Abstract

A compact, two-dimensional scanning laser slope gauge has been developed for measuring ocean ripples, leading to the determination of their directional slope spectrum in the wavelength range of 4.5–81 mm. A telecentric scanning mechanism is used to enhance the dynamic range of slope measurements and to eliminate constraints caused by water-surface undulations associated with long waves. Successful laboratory tests and field trials have been performed; sample results are provided.

© 1993 Optical Society of America

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References

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  1. Jin Wu, “Sea-surface slope and equilibrium wind-wave spectra,” Phys. Fluids 15, 741–747 (1972).
    [CrossRef]
  2. Jin Wu, “Roughness elements of the sea surface—their spectral composition,” Tellus Ser. A 38, 178–188 (1986).
    [CrossRef]
  3. R. K. Moore, “Radar sensing of the ocean,” IEEE J. Oceanic Eng. OE-10, 84–113 (1985).
    [CrossRef]
  4. C. S. Cox, “Measurements of slopes of high-frequency wind waves,” J. Mar. Res. 16, 199–225 (1958).
  5. Jin Wu, “Slope and curvature distributions of wind-disturbed water surface,” J. Opt. Soc. Am. 61, 852–858 (1971).
    [CrossRef]
  6. Jin Wu, “Directional slope and curvature distributions of wind waves,” J. Fluid. Mech. 79, 463–480 (1977).
    [CrossRef]
  7. S. R. Long, N. E. Huang, “On the variation and growth of wave-slope spectra in the capillary-gravity range with increasing wind,” J. Fluid Mech. 77, 209–228 (1976).
    [CrossRef]
  8. C. S. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 9 (1956).
  9. S. Tang, O. H. Shemdin, “Measurement of high-frequency wave using a wave follower,” J. Geophys. Res. 88, 9832–9840 (1983).
    [CrossRef]
  10. S. P. Haimbach, Jin Wu, “Field trials of an optical scanner for studying sea-surface fine structure,” IEEE J. Oceanic Eng. OE-10, 451–453 (1985).
    [CrossRef]
  11. O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
    [CrossRef]
  12. W. C. Keller, B. L. Gotwols, “Two-dimensional optical measurement of wave slope,” Appl. Opt. 22, 3476–3478 (1983).
    [CrossRef] [PubMed]
  13. B. Jähne, S. Waas, “Optical measuring technique for small scale water surface waves,” in Advanced Optical Instrumentation for Remote Sensing of the Earth's Surface From Space, G. Duchossois, F. L. Herr, K. J. Zander, eds., Proc. Soc. Photo-Opt. Instrum. Eng., 1129, 122–128 (1989).
  14. J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).
  15. Melles Griot Inc., Optics Guide 5, (Irvine, California, 1990). p. 21–7.
  16. Operating Instruction Manual (United Detector Technology, Orlando, Fla., 1984).

1988 (1)

O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
[CrossRef]

1986 (1)

Jin Wu, “Roughness elements of the sea surface—their spectral composition,” Tellus Ser. A 38, 178–188 (1986).
[CrossRef]

1985 (2)

R. K. Moore, “Radar sensing of the ocean,” IEEE J. Oceanic Eng. OE-10, 84–113 (1985).
[CrossRef]

S. P. Haimbach, Jin Wu, “Field trials of an optical scanner for studying sea-surface fine structure,” IEEE J. Oceanic Eng. OE-10, 451–453 (1985).
[CrossRef]

1983 (2)

S. Tang, O. H. Shemdin, “Measurement of high-frequency wave using a wave follower,” J. Geophys. Res. 88, 9832–9840 (1983).
[CrossRef]

W. C. Keller, B. L. Gotwols, “Two-dimensional optical measurement of wave slope,” Appl. Opt. 22, 3476–3478 (1983).
[CrossRef] [PubMed]

1977 (1)

Jin Wu, “Directional slope and curvature distributions of wind waves,” J. Fluid. Mech. 79, 463–480 (1977).
[CrossRef]

1976 (1)

S. R. Long, N. E. Huang, “On the variation and growth of wave-slope spectra in the capillary-gravity range with increasing wind,” J. Fluid Mech. 77, 209–228 (1976).
[CrossRef]

1972 (1)

Jin Wu, “Sea-surface slope and equilibrium wind-wave spectra,” Phys. Fluids 15, 741–747 (1972).
[CrossRef]

1971 (1)

1958 (1)

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

1956 (1)

C. S. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 9 (1956).

Barter, J.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Beach, K.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Cox, C. S.

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

C. S. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 9 (1956).

Gotwols, B. L.

Haimbach, S. P.

S. P. Haimbach, Jin Wu, “Field trials of an optical scanner for studying sea-surface fine structure,” IEEE J. Oceanic Eng. OE-10, 451–453 (1985).
[CrossRef]

Huang, N. E.

S. R. Long, N. E. Huang, “On the variation and growth of wave-slope spectra in the capillary-gravity range with increasing wind,” J. Fluid Mech. 77, 209–228 (1976).
[CrossRef]

Jähne, B.

B. Jähne, S. Waas, “Optical measuring technique for small scale water surface waves,” in Advanced Optical Instrumentation for Remote Sensing of the Earth's Surface From Space, G. Duchossois, F. L. Herr, K. J. Zander, eds., Proc. Soc. Photo-Opt. Instrum. Eng., 1129, 122–128 (1989).

Keller, W. C.

Kwoh, D.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Long, S. R.

S. R. Long, N. E. Huang, “On the variation and growth of wave-slope spectra in the capillary-gravity range with increasing wind,” J. Fluid Mech. 77, 209–228 (1976).
[CrossRef]

Luding, M.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Moore, R. K.

R. K. Moore, “Radar sensing of the ocean,” IEEE J. Oceanic Eng. OE-10, 84–113 (1985).
[CrossRef]

Munk, W. H.

C. S. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 9 (1956).

Rungaldier, H.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Schatzman, J.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Shemdin, O. H.

O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
[CrossRef]

S. Tang, O. H. Shemdin, “Measurement of high-frequency wave using a wave follower,” J. Geophys. Res. 88, 9832–9840 (1983).
[CrossRef]

Stonich, I.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Tang, S.

S. Tang, O. H. Shemdin, “Measurement of high-frequency wave using a wave follower,” J. Geophys. Res. 88, 9832–9840 (1983).
[CrossRef]

Tran, H. M.

O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
[CrossRef]

Waas, S.

B. Jähne, S. Waas, “Optical measuring technique for small scale water surface waves,” in Advanced Optical Instrumentation for Remote Sensing of the Earth's Surface From Space, G. Duchossois, F. L. Herr, K. J. Zander, eds., Proc. Soc. Photo-Opt. Instrum. Eng., 1129, 122–128 (1989).

Wagner, R.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Williams, A.

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Wu, Jin

Jin Wu, “Roughness elements of the sea surface—their spectral composition,” Tellus Ser. A 38, 178–188 (1986).
[CrossRef]

S. P. Haimbach, Jin Wu, “Field trials of an optical scanner for studying sea-surface fine structure,” IEEE J. Oceanic Eng. OE-10, 451–453 (1985).
[CrossRef]

Jin Wu, “Directional slope and curvature distributions of wind waves,” J. Fluid. Mech. 79, 463–480 (1977).
[CrossRef]

Jin Wu, “Sea-surface slope and equilibrium wind-wave spectra,” Phys. Fluids 15, 741–747 (1972).
[CrossRef]

Jin Wu, “Slope and curvature distributions of wind-disturbed water surface,” J. Opt. Soc. Am. 61, 852–858 (1971).
[CrossRef]

Wu, S. C.

O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
[CrossRef]

Appl. Opt. (1)

Bull. Scripps Inst. Oceanogr. (1)

C. S. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Bull. Scripps Inst. Oceanogr. 6, 9 (1956).

IEEE J. Oceanic Eng. (2)

R. K. Moore, “Radar sensing of the ocean,” IEEE J. Oceanic Eng. OE-10, 84–113 (1985).
[CrossRef]

S. P. Haimbach, Jin Wu, “Field trials of an optical scanner for studying sea-surface fine structure,” IEEE J. Oceanic Eng. OE-10, 451–453 (1985).
[CrossRef]

J. Fluid Mech. (1)

S. R. Long, N. E. Huang, “On the variation and growth of wave-slope spectra in the capillary-gravity range with increasing wind,” J. Fluid Mech. 77, 209–228 (1976).
[CrossRef]

J. Fluid. Mech. (1)

Jin Wu, “Directional slope and curvature distributions of wind waves,” J. Fluid. Mech. 79, 463–480 (1977).
[CrossRef]

J. Geophys. Res. (2)

S. Tang, O. H. Shemdin, “Measurement of high-frequency wave using a wave follower,” J. Geophys. Res. 88, 9832–9840 (1983).
[CrossRef]

O. H. Shemdin, H. M. Tran, S. C. Wu, “Directional measurement of short ocean waves with stereophotography,” J. Geophys. Res. 93, 13,891–13,901 (1988).
[CrossRef]

J. Mar. Res. (1)

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

J. Opt. Soc. Am. (1)

Phys. Fluids (1)

Jin Wu, “Sea-surface slope and equilibrium wind-wave spectra,” Phys. Fluids 15, 741–747 (1972).
[CrossRef]

Tellus Ser. A (1)

Jin Wu, “Roughness elements of the sea surface—their spectral composition,” Tellus Ser. A 38, 178–188 (1986).
[CrossRef]

Other (4)

B. Jähne, S. Waas, “Optical measuring technique for small scale water surface waves,” in Advanced Optical Instrumentation for Remote Sensing of the Earth's Surface From Space, G. Duchossois, F. L. Herr, K. J. Zander, eds., Proc. Soc. Photo-Opt. Instrum. Eng., 1129, 122–128 (1989).

J. Barter, K. Beach, D. Kwoh, M. Luding, H. Rungaldier, J. Schatzman, I. Stonich, R. Wagner, A. Williams, “Surface truth measurement system,” Rep. 53563–6005 (TRW, Redono Beach, Calif., 1990).

Melles Griot Inc., Optics Guide 5, (Irvine, California, 1990). p. 21–7.

Operating Instruction Manual (United Detector Technology, Orlando, Fla., 1984).

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Figures (10)

Fig. 1
Fig. 1

Geometrical relation among various parameters. OZ and OZ0 are, respectively, the optical axis and the mean water surface normal; θ, T, and ϕ are the angle incident to the Fresnel lens, the tilt angle, and the azimuth angle; Î, R ̂, and N ̂ represent the incident, the refracted, and the normal vectors of the water surface.

Fig. 2
Fig. 2

Schematic of SLSG/2D.

Fig. 3
Fig. 3

Schematic of underwater part of SLSG/2D.

Fig. 4
Fig. 4

Mapping between (θ, ϕ and (Vx, Vy).

Fig. 5
Fig. 5

Distribution of intensity at various incident angles. The screen is made by one piece of ground glass (×), two pieces of ground glass (△), and two pieces of ground glass adding a sheet of semitransparent paper (●).

Fig. 6
Fig. 6

Slope data collected over a still water surface. σsx, and σsy are rms slopes in X and Y directions, respectively; U is the wind speed.

Fig. 7
Fig. 7

Slope data collected at different wind speeds. S x 2 ¯ and S y 2 ¯ are mean-square slopes in X and Y directions, respectively; U is the wind speed.

Fig. 8
Fig. 8

An example of wave-number slope spectrum. U is the wind speed, the degree of freedom is 60.

Fig. 9
Fig. 9

Slope data collected in the field.

Fig. 10
Fig. 10

Motions of the pontoon boat.

Equations (19)

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n ( N ̂ × Î ) = N ̂ × R ̂ ,
Î = ( sin β ) ( cos α ) ê x + ( sin β ) ( sin α ) ê y + ( cos β ) ê z ,
R ̂ = ( sin θ ) ( cos ϕ ) ê x + ( sin θ ) ( sin ϕ ) ê y + ( cos θ ) ê z ,
N ̂ = ( sin γ ) ( cos ω ) ê x + ( sin γ ) ( sin ω ) ê y + ( cos γ ) ê z ,
tan 2 γ = ( N x 2 + N x 2 ) / N z 2 = { n 2 ( sin 2 β ) + ( sin 2 θ ) 2 n ( sin β ) ( sin θ ) × [ ( sin α ) ( sin ϕ ) + ( cos α ) ( cos ϕ ) ] } / [ n ( cos α ) ( cos θ ) ] 2
( s x , s y ) = tan γ ( cos ω , sin ω ) .
S ( k ) = ( 2 π ) 2 s ( x ) s ( x + r ) ¯ exp ( i k · r ) d r .
S 1 ( k , Ω ) = S ( k x , k y ) ( k x , k y ) ( k , Ω ) = S ( k cos Ω , k sin Ω ) k .
D 1 = Γ L λ H s ,
D 2 = D 1 + L 1 H s L ,
D 2 H s = L 1 L Γ L λ H s 2 = 0 .
H s = L ( Γ λ L 1 ) 1 / 2 .
A ( χ , ν ) = [ cos ν 0 sin ν ( sin ν ) ( sin χ ) cos χ ( cos ν ) ( sin χ ) ( sin ν ) ( cos χ ) sin χ ( cos ν ) ( cos χ ) ] ,
ν = sin 1 sin Ψ x cos Ψ y , χ = Ψ y ,
[ X 0 Y 0 Z 0 ] = A [ X Y Z ] .
n ( N y 0 I z 0 N z 0 I y 0 ) = N y 0 R z 0 N z 0 R y 0 , n ( N z 0 I x 0 N x 0 I z 0 ) = N z 0 R x 0 N x 0 R z 0 , n ( N x 0 I y 0 N y 0 I x 0 ) = N x 0 R y 0 N y 0 R x 0 ,
tan 2 γ 0 = N x 0 2 + N y 0 2 N z 0 2 = R x 0 2 + R y 0 2 + n 2 I x 0 2 + n 2 I y 0 2 2 n ( I x 0 R x 0 + I y 0 R y 0 ) ( R z 0 n I z 0 ) 2 ,
[ I x 0 I y 0 I z 0 ] = A [ I x I y I z ] ,
[ R x 0 R y 0 R z 0 ] = A [ R x R y R z ] ,

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