Abstract

A general nonlinear technique is described for determining wave slopes from photographs of an area of the ocean surface that is illuminated by diffuse skylight. This technique is evaluated using uniform, overcast, and bright sky radiance distribution models, and results from its use are compared with the approximate results obtained by previous authors. Under certain clearly defined practical experimental conditions, it is theoretically possible to determine the total wave slope magnitude at the ocean surface.

© 1978 Optical Society of America

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References

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  1. N. E. Barber, Nature 164, 458 (1949).
    [CrossRef]
  2. C. Cox, W. Munk, J. Opt. Soc. Am. 44, 838 (1954).
    [CrossRef]
  3. W. J. Pierson, N.Y. Univ. Meteorol. Pap. 2(6), (1960).
  4. G. Newmann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 221.
  5. D. Stilwell, J. Geophys. Res. 74, 1974 (1969).
    [CrossRef]
  6. R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
    [CrossRef]
  7. R. S. Kasevich, J. Geophys. Res. 80, 4535 (1975).
    [CrossRef]
  8. D. Stilwell, R. O. Pilon, J. Geophys. Res. 79, 1277 (1974).
    [CrossRef]
  9. K. S. Krishnan, N. A. Peppers, Optical techniques for the measurement of ocean-surface parameters. Final Report, contract N00014-73-C-0445, Stanford Research Institute, project 2618 (1975).
  10. P. Moon, D. E. Spencer, Illum. Eng. 37, 707 (1942).
  11. R. G. Hopkinson, J. Opt. Soc. Am. 44, 455 (1954).
    [CrossRef]
  12. G. I. Pokrowski, Phys. Z. 30, 697 (1929).

1975 (1)

R. S. Kasevich, J. Geophys. Res. 80, 4535 (1975).
[CrossRef]

1974 (1)

D. Stilwell, R. O. Pilon, J. Geophys. Res. 79, 1277 (1974).
[CrossRef]

1972 (1)

R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
[CrossRef]

1969 (1)

D. Stilwell, J. Geophys. Res. 74, 1974 (1969).
[CrossRef]

1960 (1)

W. J. Pierson, N.Y. Univ. Meteorol. Pap. 2(6), (1960).

1954 (2)

1949 (1)

N. E. Barber, Nature 164, 458 (1949).
[CrossRef]

1942 (1)

P. Moon, D. E. Spencer, Illum. Eng. 37, 707 (1942).

1929 (1)

G. I. Pokrowski, Phys. Z. 30, 697 (1929).

Barber, N. E.

N. E. Barber, Nature 164, 458 (1949).
[CrossRef]

Cox, C.

Hendriksen, S. W.

R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
[CrossRef]

Hopkinson, R. G.

Kasevich, R. S.

R. S. Kasevich, J. Geophys. Res. 80, 4535 (1975).
[CrossRef]

R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
[CrossRef]

Krishnan, K. S.

K. S. Krishnan, N. A. Peppers, Optical techniques for the measurement of ocean-surface parameters. Final Report, contract N00014-73-C-0445, Stanford Research Institute, project 2618 (1975).

Moon, P.

P. Moon, D. E. Spencer, Illum. Eng. 37, 707 (1942).

Munk, W.

Newmann, G.

G. Newmann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 221.

Peppers, N. A.

K. S. Krishnan, N. A. Peppers, Optical techniques for the measurement of ocean-surface parameters. Final Report, contract N00014-73-C-0445, Stanford Research Institute, project 2618 (1975).

Pierson, W. J.

W. J. Pierson, N.Y. Univ. Meteorol. Pap. 2(6), (1960).

G. Newmann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 221.

Pilon, R. O.

D. Stilwell, R. O. Pilon, J. Geophys. Res. 79, 1277 (1974).
[CrossRef]

Pokrowski, G. I.

G. I. Pokrowski, Phys. Z. 30, 697 (1929).

Spencer, D. E.

P. Moon, D. E. Spencer, Illum. Eng. 37, 707 (1942).

Stilwell, D.

D. Stilwell, R. O. Pilon, J. Geophys. Res. 79, 1277 (1974).
[CrossRef]

D. Stilwell, J. Geophys. Res. 74, 1974 (1969).
[CrossRef]

Tang, C. H.

R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
[CrossRef]

IEEE Trans. Geosci, Electron. (1)

R. S. Kasevich, C. H. Tang, S. W. Hendriksen, IEEE Trans. Geosci, Electron. GE-10, 51 (1972).
[CrossRef]

Illum. Eng. (1)

P. Moon, D. E. Spencer, Illum. Eng. 37, 707 (1942).

J. Geophys. Res. (3)

R. S. Kasevich, J. Geophys. Res. 80, 4535 (1975).
[CrossRef]

D. Stilwell, R. O. Pilon, J. Geophys. Res. 79, 1277 (1974).
[CrossRef]

D. Stilwell, J. Geophys. Res. 74, 1974 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

N.Y. Univ. Meteorol. Pap. (1)

W. J. Pierson, N.Y. Univ. Meteorol. Pap. 2(6), (1960).

Nature (1)

N. E. Barber, Nature 164, 458 (1949).
[CrossRef]

Phys. Z. (1)

G. I. Pokrowski, Phys. Z. 30, 697 (1929).

Other (2)

G. Newmann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1965), p. 221.

K. S. Krishnan, N. A. Peppers, Optical techniques for the measurement of ocean-surface parameters. Final Report, contract N00014-73-C-0445, Stanford Research Institute, project 2618 (1975).

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Figures (7)

Fig. 1
Fig. 1

Experimental geometry and definition of symbols.

Fig. 2
Fig. 2

Film irradiance function H(α,β) vs the wave slope component S r ˆ for a uniform sky.

Fig. 3
Fig. 3

Film irradiance function H(α,β) vs the wave slope component S r ˆ for a fully overcast sky.

Fig. 4
Fig. 4

Three-dimensional polar plot of the radiance distribution of a bright clear sky as given by Pokrowski’s model.

Fig. 5
Fig. 5

Film irradiance function H(α,β) vs the wave slope component S r ˆ for a bright sky.

Fig. 6
Fig. 6

Film irradiance function H(α,β) vs the wave slope component S r ˆ for a bright polarized sky.

Fig. 7
Fig. 7

Resolution of the ambiguity in slope determination by cross plotting.

Equations (35)

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H ( α , β ) = η ( ω ) N ( A , B ) ( W / m 2 ) .
i ˆ n · i ˆ r = i ˆ i · i ˆ n ,
i ˆ n × i ˆ r = i ˆ i × i ˆ n .
H ( α , β ) η ( β ) N ( A , B ) { 1 + 2 S r ˆ cot β [ ln N ( A , B ) A ] μ = 0 + S r ˆ [ 2 ln N ( A , B ) B + 1 η ( ω ) d η ( ω ) d ω ] μ = 0 } ,
H ( α , β ) = η s ( ω ) N s ( A , B ) sin 2 ( ϕ γ ) + η p ( ω ) N p ( A , B ) cos 2 ( ϕ γ ) .
N s ( A , B ) = N p ( A , B ) = 1 2 N o = constant .
N s ( A , B ) = N p ( A , B ) = N o 2 ( 1 + 2 cos B 3 ) ,
N s ( A , B ) = N p ( A , B ) = N o 2 ( 1 + cos 2 ξ 1 cos ξ ) [ 1 exp ( P cos B ) ] ,
N ( A , B ) = N o 2 ( cos 2 ξ 1 cos ξ ) [ 1 exp ( P cos B ) ] ,
N ( A , B ) = N o 2 ( 1 1 cos ξ ) [ 1 exp ( P cos B ) ] .
N p ( A , B ) = N ( A , B ) cos 2 Ω + N ( A , B ) sin 2 Ω ,
N s ( A , B ) = N ( A , B ) sin 2 Ω + N ( A , B ) cos 2 Ω ,
i ˆ i = i ˆ sin B cos A j ˆ sin B sin A k ˆ cos B .
i ˆ n = i ˆ sin μ cos ν + j ˆ sin μ sin ν + k ˆ cos μ .
i ˆ r = i ˆ sin β cos α j ˆ sin β sin α + k ˆ cos β .
i ˆ s = i ˆ sin D cos C + j ˆ sin D sin C + k ˆ cos D .
w ( x , y ) = i ˆ w ( x , y ) x + j ˆ w ( x , y ) y
| w ( x , y ) | = tan μ ,
S r ˆ = tan μ cos ( ν α ) ;
S r ˆ = tan μ sin ( ν α ) .
i ˆ n · i ˆ r = i ˆ i · i ˆ n ,
i ˆ n × i ˆ r = i ˆ i × i ˆ n .
i ˆ r = i ˆ i 2 ( i ˆ n · i ˆ i ) i ˆ n ,
A = tan 1 ( sin β sin α + 2 cos ω sin μ sin ν sin β cos α + 2 cos ω sin μ cos ν ) .
B = cos 1 ( 2 cos ω cos μ cos β ) .
ω = cos 1 [ cos μ cos β sin μ sin β cos ( ν α ) ] .
cos ϕ = [ ( i ˆ r × i ˆ n ) × i ˆ r ] · ( k ˆ × i ˆ r ) | ( i ˆ r × i ˆ n ) × i ˆ r | | k ˆ × i ˆ r | ,
ϕ = cos 1 [ sin μ sin ( ν α ) sin ω ] .
ξ = cos 1 [ sin B sin D cos ( A C ) + cos B cos D ] .
cos Ω = ( i ˆ i × i ˆ n ) · ( i ˆ i × i ˆ s ) | i ˆ i × i ˆ n | | i ˆ i × i ˆ s | ,
Ω = cos 1 [ sin μ sin D cos ( ν C ) + cos μ cos D cos ξ cos ω sin ξ sin ω ] .
η s ( ω ) = sin 2 ( ω ω ) sin 2 ( ω + ω ) ,
η p ( ω ) = tan 2 ( ω ω ) tan 2 ( ω + ω ) ,
sin ω = n sin ω ,
η ( ω ) = [ η p ( ω ) + η s ( ω ) ] / 2 .

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