Abstract

Time-averaged intensities are computed for the glitter pattern of sunlight on a wind-ruffled sea. Isopleths are drawn from these on graphs which simulate glitter-pattern photographs through projections of sea-surface grid points on an inclined plane assumed to be in front of the observer. The intensity computed for each grid point is based on a calculation of the wave-surface orientation required for direct reflection from source to observer at that point; the probability of occurrence of this orientation, determined from the Cox-Munk distribution, is the principal factor in the computed intensity. The curvature of the earth is taken into account, and calculations are made for various cases of source elevation angle, observer altitude, and wind speed (the controlling parameter for the distribution of wave inclinations). Percent polarization is computed for the glitter patterns, and projected isopleths of this quantity are plotted. The effects of variations in wind speed, source elevation angle, and observer height on the morphology of the glitter pattern are shown, and such phenomena as the shifting of a reflected image toward the horizon are clearly demonstrated. It is suggested that the technique developed here could be useful in evaluating models of ocean wave structure and in making remote determinations of the sea state in the region of the glitter pattern.

© 1977 Optical Society of America

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References

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  1. E. O. Hulburt, J. Opt. Soc. Am. 24, 35 (1934).
    [CrossRef]
  2. M. Minnaert, Physica 9, 925 (1942).
    [CrossRef]
  3. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), pp. 15–26.
  4. R. A. R. Tricker, Bores, Breakers, Waves and Wakes (American Elsevier, New York, 1965), pp. 240–246.
  5. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 14, 1924 (1975).
    [CrossRef] [PubMed]
  6. G. N. Plass, G. W. Kattawar, J. A. Guinn, Appl. Opt. 15, 3161 (1976).
    [CrossRef] [PubMed]
  7. C. Cox, W. Munk, J. Opt. Soc. Am. 44, 838 (1954).
    [CrossRef]
  8. J. I. Gordon, Directional Radiance (Luminance) of the Sea Surface, Scripps Institution of Oceanography Reference 69-20 (1969).

1976 (1)

1975 (1)

1954 (1)

1942 (1)

M. Minnaert, Physica 9, 925 (1942).
[CrossRef]

1934 (1)

Cox, C.

Gordon, J. I.

J. I. Gordon, Directional Radiance (Luminance) of the Sea Surface, Scripps Institution of Oceanography Reference 69-20 (1969).

Guinn, J. A.

Hulburt, E. O.

Kattawar, G. W.

Minnaert, M.

M. Minnaert, Physica 9, 925 (1942).
[CrossRef]

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), pp. 15–26.

Munk, W.

Plass, G. N.

Tricker, R. A. R.

R. A. R. Tricker, Bores, Breakers, Waves and Wakes (American Elsevier, New York, 1965), pp. 240–246.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Physica (1)

M. Minnaert, Physica 9, 925 (1942).
[CrossRef]

Other (3)

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), pp. 15–26.

R. A. R. Tricker, Bores, Breakers, Waves and Wakes (American Elsevier, New York, 1965), pp. 240–246.

J. I. Gordon, Directional Radiance (Luminance) of the Sea Surface, Scripps Institution of Oceanography Reference 69-20 (1969).

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Figures (23)

Fig. 1
Fig. 1

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 20°, and a wind speed of 1.0 m/sec. The maximum value of log10 intensity is −3.308. The coordinates θx and θy are defined in Sec. II.

Fig. 2
Fig. 2

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 20°, and a wind speed of 2.5 m/sec. The maximum value of log10 intensity is −3.457.

Fig. 3
Fig. 3

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 5°, and a wind speed of 1.0 m/sec. The maximum value of log10 intensity is −1.764.

Fig. 4
Fig. 4

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 5°, and a wind speed of 2.5 m/sec. The maximum value of log10 intensity is −2.287.

Fig. 5
Fig. 5

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 30°, and a wind speed of 2.5 m/sec. The maximum value of log10 intensity is −4.196.

Fig. 6
Fig. 6

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 30°, and a wind speed of 5.0 m/sec. The maximum value of log10 intensity is −4.249.

Fig. 7
Fig. 7

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 5°, and a wind speed of 15.0 m/sec. The maximum value of log10 intensity is −3.571.

Fig. 8
Fig. 8

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 20°, and a wind speed of 15.0 m/sec. The maximum values of log10 intensity is −3.763.

Fig. 9
Fig. 9

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 45°, and a wind speed of 15.0 m/sec. The maximum value of log10 intensity is −5.094.

Fig. 10
Fig. 10

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 60°, and a wind speed of 0.5 m/sec. The maximum value of log10 intensity is −4.246.

Fig. 11
Fig. 11

Log10 intensity isopleths for an observer height of 5 m, a source elevation of 60°, and a wind speed of 15.0 m/sec. The maximum value of log10 intensity is −5.699.

Fig. 12
Fig. 12

Log10 intensity isopleths for an observer height of 150 km, a source elevation of 20°, and a wind speed of 1.0 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −3.503.

Fig. 13
Fig. 13

Log10 intensity isopleths for an observer height of 150 km, a source elevation of 20°, and a wind speed of 2.5 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −3.854.

Fig. 14
Fig. 14

Log10 intensity isopleths for an observer height of 150 km, a source elevation of 5°, and a wind speed of 2.5 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −2.967.

Fig. 15
Fig. 15

Log10 intensity isopleths for an observer height of 150 km, a source elevation of 5°, and a wind speed of 15.0 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −3.663.

Fig. 16
Fig. 16

Log10 intensity isopleths for an observer height of 150 km, a source elevation of 20°, and a wind speed of 15.0 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −4.205.

Fig. 17
Fig. 17

Log10 intensity isopleths for an observer height of 35,800 km, a source elevation of 20°, and a wind speed of 0.5 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −4.167.

Fig. 18
Fig. 18

Log10 intensity isopleths for an observer height of 35,800 km, a source elevation of 20°, and a wind speed of 2.5 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −4.871.

Fig. 19
Fig. 19

Log10 intensity isopleths for an observer height of 35,800 km, a source elevation of 20°, and a wind speed of 15.0 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −5.655.

Fig. 20
Fig. 20

Log10 intensity isopleths for an observer height of 35,800 km, a source elevation of −30°, and a wind speed of 0.5 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −3.393.

Fig. 21
Fig. 21

Log10 intensity isopleths for an observer height of 35,800 km, a source elevation of −30°, and a wind speed of 15.0 m/sec. The top curve is the horizon. The maximum value of log10 intensity is −4.849.

Fig. 22
Fig. 22

Percent polarization isopleths for an observer height of 5 m and a source elevation of 5°.

Fig. 23
Fig. 23

Percent polarization isopleths for an observer height of 5 m and a source elevation of 30°.

Equations (1)

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θ r = tan - 1 [ ( tan θ x ) 2 + ( tan θ y ) 2 ] 1 / 2 .

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