Abstract

The effects of ocean waves on lidar imaging of submerged objects are investigated. Two significant consequences of wave focusing or defocusing are quantified: (a) intensification of near-surface backscatter in which the mean return is increased relative to that for a flat interface, and (b) spatial–temporal modulations of the backscattered return. For the former, mean returns can be as much as 50% larger than flat surface returns at shallow depth. For the latter, the strong modulations induced by wave motion present a dominant clutter field that significantly affects the imaging of shallow objects. Both effects are compensated at greater depths by beam spreading caused by multiple scattering, which diminishes the intensity of the wave focusing.

© 1996 Optical Society of America

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References

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  1. M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954).
  2. R. Walker, Marine Light Field Statistics (Wiley, New York, 1994).
  3. A. G. Luchinin, “Some properties of the backscattered signal in laser sounding of the upper ocean through a wavy surface,” Izv. Atmos. Oceanic Phys. 23, 725–729 (1987).
  4. C. D. Mobley, Light and Water (Academic, New York, 1994).
  5. W H. Wells, “Theory of small angle scattering,” AGARD Lect. Ser. 61, 3.3.1–3.3-17 (1973).
  6. C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  7. M. A. Donelan, W J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry” J. Geophys. Res. 92, 4971–5029 (1987).
    [CrossRef]
  8. T. S. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO 72-28 (Scripps Institute of Oceanography, University of California, San Diego, Calif., 1972).
  9. J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968).
    [CrossRef]
  10. R. L. Snyder, J. Dera, “Wave induced light fluctuations in the sea,” J. Opt. Soc. Am. 60, 1072–1079 (1970).
    [CrossRef]
  11. A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
    [CrossRef]
  12. A. G. Luchinin, “The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,” Izv. Atmos. Oceanic Phys. 18, 431–434 (1982).
  13. N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).
  14. N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).
  15. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

1987

A. G. Luchinin, “Some properties of the backscattered signal in laser sounding of the upper ocean through a wavy surface,” Izv. Atmos. Oceanic Phys. 23, 725–729 (1987).

M. A. Donelan, W J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry” J. Geophys. Res. 92, 4971–5029 (1987).
[CrossRef]

1982

A. G. Luchinin, “The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,” Izv. Atmos. Oceanic Phys. 18, 431–434 (1982).

1980

A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
[CrossRef]

1973

W H. Wells, “Theory of small angle scattering,” AGARD Lect. Ser. 61, 3.3.1–3.3-17 (1973).

1970

1968

J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968).
[CrossRef]

1954

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

Brown, D.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Cox, C.

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

Dera, J.

R. L. Snyder, J. Dera, “Wave induced light fluctuations in the sea,” J. Opt. Soc. Am. 60, 1072–1079 (1970).
[CrossRef]

J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968).
[CrossRef]

Donelan, M. A.

M. A. Donelan, W J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry” J. Geophys. Res. 92, 4971–5029 (1987).
[CrossRef]

Estep, L.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Fraser, A. B.

A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
[CrossRef]

Gordon, H. R.

J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

Holloway, J.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

Jurgens, F. C.

A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
[CrossRef]

Luchinin, A. G.

A. G. Luchinin, “Some properties of the backscattered signal in laser sounding of the upper ocean through a wavy surface,” Izv. Atmos. Oceanic Phys. 23, 725–729 (1987).

A. G. Luchinin, “The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,” Izv. Atmos. Oceanic Phys. 18, 431–434 (1982).

Miller, R.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Minnaert, M.

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954).

Mobley, C. D.

C. D. Mobley, Light and Water (Academic, New York, 1994).

Munk, W.

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

Petzold, T. S.

T. S. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO 72-28 (Scripps Institute of Oceanography, University of California, San Diego, Calif., 1972).

Pierson, W J.

M. A. Donelan, W J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry” J. Geophys. Res. 92, 4971–5029 (1987).
[CrossRef]

Price, B.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

Snyder, R. L.

Strand, M.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

Walker, R.

R. Walker, Marine Light Field Statistics (Wiley, New York, 1994).

Walker, R. E.

A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
[CrossRef]

Wells, W H.

W H. Wells, “Theory of small angle scattering,” AGARD Lect. Ser. 61, 3.3.1–3.3-17 (1973).

Witherspoon, N.

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

AGARD Lect. Ser.

W H. Wells, “Theory of small angle scattering,” AGARD Lect. Ser. 61, 3.3.1–3.3-17 (1973).

IEEE J. Oceanic Eng.

A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. QE-5, 195–198 (1980).
[CrossRef]

Izv. Atmos. Oceanic Phys.

A. G. Luchinin, “The brightness fluctuation spectrum of the natural light field escaping from under a wavy sea surface,” Izv. Atmos. Oceanic Phys. 18, 431–434 (1982).

A. G. Luchinin, “Some properties of the backscattered signal in laser sounding of the upper ocean through a wavy surface,” Izv. Atmos. Oceanic Phys. 23, 725–729 (1987).

J. Geophys. Res.

M. A. Donelan, W J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry” J. Geophys. Res. 92, 4971–5029 (1987).
[CrossRef]

J. Mar. Res.

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

J. Opt. Soc. Am.

Limnol. Oceanogr.

J. Dera, H. R. Gordon, “Light field fluctuations in the photic zone,” Limnol. Oceanogr. 13, 697–699 (1968).
[CrossRef]

Other

N. Witherspoon, J. Holloway, D. Brown, M. Strand, B. Price, R. Miller, L. Estep, “Measured degradation in image quality when imaging through a wavy air-water interface,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 383–390 (1988).

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

T. S. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO 72-28 (Scripps Institute of Oceanography, University of California, San Diego, Calif., 1972).

C. D. Mobley, Light and Water (Academic, New York, 1994).

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954).

R. Walker, Marine Light Field Statistics (Wiley, New York, 1994).

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Figures (13)

Fig. 1
Fig. 1

Geometry for airborne lidar imaging. Refraction at the interface results in focusing (convergence) and defocusing (divergence) of the rays at the wave crests and troughs, respectively. Multiple scattering in water (represented by the PSF) mitigates the focusing effect.

Fig. 2
Fig. 2

Gray-scale rendering of surface-wave elevation. Realization is 1024 × 1024 0.5-cm pixels, for a 5-kn wind speed (∼5 m total realization size). Wind direction is left to right. Gray-scale band represents surface elevation in meters.

Fig. 3
Fig. 3

Intersection coordinates on an irradiance plane at a 2-m depth, for the surface of Fig. 2.

Fig. 4
Fig. 4

Radial cross section of the PSF at a 2-m depth, for b = 0.20/m, 0.5-cm resolution. The peak in the PSF at small angles is smoothed by an antialias filter (see App. A).

Fig. 5
Fig. 5

Normalized downwelling irradiance at a 2-m depth for the surface of Fig. 2. Water is Jerlov II (see Table 1). The irradiance is normalized by the value just above the surface; thus the mean per pixel irradiance of 0.86 is the product of the Fresnel transmission (0.98) and the diffuse attenuation [exp(−2 × 0.063) = 0.88]. The peak per pixel irradiance is nearly six times the mean value.

Fig. 6
Fig. 6

Normalized upwelling radiance from a range-gated return at a 2-m depth, corresponding to the surface of Fig. 2. The radiance is normalized by the value just above the surface; thus the mean per pixel radiance for a flat interface would be 0.75, the product of the Fresnel transmission squared times the round-trip diffuse attenuation. The mean for this realization is 1.04, yielding an intensified backscatter of 39%. Note that the peak per pixel value is more than three times the mean return.

Fig. 7
Fig. 7

Fractional fluctuations of downwelling irradiance. Experimental data are for solar illumination, where the finite solar disk provides some spatial averaging of short scale fluctuations. Simulation results are for Jerlov II water, with no spatial averaging.

Fig. 8
Fig. 8

Intensified backscatter of the lidar return caused by double focusing by surface waves, simulation results, and linearized theory The quantity plotted is the mean return in the presence of a wavy surface normalized by the comparable flat surface value: (a) sensitivity to water turbidity, (b) sensitivity to wind speed.

Fig. 9
Fig. 9

Fractional fluctuations of upwelling radiance, simulation results, and linearized theory: (a) sensitivity to water turbidity, (b) sensitivity to wind speed.

Fig. 10
Fig. 10

Image sequence for downwelling and upwelling fluctuations, 1-m to 6-m depth, 5-kn wind speed, and Jerlov II water. Images are 5 m on a side.

Fig. 11
Fig. 11

Lidar image of the resolution panel at a depth of 0.2, 1, 2, and 3 m, with Jerlov III water. The left-hand column corresponds to a flat surface, and the right-hand column includes waves from a 5-kn wind. Resolution bars are 1, 2, 4, and 8 cm in width. The total image size is 0.64 m.

Fig. 12
Fig. 12

Algebraic fit to Petzold data: Atlantic Underseas Test and Evaluation Center (AUTEC) 161 station 9 (Bahamas), Avalon Harbor Catalina Island (HAOCE) station 5 (offshore Southern California), Naval Undersea Center (NUC) station 2200 (San Diego Harbor, California), Wells fit, θ0 = 0.03, and Algebraic fit, Eq. (A1), θ0 = 0.12.

Fig. 13
Fig. 13

Transformed phase function Σ (ψ) and MTF exponent D(ψ) for an algebraic fit to Petzold's phase function (θ0= 0.12).

Tables (1)

Tables Icon

Table 1 Parameters for Image Simulations

Equations (11)

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z = ( n n 1 ) ( 1 a k ) λ 2 π 0.64 ak λ ,
s ( θ ) = s 0 θ 3 / 2 ( θ 0 2 + θ 2 ) 1 / 2 , 0 θ π
( ψ ) = 0 s ( θ ) J 0 ( 2 π θ ψ ) 2 π θ d θ ,
D ( ψ ) = 1 ψ 0 ψ ( ψ ) d ψ ,
MTF ( ψ ) = exp ( cz ) exp [ b f zD ( ψ ) ] .
0 π J 0 ( 2 π θ ψ ) [ θ ( θ 0 2 + θ 2 ) ] 1 / 2 = 0 π J 0 ( 2 π θ ψ ) 1 [ θ ( θ 0 2 + θ 2 ) ] 1 / 2 + 0 π 1 [ θ ( θ 0 2 + θ 2 ) ] 1 / 2 = 0 π J 0 ( 2 π θ ψ ) 1 [ θ ( θ 0 2 + θ 2 ) ] 1 / 2 + 2 0 π ( θ θ 0 2 + θ 2 ) 3 / 2 + 2 π ( θ 0 2 + π 2 ) ,
1 θ 0 2 π ψ 0 2 π 2 ψ J 0 ( ξ ) { ξ [ 1 + ( ξ / a ) 2 ] } 1 / 2 1 θ 0 2 π ψ 0 J 0 ( ξ ) ξ d ξ
( σ d μ d ) 2 = [ z ( n 1 n ) ] 2 1 ( 2 π ) 2 0 | Λ ( k , z ) | 2 × | Φ ( k , z ) | 2 | Φ ( 0 , z ) | 2 k 4 H ζ ζ ( k ) k d k ,
Λ ( z , k ) = exp [ 1 4 k 2 z 2 ( n 1 n ) 2 σ η 2 ] ,
μ u μ 0 = 1 + ( σ d μ d ) 2 .
( σ u μ u ) 2 = [ z ( n 1 n ) ] 2 1 ( 2 π ) 2 0 | Λ ( k , z ) | 4 × | Φ ( k , z ) | 4 | Φ ( 0 , z ) | k 4 H ζ ζ ( k ) k d k .

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