Abstract

Monte Carlo computations of the diffuse reflectance of an ocean consisting of two homogeneous layers with differing optical properties are presented, along with a simplified method of computation that uses results of previous Monte Carlo simulations. It is demonstrated that it is impossible to distinguish between thin layers of strong scattering and thick layers of weak scattering through measurement of the diffuse reflectance. Analyzing the two-layer reflectance under the assumption of a homogeneous ocean yields an optical property that is shown to be nearly the average of the associated property over the penetration depth of the medium, i.e., the depth over which the downwelling irradiance falls to 1/e of its value at the surface.

© 1975 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, Appl. Opt. 12, 1549 (1973).
    [CrossRef] [PubMed]
  2. H. R. Gordon, Appl. Opt. 12, 2803 (1973).
    [CrossRef] [PubMed]
  3. M. M. Jacobs, H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 55, 289 (1974).
  4. H. R. Gordon, W. R. McCluney, Appl. Opt. 14, 413 (1975).
    [CrossRef] [PubMed]
  5. N. J. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968).
  6. G. Kullenberg, Deep Sea Res. 15, 423 (1968).
  7. J. E. Tyler, R. C. Smith, W. H. Wilson, J. Opt. Soc. Am. 62, 83 (1972).
    [CrossRef]
  8. H. R. Gordon, O. B. Brown, M. M. Jacobs, Appl. Opt. 14, 417 (1975).
    [CrossRef] [PubMed]
  9. H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974).
    [CrossRef] [PubMed]

1975

1974

M. M. Jacobs, H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 55, 289 (1974).

H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974).
[CrossRef] [PubMed]

1973

1972

1968

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

Brown, O. B.

Gordon, H. R.

Jacobs, M. M.

H. R. Gordon, O. B. Brown, M. M. Jacobs, Appl. Opt. 14, 417 (1975).
[CrossRef] [PubMed]

M. M. Jacobs, H. R. Gordon, O. B. Brown, Trans. Am. Geophys. Union 55, 289 (1974).

Jerlov, N. J.

N. J. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968).

Kullenberg, G.

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

McCluney, W. R.

Smith, R. C.

Tyler, J. E.

Wilson, W. H.

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Figures (5)

Fig. 1
Fig. 1

The diffuse reflectance of a two-layer ocean as a function of the thickness (in meters) and the ratio of scattering to absorption of the upper layer. The lower layer is similar to Sargasso Sea water at a wavelength of 530 nm.

Fig. 2
Fig. 2

Results shown in Fig. 1 replotted to show clearly the influence of the upper layer thickness (z) on the diffuse reflectance.

Fig. 3
Fig. 3

Comparison between xeq computed from Eq. (3) and x ¯ from Eq. (4a).

Fig. 4
Fig. 4

Comparison between ωeq computed from Eqs. (4) and (1) and ω ¯ 0 from Eq. (4b).

Fig. 5
Fig. 5

Comparison between Rd computed from direct Monte Carlo simulations (Rmonte carlo) and Rd from Eq. (A2) (Rapproximate).

Equations (8)

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x = ω 0 ( 1 F ) / ( 1 ω 0 F ) ,
F = 2 π 0 π / 2 p ( θ ) sin θ d θ ,
R d = 0.179 x + 0.051 x 2 + 0.171 x 3
x eq = 5.6613 R d 15.526 R d 2 + 20.571 R d 3 ,
x ¯ = 0 τ 90 x ( τ ) d τ / τ 90 ,
ω 0 ¯ = 0 τ 90 ω 0 ( τ ) d τ / τ 90
R b ( τ t , ) = n = 0 3 r n ( τ t ) x b n ,
R d = R 1 + R 2 A / ( 1 A r ) ,

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