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References

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  1. L. F. Gate, J. Phys. D: Appl. Phys. 4, 1049 (1971).
    [CrossRef]
  2. R. G. Giovanelli, Opt. Acta 2, 153 (1955).
    [CrossRef]
  3. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  4. W. R. Blevin, W. J. Brown, J. Opt. Soc. Am. 52, 1250 (1962).
    [CrossRef]
  5. P. S. Mudgett, L. W. Richards, Appl. Opt. 10, 1485 (1971).
    [CrossRef] [PubMed]
  6. K. Klier, J. Opt. Soc. Am. 62, 882 (1973).
    [CrossRef]
  7. B. J. Brinkworth, J. Phys. D: Appl. Phys. 4, 1105 (1971).
    [CrossRef]

1973 (1)

1971 (3)

B. J. Brinkworth, J. Phys. D: Appl. Phys. 4, 1105 (1971).
[CrossRef]

L. F. Gate, J. Phys. D: Appl. Phys. 4, 1049 (1971).
[CrossRef]

P. S. Mudgett, L. W. Richards, Appl. Opt. 10, 1485 (1971).
[CrossRef] [PubMed]

1962 (1)

1955 (1)

R. G. Giovanelli, Opt. Acta 2, 153 (1955).
[CrossRef]

Blevin, W. R.

Brinkworth, B. J.

B. J. Brinkworth, J. Phys. D: Appl. Phys. 4, 1105 (1971).
[CrossRef]

Brown, W. J.

Chandrasekhar, S.

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

Gate, L. F.

L. F. Gate, J. Phys. D: Appl. Phys. 4, 1049 (1971).
[CrossRef]

Giovanelli, R. G.

R. G. Giovanelli, Opt. Acta 2, 153 (1955).
[CrossRef]

Klier, K.

Mudgett, P. S.

Richards, L. W.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Phys. D: Appl. Phys. (2)

B. J. Brinkworth, J. Phys. D: Appl. Phys. 4, 1105 (1971).
[CrossRef]

L. F. Gate, J. Phys. D: Appl. Phys. 4, 1049 (1971).
[CrossRef]

Opt. Acta (1)

R. G. Giovanelli, Opt. Acta 2, 153 (1955).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

The reflectance of a semi-infinite diffuser (for diffuse incident radiation) as a function of the ratio of the absorption to scattering cross sections for two types of scattering phase function given by the exact solution to the radiative transfer equation and the photon diffusion model.

Fig. 2
Fig. 2

The reflectance of a semi-infinite diffuser with diffuse incident radiation and isotropic scatter given by the Kubelka-Munk function compared with the exact solution of the radiative transport equation.

Fig. 3
Fig. 3

The ratio of the Kubelka-Munk scattering coefficient to the scattering cross section as given by Klier’s solution (full line) and the photon diffusion model (broken line).

Fig. 4
Fig. 4

The ratio of the Kubelka-Munk absorption coefficient to the absorption cross section as given by Klief’s solution (full line) and the photon diffusion model (broken line).

Equations (14)

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R = 1 - 2 ( 1 - ω 0 ) 1 / 2 α 1 ,
α 1 = 0 1 μ H ( μ ) d μ ,
α / σ = Σ a / Σ s = ω 0 / ( 1 - ω 0 ) .
R = 1 - ( 4 Σ a / 3 Σ s ) 1 / 2 1 + ( 4 Σ a / 3 Σ s ) 1 / 2
R = 1 - 2 α 1 [ 1 - ( ω 0 / 2 ) ( α 0 - C α 1 ) ] ,
α 0 = 0 1 H ( μ ) d μ ,
C = ω 0 ( 1 - ω 0 ) [ α 1 / ( 2 - ω 0 α 0 ) ] .
μ ¯ = - 1 + 1 P ( μ ) μ d μ / - 1 + 1 P ( μ ) d μ .
R = 1 - ( 2 Σ a / Σ s ) 1 / 2 1 + ( 2 Σ a / Σ s ) 1 / 2 .
R = 1 - [ K / ( K + 2 S ) ] 1 / 2 1 + [ K / ( K + 2 S ) ] 1 / 2 ,
S / K = ( 3 Σ s - 4 Σ a ) / 8 Σ a .
K / S = ( 8 / 3 ) ( Σ a / Σ s ) ,
K / S = [ ( 1 - R ) 2 ] / 2 R ,
K / Σ a = 2 and S / Σ s = ( 3 / 4 ) - ( Σ a / Σ s ) ,

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