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  1. For a general summary see W. E. K. Middleton, Visibility in Meteorology (University of Toronto Press, 1941), second edition.
  2. W. E. K. Middleton, J. Opt. Soc. Am. 27, 112–116 (1937).
    [Crossref]
  3. M. G. Bennett, Q. J. Roy Met. Soc. 56, 1–29 (1930).
    [Crossref]
  4. The relations between flux, illumination, and brightness that are implied in the above are clarified by the adoption of the modern definition of brightness due to A. Gershun, J. Math. Phys. 18, 51–151 (1939), p. 61: “The brightness of a luminous source may be defined as the normal component of illumination produced by that source per unit solid angle.”
  5. C. Wiener, Nova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle73, 1–240 (1900); andNova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle 91, 1–292 (1909).
  6. H. G. Houghton, J. Aer. Sci. 6, 408–411 (1939).

1939 (2)

The relations between flux, illumination, and brightness that are implied in the above are clarified by the adoption of the modern definition of brightness due to A. Gershun, J. Math. Phys. 18, 51–151 (1939), p. 61: “The brightness of a luminous source may be defined as the normal component of illumination produced by that source per unit solid angle.”

H. G. Houghton, J. Aer. Sci. 6, 408–411 (1939).

1937 (1)

1930 (1)

M. G. Bennett, Q. J. Roy Met. Soc. 56, 1–29 (1930).
[Crossref]

Bennett, M. G.

M. G. Bennett, Q. J. Roy Met. Soc. 56, 1–29 (1930).
[Crossref]

Gershun, A.

The relations between flux, illumination, and brightness that are implied in the above are clarified by the adoption of the modern definition of brightness due to A. Gershun, J. Math. Phys. 18, 51–151 (1939), p. 61: “The brightness of a luminous source may be defined as the normal component of illumination produced by that source per unit solid angle.”

Houghton, H. G.

H. G. Houghton, J. Aer. Sci. 6, 408–411 (1939).

Middleton, W. E. K.

W. E. K. Middleton, J. Opt. Soc. Am. 27, 112–116 (1937).
[Crossref]

For a general summary see W. E. K. Middleton, Visibility in Meteorology (University of Toronto Press, 1941), second edition.

Wiener, C.

C. Wiener, Nova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle73, 1–240 (1900); andNova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle 91, 1–292 (1909).

J. Aer. Sci. (1)

H. G. Houghton, J. Aer. Sci. 6, 408–411 (1939).

J. Math. Phys. (1)

The relations between flux, illumination, and brightness that are implied in the above are clarified by the adoption of the modern definition of brightness due to A. Gershun, J. Math. Phys. 18, 51–151 (1939), p. 61: “The brightness of a luminous source may be defined as the normal component of illumination produced by that source per unit solid angle.”

J. Opt. Soc. Am. (1)

Q. J. Roy Met. Soc. (1)

M. G. Bennett, Q. J. Roy Met. Soc. 56, 1–29 (1930).
[Crossref]

Other (2)

C. Wiener, Nova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle73, 1–240 (1900); andNova Acta d. k. Leop. Carol. Akad. d. Naturf. Halle 91, 1–292 (1909).

For a general summary see W. E. K. Middleton, Visibility in Meteorology (University of Toronto Press, 1941), second edition.

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Figures (4)

F. 1
F. 1

Geometrical assumptions.

F. 2
F. 2

Calculation of η

F. 3
F. 3

Wiener’s Function .

F. 4
F. 4

Distribution of brightness across the edge of the object in a fog permitting a visual range of 0.1 km.

Equations (21)

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d τ = r 2 drdf
d ω = d s / r 1 2
d E ϕ = B π sin ϕ d ϕ
d F ϕ = B π sin ϕ d ϕ · d ω d τ · σ · l ( ϕ ) ;
d F ϕ = B π sin ϕ · d ω d τ · σ · l ( ϕ ) e σ r d ϕ
d F ϕ = B π sin ϕ · d s · d r · d f · σ · l ( ϕ ) e σ r d ϕ .
d E ϕ = B π sin ϕ · d f · σ · l ( ϕ ) e σ r drd ϕ
d B 1 = B π sin ϕ · σ · l ( ϕ ) e σ r drd ϕ .
B 1 = B π ϕ 1 π 0 s l ( ϕ ) sin ϕ · σ e σ r drd ϕ ,
B 1 = B π ( 1 e σ s ) ϕ 1 π l ( ϕ ) sin ϕ d ϕ .
ψ = θ s / ( s r ) .
d Ω = 2 η sin ϕ d ϕ
d E ϕ = B · 2 η sin ϕ d ϕ .
d E ϕ = B · 2 cos 1 [ s θ / ( s r ) ϕ ] sin ϕ d ϕ .
B 2 = 2 B θ ϕ 1 0 s cos 1 s θ ( s r ) ϕ · l ( ϕ ) sin ϕ · σ e σ r drd ϕ .
0 180 l ( ϕ ) sin ϕ
B s = B π ( 1 e σ s ) 0 π l ( ϕ ) sin ϕ d ϕ
B = B π 0 π l ( ϕ ) sin ϕ d ϕ .
1 = 0.01745 π 0 180 l ( ϕ ) sin ϕ
0 180 l ( ϕ ) sin ϕ = 18.238 .
B s = B ( 1 e σ s )