Abstract

We present new observations of glitter and glints using short and long time exposure photographs and high frame rate videos. Using the sun and moon as light sources to illuminate the ocean and laboratory water basins, we found that (1) most glitter takes place on capillary waves rather than on gravity waves, (2) certain aspects of glitter morphology depend on the presence or absence of thin clouds between the light source and the water, and (3) bent glitter paths are caused by asymmetric wave slope distributions We present computer simulations that are able to reproduce the observations and make predictions about the brightness, polarization, and morphology of glitter and glints. We demonstrate that the optical catastrophe represented by creation and annihilation of a glint can be understood using both ray optics and diffraction theory.

© 2011 Optical Society of America

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References

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  1. M. Montagu-Pollack, Light and Water: A Study of Reflexion and Colour in River, Lake and Sea (George Bell and Sons, 1903).
  2. V. V. Shuleikin, Fizika Moria (Physics of the Sea) (Izdatelstvo Akad. Nauk. U.S.S.R., 1941).
  3. A. Stelenau, “Uber die reflexion der sonnenstrahlung an wisserflachen und die ihre bedeutung fur das strahlungsklima von seeufern,” Beitr. Angew. Geophys. 70, 90–123 (1961).
  4. D. K. Lynch and W. C. Livingston, Color and Light in Nature, 2nd ed. (Cambridge University, 2001, reprinted by Thule Scientific, 2010).
  5. R. Fleet, “Glows, bows and haloes,” http://www.dewbow.co.uk/glows/glitterpath.html.
  6. M. Minnaert, The Nature of Light and Colour in the Open Air (George Bell and Sons, 1939, reprinted by Dover, 1954), pp. 130–131.
  7. K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, “Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces,” J. Opt. Soc. Am. A 56, 916–925 (1966).
    [CrossRef]
  8. E. O. Hulburt, “The polarization of light at sea,” J. Opt. Soc. Am. 24, 35–42 (1934).
    [CrossRef]
  9. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  10. C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  11. M. S. Longuet-Higgins, “Reflection and refraction at a random moving surface. i. pattern and paths of specular points,” J. Opt. Soc. Am. 50, 838–844 (1960).
    [CrossRef]
  12. M. S. Longuet-Higgins, “Reflection and refraction at a random moving surface. ii. number of specular points in a Gaussian surface,” J. Opt. Soc. Am. 50, 845–850 (1960).
    [CrossRef]
  13. M. S. Longuet-Higgins, “Reflection and refraction at a random moving surface. iii. frequency of twinkling in a Gaussian surface,” J. Opt. Soc. Am. 50, 851–856 (1960).
    [CrossRef]
  14. K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).
  15. M. V. Berry, “Catastrophe theory: a new mathematical tool for scientists,” J. Sci. Ind. Res. 36, 103–105 (1977).
  16. M. V. Berry, “Disruption of images: the caustic-touching theorem,” J. Opt. Soc. Am. A 4, 561–569 (1987).
    [CrossRef]
  17. J. A. Lock and C. L. Adler, “Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1316–1328 (1997).
    [CrossRef]
  18. C. S. Cox, “Measurements of slopes of high-frequency wind waves,” J. Mar. Res. 16, 199–225 (1958).
  19. M. S. Longuet-Higgins, “The generation of capillary waves by steep gravity waves,” J. Fluid Mech. 16, 138–159 (1963).
    [CrossRef]
  20. M. S. Longuet-Higgins, “Parasitic capillary waves: a direct calculation,” J. Fluid Mech. 301, 79–107 (1995).
    [CrossRef]
  21. D. M. Williams and E. Gaidos, “Detecting the glint of starlight on the oceans of distant planets,” Icarus 195, 927–937 (2008).
    [CrossRef]
  22. D. K. Lynch, “Reflections on closed loops,” Nature 316, 216–217 (1985).
    [CrossRef]
  23. D. K. Lynch, “Reflection on water,” http://epod.usra.edu/blog/2010/07/reflection-on-water.html.
  24. P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A.D.Pierce and R.N.Thurston, eds. (Academic, 1992), Vol.  21, pp. 1–234.

2008 (1)

D. M. Williams and E. Gaidos, “Detecting the glint of starlight on the oceans of distant planets,” Icarus 195, 927–937 (2008).
[CrossRef]

1997 (1)

1995 (1)

M. S. Longuet-Higgins, “Parasitic capillary waves: a direct calculation,” J. Fluid Mech. 301, 79–107 (1995).
[CrossRef]

1987 (1)

1985 (1)

D. K. Lynch, “Reflections on closed loops,” Nature 316, 216–217 (1985).
[CrossRef]

1977 (1)

M. V. Berry, “Catastrophe theory: a new mathematical tool for scientists,” J. Sci. Ind. Res. 36, 103–105 (1977).

1966 (1)

K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, “Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces,” J. Opt. Soc. Am. A 56, 916–925 (1966).
[CrossRef]

1963 (1)

M. S. Longuet-Higgins, “The generation of capillary waves by steep gravity waves,” J. Fluid Mech. 16, 138–159 (1963).
[CrossRef]

1961 (1)

A. Stelenau, “Uber die reflexion der sonnenstrahlung an wisserflachen und die ihre bedeutung fur das strahlungsklima von seeufern,” Beitr. Angew. Geophys. 70, 90–123 (1961).

1960 (3)

1958 (1)

C. S. Cox, “Measurements of slopes of high-frequency wind waves,” J. Mar. Res. 16, 199–225 (1958).

1954 (2)

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

1934 (1)

Adler, C. L.

Barnett, T. P.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Berry, M. V.

M. V. Berry, “Disruption of images: the caustic-touching theorem,” J. Opt. Soc. Am. A 4, 561–569 (1987).
[CrossRef]

M. V. Berry, “Catastrophe theory: a new mathematical tool for scientists,” J. Sci. Ind. Res. 36, 103–105 (1977).

Birkebak, R. C.

K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, “Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces,” J. Opt. Soc. Am. A 56, 916–925 (1966).
[CrossRef]

Bouws, E.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Carlson, H.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Cartwright, D. E.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Cox, C.

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Cox, C. S.

C. S. Cox, “Measurements of slopes of high-frequency wind waves,” J. Mar. Res. 16, 199–225 (1958).

Enke, K.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Ewing, J. A.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Fleet, R.

R. Fleet, “Glows, bows and haloes,” http://www.dewbow.co.uk/glows/glitterpath.html.

Gaidos, E.

D. M. Williams and E. Gaidos, “Detecting the glint of starlight on the oceans of distant planets,” Icarus 195, 927–937 (2008).
[CrossRef]

Gienapp, H.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Hasselmann, D. E.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Hasselmann, K.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Hulburt, E. O.

Kruseman, P.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Livingston, W. C.

D. K. Lynch and W. C. Livingston, Color and Light in Nature, 2nd ed. (Cambridge University, 2001, reprinted by Thule Scientific, 2010).

Lock, J. A.

Longuet-Higgins, M. S.

Lynch, D. K.

D. K. Lynch, “Reflections on closed loops,” Nature 316, 216–217 (1985).
[CrossRef]

D. K. Lynch, “Reflection on water,” http://epod.usra.edu/blog/2010/07/reflection-on-water.html.

D. K. Lynch and W. C. Livingston, Color and Light in Nature, 2nd ed. (Cambridge University, 2001, reprinted by Thule Scientific, 2010).

Marston, P. L.

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A.D.Pierce and R.N.Thurston, eds. (Academic, 1992), Vol.  21, pp. 1–234.

Meerburg, A.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Miller, P.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Minnaert, M.

M. Minnaert, The Nature of Light and Colour in the Open Air (George Bell and Sons, 1939, reprinted by Dover, 1954), pp. 130–131.

Montagu-Pollack, M.

M. Montagu-Pollack, Light and Water: A Study of Reflexion and Colour in River, Lake and Sea (George Bell and Sons, 1903).

Munk, W.

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

Olbers, D. J.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Richter, K.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Sell, W.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Shuleikin, V. V.

V. V. Shuleikin, Fizika Moria (Physics of the Sea) (Izdatelstvo Akad. Nauk. U.S.S.R., 1941).

Sparrow, E. M.

K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, “Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces,” J. Opt. Soc. Am. A 56, 916–925 (1966).
[CrossRef]

Stelenau, A.

A. Stelenau, “Uber die reflexion der sonnenstrahlung an wisserflachen und die ihre bedeutung fur das strahlungsklima von seeufern,” Beitr. Angew. Geophys. 70, 90–123 (1961).

Torrance, K. E.

K. E. Torrance, E. M. Sparrow, and R. C. Birkebak, “Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces,” J. Opt. Soc. Am. A 56, 916–925 (1966).
[CrossRef]

Walden, H.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

Williams, D. M.

D. M. Williams and E. Gaidos, “Detecting the glint of starlight on the oceans of distant planets,” Icarus 195, 927–937 (2008).
[CrossRef]

Beitr. Angew. Geophys. (1)

A. Stelenau, “Uber die reflexion der sonnenstrahlung an wisserflachen und die ihre bedeutung fur das strahlungsklima von seeufern,” Beitr. Angew. Geophys. 70, 90–123 (1961).

Icarus (1)

D. M. Williams and E. Gaidos, “Detecting the glint of starlight on the oceans of distant planets,” Icarus 195, 927–937 (2008).
[CrossRef]

J. Fluid Mech. (2)

M. S. Longuet-Higgins, “The generation of capillary waves by steep gravity waves,” J. Fluid Mech. 16, 138–159 (1963).
[CrossRef]

M. S. Longuet-Higgins, “Parasitic capillary waves: a direct calculation,” J. Fluid Mech. 301, 79–107 (1995).
[CrossRef]

J. Mar. Res. (2)

C. S. Cox, “Measurements of slopes of high-frequency wind waves,” J. Mar. Res. 16, 199–225 (1958).

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (3)

J. Sci. Ind. Res. (1)

M. V. Berry, “Catastrophe theory: a new mathematical tool for scientists,” J. Sci. Ind. Res. 36, 103–105 (1977).

Nature (1)

D. K. Lynch, “Reflections on closed loops,” Nature 316, 216–217 (1985).
[CrossRef]

Other (8)

D. K. Lynch, “Reflection on water,” http://epod.usra.edu/blog/2010/07/reflection-on-water.html.

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A.D.Pierce and R.N.Thurston, eds. (Academic, 1992), Vol.  21, pp. 1–234.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Miller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. “Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP),” Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe 8, 95 (1973).

M. Montagu-Pollack, Light and Water: A Study of Reflexion and Colour in River, Lake and Sea (George Bell and Sons, 1903).

V. V. Shuleikin, Fizika Moria (Physics of the Sea) (Izdatelstvo Akad. Nauk. U.S.S.R., 1941).

D. K. Lynch and W. C. Livingston, Color and Light in Nature, 2nd ed. (Cambridge University, 2001, reprinted by Thule Scientific, 2010).

R. Fleet, “Glows, bows and haloes,” http://www.dewbow.co.uk/glows/glitterpath.html.

M. Minnaert, The Nature of Light and Colour in the Open Air (George Bell and Sons, 1939, reprinted by Dover, 1954), pp. 130–131.

Supplementary Material (4)

» Media 1: AVI (5987 KB)     
» Media 2: MOV (271 KB)     
» Media 3: MOV (367 KB)     
» Media 4: MOV (47226 KB)     

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Figures (24)

Fig. 1
Fig. 1

Elliptical high sun glitter (ocean).

Fig. 2
Fig. 2

Elongated low sun glitter reaching to the horizon (ocean).

Fig. 3
Fig. 3

4 s exposure of moon glitter showing myriad closed trajectories of the glints (ocean).

Fig. 4
Fig. 4

Single frame from a 1000 fps movie showing glint evolution and morphology (bucket).

Fig. 5
Fig. 5

High sun glitter resolved. The individual glints are not randomly distributed but cluster together, primarily in capillary wave groups (ocean).

Fig. 6
Fig. 6

Top: image of resolved glitter adjusted to show only the glints. Bottom: same image adjusted to show the glints and the water’s surface (ocean).

Fig. 7
Fig. 7

Close-up time exposure of a loop showing the C/A flashes at the cusps (bucket).

Fig. 8
Fig. 8

High frame rate glitter morphology: (a) clear sky, (b) hazy sky with a bright solar aureole (bucket).

Fig. 9
Fig. 9

High frame rate ( 1000 fps ) time sequence of loop evolution in a bucket showing C/A in less than 1 ms . The faint static glint near bottom center of each frame is due to a bubble.

Fig. 10
Fig. 10

Single frame from 1000 fps Media 2. This shows a single C/A event near the center of the frame. The direction of time is reversible (bucket).

Fig. 11
Fig. 11

Single frame from 1000 fps Media 3 showing two glints from different C/A events that recombine and vanish (lower right side of the frame) (bucket).

Fig. 12
Fig. 12

Single frame from simulation movie (Media 4). The small dots show the locations of the glints. Amplitude of the waves is shown by the color scale at the right. Computational parameters were solar elevation, 45 ° ; solar diameter, 0.5 field; degrees size on the water, 200 m × 200 m ; and observer distance from the center of the frame, 200 m . Four deep water traveling waves were used, each of amplitude 0.5 m with arbitrary phases. Wavelengths were 50, 40, 30, and 20 m .

Fig. 13
Fig. 13

Theoretical computation of glitter showing time-integrated glint tracks forming closed loops.

Fig. 14
Fig. 14

Geometry of glitter formation illustrated using a monochromatic sinusoidal wave in one dimension and a point source of light. At any instant, light reflected from one complete wavelength will be scattered into a finite range of angles corresponding to four times the inclination angle of the steepest part of the wave.

Fig. 15
Fig. 15

Instantaneous C/A of glints can be understood by an observer passing through the reflection envelope from right to left. While outside the envelope (far right), no glint is seen. When the observer reaches the edge of the envelope, the glint first appears, i.e., creation takes place. As the observer enters the envelope, the glint splits in two. While inside the envelope, two glints are seen (see Fig. 9). As the observer approaches the opposite side of the envelope (left), the two glints come together, then disappear when the observer reaches the edge of the envelope (annihilation).

Fig. 16
Fig. 16

When inside the reflection envelope, two glints are seen by the observer O because from one wavelength on a smooth monochromatic surface, there will always be two and only two rays that reach the observer. One image is real and the other is virtual.

Fig. 17
Fig. 17

C/A can be understood in terms of a closed manifold in space–time where glints occur at the intersection of a horizontal “time line” and the closed curve. Time runs from bottom to top. Upper: If the time line does not intersect the curve, no glints are seen. When it reaches the curve and is tangent to it, creation occurs. At later times, two intersections occur so two glints are seen. Annihilation occurs in the reverse process. Lower: When the manifold is more complex, more complex behavior is seen. Here two creation events (C1 and C2) (lower two lobes of the manifold) produce two glint pairs (four intersections). As time progresses, single glints from different pairs merge to produce an annihilation (A1) near the center of the manifold, thus leaving two “unpaired” glints at the extreme left and right of the manifold. A third creation happens at C3, producing another pair of glints that separate. Then, each member of the newly created pair joins with one of the two outer glints and two more annihilations occur (A2 and A3). The manifolds—even when quite complex—represent the continuity of the surface. Being closed loops themselves, they can explain in a simple way the complex glint behavior seen in the media.

Fig. 18
Fig. 18

Bent or tilted glitter occurs when there is an asymmetric distribution of waves slopes. The most common occurrence is when wind blows continuously from one direction but can also occur when a wave whose wavelength is large compared to the observed glitter path encroaches on glitter produced by much smaller wavelength waves. In this picture, the long bow wave from a ship slides under the ambient short waves, causing them to be tilted more in one direction than the other (ocean).

Fig. 19
Fig. 19

Bent glitter simulated by our theoretical code. Wave slopes in the background are uniformly distributed but those in the foreground have been skewed, thereby making the glitter deviate from the vertical plane containing the sun and observer.

Fig. 20
Fig. 20

Glitter observed from space. The optical signature of glitter from oceans on extrasolar planets might be detectable from Earth, thereby providing a way to search for such planets. (Photograph courtesy of NASA).

Fig. 21
Fig. 21

When the sun is replaced by an extended source of light like sky, clouds, and mountains, glitter blossoms into a complex field of graceful loops and swirls. These structures are formed in exactly the same way as pointlike glints, but exhibit a vastly richer morphology, just as a sky full of clouds is more complex than a single sun (ocean).

Fig. 22
Fig. 22

Computer simulation of reflections from a scene with sky, clouds, and mountains.

Fig. 23
Fig. 23

Coordinate systems of the incident plane wave (i), a flat horizontal surface (s), and the wave specularly reflected from the flat surface to the observer (o). The actual rippled reflecting surface is given by z s as a function of x s and y s and lies alternately above and below the x s , y s plane.

Fig. 24
Fig. 24

Trajectories of alternately one or three glints as a function of time between the creation (C) and annihilation (A) events.

Equations (30)

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E o ( x o , y o , t o ) = [ i k E cos ( α ) / ( 2 π z o ) ] exp [ i ( k z o ω t o ) ] d x s d y s exp [ i k Φ ( x o , y o , x s , y s ) ] ,
Φ ( x o , y o , x s , y s ) = 2 z s cos ( α ) + [ x o x s cos ( α ) ] 2 / ( 2 z o ) + ( y o y s ) 2 / ( 2 z o ) ,
z s = A cos ( K x s Ω t ) .
Φ ( x s , t ) = 2 A cos ( α ) cos ( K x s Ω t ) + x s 2 cos 2 ( α ) / ( 2 z o ) + y s 2 / ( 2 z o ) .
Φ / x s = 0 = 2 A K cos ( α ) sin ( K x s Ω t ) + x s cos 2 ( α ) / z o .
X = K x s ,
u = X Ω t ,
M = cos ( α ) / ( 2 A K 2 z o ) ,
N = ( 1 M 2 ) 1 / 2 / M ,
M ( u + Ω t ) = sin ( u ) .
M = cos ( u ) .
Ω t = tan ( u ) u ,
X A , C = ± N ,
t A , C = ± [ N arc tan ( N ) ] / Ω ,
X = X A ± δ ,
Ω t = Ω t A N δ 2 / 2 + O ( δ 3 ) ,
t t A N ( X X A ) 2 / ( 2 Ω ) .
t t C + N ( X C X ) 2 / ( 2 Ω ) .
X R = ( N 2 + 1 ) 1 / 2 ,
t R = [ ( N 2 + 1 ) 1 / 2 π / 2 ] Ω .
X L = X R ,
t L = t R .
X = X L + δ ,
δ ( N 2 + 1 ) 1 / 2 Ω 2 ( t t L ) 2 / 2 ,
X X L + ( N 2 + 1 ) 1 / 2 Ω 2 ( t t L ) 2 / 2 .
δ Ω t / ( 1 M )
t ( 1 M ) X / Ω ,
t [ π + ( 1 + M ) X ] / Ω .
Δ t = 2 π / Ω .
Φ / x s = Φ / y s = 0 .

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