GPO, Washington, D.C., 1965).

Koschmieder, H.

H. Koschmieder, Beitr. Phys. Freien Atmos. 12, 33, 171 (1924).

Middleton, W. E. K.

W. E. K. Middleton, A. G. Mungall, J. Opt. Soc. Am. 42, 572 (1952).
[CrossRef]

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952, 1963).

Mungall, A. G.

Nicodemus, F. E.

Overington, J.

J. Overington, Vision and Acquisition (Pentech, London, 1976).

Penndorf, R.

R. Penndorf, “The Vertical Distribution of Mie Particles in the Atmosphere,” Geophysical Research Paper 20 (AFCRL, Bedford, Mass., 1954).

Preisendorfer, R. W.

Taylor, J. H.

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, 556 (1964).
[CrossRef]

Tyler, J. E.

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, 556 (1964).
[CrossRef]

White, C. T.

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, 556 (1964).
[CrossRef]

Appl. Opt. (5)

Atmos. Environ. (2)

H. Horvath, Atmos. Environ. 15, 1785 (1980).

H. Horvath, Atmos. Environ. 4, 177 (1971).

Beitr. Phys. Freien Atmos. (1)

H. Koschmieder, Beitr. Phys. Freien Atmos. 12, 33, 171 (1924).

J. Opt. Soc. Am. (2)

Proceedings, Institute of Environmental Sciences (1)

D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Proceedings, Institute of Environmental Sciences (1963).

Other (7)

J. Overington, Vision and Acquisition (Pentech, London, 1976).

K. Kondratyev, “Actinometry,” NASA TTF-9712 (U.S. GPO, Washington, D.C., 1965).

A. G. Crowther, “Polar Luminance and Contrast,” Annex A, Final Report, Third Visual Studies Contrast, BAC (GW), Ref. L50/196/1535 (1972).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

A. G. Crowther, “A Note of Comparative Measurement of the Bidirectional Reflectance of Black Nylon Velvet and Matt Black Paint,” BAC (GW) Tech. Memo. 7, Ref. L50/249 (1971).

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952, 1963).

R. Penndorf, “The Vertical Distribution of Mie Particles in the Atmosphere,” Geophysical Research Paper 20 (AFCRL, Bedford, Mass., 1954).

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Figures (2)

Fig. 1
Fig. 1

Calculated contrasts as a function of the distance for four kinds of nonuniform ground. The dashed lines represent the calculated contrast threshold of each observer. The points of intersection between the curves and the dashed lines give the visibility of the corresponding observer.

Fig. 2
Fig. 2

Calculated ratios of the visibility for different nonuniform grounds to the visibility for uniform ground disregarding multiple scattering. The visibilities were determined for observer 1 and for an observer with a standard contrast threshold of 0.02.

Tables (2)

Tables Icon

Table I Visibility in Centimeters of Black Objects Measured for Different Grounds by Three Observers (V1 was Determined by Observer 1, V2 by Observer 2, and V3 by Observer 3)

Tables Icon

Table II Relative Values of the Scattered Light over the Black Ground BB and over the While One BW

Equations (17)

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B o = 0 L A ( x ) σ e exp ( σ e x ) d x .
B h = 0 A ( x ) σ e exp ( σ e x ) d x .
C = B o B h B h = L A ( x ) σ e exp ( σ e x ) d x 0 A ( x ) σ e exp ( σ e x ) d x ;
ɛ = V b A ( x ) σ e exp ( σ e x ) d x 0 A ( x ) σ e exp ( σ e x ) d x .
0.02 = V b A ( x ) σ e exp ( σ e x ) d x 0 A ( x ) σ e exp ( σ e x ) d x .
0.02 = exp ( σ e V b ) ,
0.02 = V b A 2 σ e exp ( σ e x ) d x 0 V b A 1 σ e exp ( σ e x ) d x + V b A 2 σ e exp ( σ e x ) d x .
0.02 = V b A 2 σ e exp ( σ e x ) d x 0 A 2 σ e exp ( σ e x ) d x + 0 V b Δ A σ e exp ( σ e x ) d x .
0.02 = A 2 exp ( σ e V b ) A 2 + Δ A [ exp ( σ e V b ) + 1 ] ,
V b = 3.9 ln | ( 1 + Δ A / A 2 ) / ( 1 + 0.02 Δ A / A 2 ) | σ e .
B h = B B + exp ( σ e X 1 ) 1 exp [ σ e ( X 2 X 1 ) ] ( B w B B ) ,
B x = [ 1 exp ( σ ɛ X ) ] B B ,
B x = [ 1 exp ( σ e X ) ] B B + exp ( σ e X 1 ) + { 1 exp [ σ e ( X X 1 ) ] } ( B W B B ) ,
B h = B W exp ( σ e X 2 ) { 1 exp [ σ e ( 100 X 2 ) ] } ( B W B B ) .
B x = [ 1 exp ( σ e X ) ] B W ,
B x = [ 1 exp ( σ e x ) ] B W exp ( σ e X 2 ) { 1 exp [ σ e ( X X 2 ) ] } ( B W B B ) ,
V ̅

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