Abstract

The theory for atmospheric contrast reduction is extended to include the effects of spectral dependence for broadband optical signals. A result with the same form as the monochromatic theory is achieved and the broadband extinction coefficient is defined. A comparison of atmospheric transmittance for the broadband model with that for the single wavelength average transmittance indicates little error except for applications where the slant range is larger than the meteorological range.

© 1978 Optical Society of America

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References

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  1. H. Koschmieder, “Theorie der horizontalen Sichtweite,” Beitr. Phys. freien Atm.,  12, 33–53 (1924); Beitr. Phys. freien Atm. 12, 171–181 (1924).
  2. Seibert Q. Duntley, “The Reduction of Apparent Contrast by the Atmosphere,” J. Opt. Soc. Am.,  38, 179–191 (1948).
    [CrossRef]
  3. W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto, Toronto, 1952).
  4. J. B. Farrow and A. F. Gibson, “Influence of the Atmosphere on Optical Systems,” Opt. Acta,  17, 317–336 (1970).
    [CrossRef]
  5. F. Loehle, “Ueber die Lichtzerstrewing im Nebel,” Phys. Z.,  45, 199–205 (1944).
  6. Franklin S. Harris, “The Physics of Light Scattering,” Opt. Spectra,  4, 52–56 (1970).

1970 (2)

J. B. Farrow and A. F. Gibson, “Influence of the Atmosphere on Optical Systems,” Opt. Acta,  17, 317–336 (1970).
[CrossRef]

Franklin S. Harris, “The Physics of Light Scattering,” Opt. Spectra,  4, 52–56 (1970).

1948 (1)

1944 (1)

F. Loehle, “Ueber die Lichtzerstrewing im Nebel,” Phys. Z.,  45, 199–205 (1944).

1924 (1)

H. Koschmieder, “Theorie der horizontalen Sichtweite,” Beitr. Phys. freien Atm.,  12, 33–53 (1924); Beitr. Phys. freien Atm. 12, 171–181 (1924).

Duntley, Seibert Q.

Farrow, J. B.

J. B. Farrow and A. F. Gibson, “Influence of the Atmosphere on Optical Systems,” Opt. Acta,  17, 317–336 (1970).
[CrossRef]

Gibson, A. F.

J. B. Farrow and A. F. Gibson, “Influence of the Atmosphere on Optical Systems,” Opt. Acta,  17, 317–336 (1970).
[CrossRef]

Harris, Franklin S.

Franklin S. Harris, “The Physics of Light Scattering,” Opt. Spectra,  4, 52–56 (1970).

Koschmieder, H.

H. Koschmieder, “Theorie der horizontalen Sichtweite,” Beitr. Phys. freien Atm.,  12, 33–53 (1924); Beitr. Phys. freien Atm. 12, 171–181 (1924).

Loehle, F.

F. Loehle, “Ueber die Lichtzerstrewing im Nebel,” Phys. Z.,  45, 199–205 (1944).

Middleton, W. E. K.

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

Beitr. Phys. freien Atm. (1)

H. Koschmieder, “Theorie der horizontalen Sichtweite,” Beitr. Phys. freien Atm.,  12, 33–53 (1924); Beitr. Phys. freien Atm. 12, 171–181 (1924).

J. Opt. Soc. Am. (1)

Opt. Acta (1)

J. B. Farrow and A. F. Gibson, “Influence of the Atmosphere on Optical Systems,” Opt. Acta,  17, 317–336 (1970).
[CrossRef]

Opt. Spectra (1)

Franklin S. Harris, “The Physics of Light Scattering,” Opt. Spectra,  4, 52–56 (1970).

Phys. Z. (1)

F. Loehle, “Ueber die Lichtzerstrewing im Nebel,” Phys. Z.,  45, 199–205 (1944).

Other (1)

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

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Figures (1)

FIG. 1
FIG. 1

Ratio of broadband transmittance to average transmittance as a function of slant range (RBAR) for various visibilities.

Equations (16)

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L λ ( R ) = [ L a , λ ( 0 ) / σ λ ( 0 ) ] ( 1 - T λ ) + L λ ( 0 ) T λ ,
T λ = exp [ - σ λ ( 0 ) R ¯ λ ] ,
L Δ λ ( R ) = Δ λ ( L a , λ ( 0 ) σ λ ( 0 ) ( 1 - T λ ) + L λ ( 0 ) T λ ) d λ .
L Δ λ ( R ) = Δ λ ( L a , λ ( 0 ) σ λ ( 0 ) ( 1 - T λ ) + L λ ( 0 ) T λ ) d λ .
C Δ λ ( R ) = Δ λ { [ L λ ( 0 ) - L λ ( 0 ) ] T λ } d λ / L Δ λ ( R ) .
C Δ λ ( 0 ) = Δ λ { L λ ( 0 ) - L λ ( 0 ) } d λ / L Δ λ ( 0 ) ,
C Δ λ ( R ) / C Δ λ ( 0 ) = [ L Δ λ ( 0 ) / L Δ λ ( R ) ] T Δ λ .
σ Δ λ ( 0 ) = - 1 R ¯ Δ λ ln             Δ λ { [ L λ ( 0 ) - L λ ( 0 ) ] T λ } d λ Δ λ { L λ ( 0 ) - L λ ( 0 ) } d λ .
σ Δ λ ( 0 ) = - 1 R ¯ Δ λ ln 1 Δ λ ( Δ λ exp [ - σ λ ( 0 ) R ¯ λ ] d λ ) .
σ λ ( r ) = σ λ ( 0 ) f ( r ) and R ¯ = 0 R f ( r ) d r ,
R ¯ Δ λ = R ¯ λ = R ¯ .
σ Δ λ ( 0 ) = 1 R ¯ ln             Δ λ { L λ ( 0 ) - L λ ( 0 ) } d λ Δ λ { [ L λ ( 0 ) - L λ ( 0 ) ] T λ } d λ ,
σ Δ λ ( 0 ) = - 1 R ¯ ln ( 1 Δ λ Δ λ exp [ - σ λ ( 0 ) R ¯ ] d λ ) .
E = σ Δ λ ( 0 ) σ av ( 0 ) = - 1 R ¯ ln ( 1 Δ λ Δ λ exp [ - σ λ ( 0 ) R ¯ ] d λ ) 1 Δ λ Δ λ σ λ ( 0 ) d λ .
σ λ ( 0 ) = σ 0.55 ( 0 ) ( a / λ ) q ,
ρ = T Δ λ / T av = exp [ - σ Δ λ ( 0 ) R ¯ ] / exp [ - σ av ( 0 ) R ¯ ] .