Abstract

The influence of surface waves and multiple scattering in water on the parameters of light pulses from an airborne source is studied. The contributions of various mechanisms to variations in delay of pulse and its variance are estimated. It is shown that waves make the main contribution to these values at small depths. With strong wind, the allowance for waves is important for small receiving apertures in the whole practically important depth range. For large receiving apertures or/and large widths of light beams incident on the surface, the determining factor is multiple scattering of light in water.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. G. Luchinin, “The spatial structure of a sinusoidally modulated light beam in a medium having strongly anisotropic scattering,” Radiophys. Quantum Electron. 14, 1507–1509(1971).
    [CrossRef]
  2. A. G. Luchinin, “Spatial spectrum of a narrow sine-wave-modulated light beam,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 10, 1312–1317 (1974).
  3. L. S. Dolin, “Solution of the radiative transfer equation in a small-angle approximation for stratified turbid medium with photon path dispersion taken into account,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 16, 34–39 (1980).
  4. L. S. Dolin, “Self-similar approximation of the multiple small-angle scattering theory,” Sov. Phys. Dokl. 26, 976–979 (1981).
  5. V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
    [CrossRef]
  6. L. S. Dolin, “Passage of a pulsed light signal through an absorbing medium with strongly anisotropic scattering,” Radiophys. Quantum Electron. 26, 220–228 (1983).
    [CrossRef]
  7. H. C. van de Hulst and G. W. Kattawar, “Exact spread function for a pulsed collimated beam in a medium with small-angle scattering,” Appl. Opt. 33, 5820–5829 (1994).
    [CrossRef] [PubMed]
  8. W. J. McLean, J. D. Freemen, and R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711(1998).
    [CrossRef]
  9. L. S. Dolin and I. M. Levin, Spravochnik po teorii podvodnogo videnya (Handboook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).
  10. A. G. Luchinin and L. S. Dolin, “Effect of sea waves on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660–669 (2008).
    [CrossRef]
  11. W. Pierson and L. Moskowitz, “A proposed spectral form for fully-developed wind seas based on the similarity theory of S. A. Kitaygorodsky,” J. Geophys. Res. 13, 198–227 (1954).
  12. C. Cox and W. Munk, “Measurements of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  13. I. M. Levin and O. V. Kopelevich, “Correlations between the inherent hydrooptical characteristics in the spectral range close to 550nm,” Oceanology 47, 334–339 (2007).
    [CrossRef]
  14. L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

2008

A. G. Luchinin and L. S. Dolin, “Effect of sea waves on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660–669 (2008).
[CrossRef]

2007

I. M. Levin and O. V. Kopelevich, “Correlations between the inherent hydrooptical characteristics in the spectral range close to 550nm,” Oceanology 47, 334–339 (2007).
[CrossRef]

1998

1994

1988

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

1983

L. S. Dolin, “Passage of a pulsed light signal through an absorbing medium with strongly anisotropic scattering,” Radiophys. Quantum Electron. 26, 220–228 (1983).
[CrossRef]

1982

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
[CrossRef]

1981

L. S. Dolin, “Self-similar approximation of the multiple small-angle scattering theory,” Sov. Phys. Dokl. 26, 976–979 (1981).

1980

L. S. Dolin, “Solution of the radiative transfer equation in a small-angle approximation for stratified turbid medium with photon path dispersion taken into account,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 16, 34–39 (1980).

1974

A. G. Luchinin, “Spatial spectrum of a narrow sine-wave-modulated light beam,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 10, 1312–1317 (1974).

1971

A. G. Luchinin, “The spatial structure of a sinusoidally modulated light beam in a medium having strongly anisotropic scattering,” Radiophys. Quantum Electron. 14, 1507–1509(1971).
[CrossRef]

1954

W. Pierson and L. Moskowitz, “A proposed spectral form for fully-developed wind seas based on the similarity theory of S. A. Kitaygorodsky,” J. Geophys. Res. 13, 198–227 (1954).

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

Cox, C.

Dolin, L. S.

A. G. Luchinin and L. S. Dolin, “Effect of sea waves on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660–669 (2008).
[CrossRef]

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

L. S. Dolin, “Passage of a pulsed light signal through an absorbing medium with strongly anisotropic scattering,” Radiophys. Quantum Electron. 26, 220–228 (1983).
[CrossRef]

L. S. Dolin, “Self-similar approximation of the multiple small-angle scattering theory,” Sov. Phys. Dokl. 26, 976–979 (1981).

L. S. Dolin, “Solution of the radiative transfer equation in a small-angle approximation for stratified turbid medium with photon path dispersion taken into account,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 16, 34–39 (1980).

L. S. Dolin and I. M. Levin, Spravochnik po teorii podvodnogo videnya (Handboook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

Feygels, V. I.

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

Freemen, J. D.

Kattawar, G. W.

Kopelevich, O. V.

I. M. Levin and O. V. Kopelevich, “Correlations between the inherent hydrooptical characteristics in the spectral range close to 550nm,” Oceanology 47, 334–339 (2007).
[CrossRef]

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

Levin, I. M.

I. M. Levin and O. V. Kopelevich, “Correlations between the inherent hydrooptical characteristics in the spectral range close to 550nm,” Oceanology 47, 334–339 (2007).
[CrossRef]

L. S. Dolin and I. M. Levin, Spravochnik po teorii podvodnogo videnya (Handboook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

Levin, M.

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

Luchinin, A. G.

A. G. Luchinin and L. S. Dolin, “Effect of sea waves on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660–669 (2008).
[CrossRef]

A. G. Luchinin, “Spatial spectrum of a narrow sine-wave-modulated light beam,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 10, 1312–1317 (1974).

A. G. Luchinin, “The spatial structure of a sinusoidally modulated light beam in a medium having strongly anisotropic scattering,” Radiophys. Quantum Electron. 14, 1507–1509(1971).
[CrossRef]

McLean, W. J.

Moskowitz, L.

W. Pierson and L. Moskowitz, “A proposed spectral form for fully-developed wind seas based on the similarity theory of S. A. Kitaygorodsky,” J. Geophys. Res. 13, 198–227 (1954).

Munk, W.

Pierson, W.

W. Pierson and L. Moskowitz, “A proposed spectral form for fully-developed wind seas based on the similarity theory of S. A. Kitaygorodsky,” J. Geophys. Res. 13, 198–227 (1954).

Remizovich, V. S.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
[CrossRef]

Rogozkin, D. B.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
[CrossRef]

Ryazanov, M. I.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
[CrossRef]

van de Hulst, H. C.

Walker, R. E.

Appl. Opt.

Izv. Acad. Sci. USSR Atmos. Oceanic Phys.

L. S. Dolin, O. V. Kopelevich, M. Levin, and V. I. Feygels, “Few-parameter models of light field in the sea and integral characteristics of the scattering phase function of water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 24, 893–896 (1988).

A. G. Luchinin, “Spatial spectrum of a narrow sine-wave-modulated light beam,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 10, 1312–1317 (1974).

L. S. Dolin, “Solution of the radiative transfer equation in a small-angle approximation for stratified turbid medium with photon path dispersion taken into account,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 16, 34–39 (1980).

Izv. Atmos. Ocean. Phys.

A. G. Luchinin and L. S. Dolin, “Effect of sea waves on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660–669 (2008).
[CrossRef]

J. Geophys. Res.

W. Pierson and L. Moskowitz, “A proposed spectral form for fully-developed wind seas based on the similarity theory of S. A. Kitaygorodsky,” J. Geophys. Res. 13, 198–227 (1954).

J. Opt. Soc. Am.

Oceanology

I. M. Levin and O. V. Kopelevich, “Correlations between the inherent hydrooptical characteristics in the spectral range close to 550nm,” Oceanology 47, 334–339 (2007).
[CrossRef]

Radiophys. Quantum Electron.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a narrow modulated light beam in a scattering medium with fluctuations of the photon path lengths in multiple scattering,” Radiophys. Quantum Electron. 25, 639–645(1982).
[CrossRef]

L. S. Dolin, “Passage of a pulsed light signal through an absorbing medium with strongly anisotropic scattering,” Radiophys. Quantum Electron. 26, 220–228 (1983).
[CrossRef]

A. G. Luchinin, “The spatial structure of a sinusoidally modulated light beam in a medium having strongly anisotropic scattering,” Radiophys. Quantum Electron. 14, 1507–1509(1971).
[CrossRef]

Sov. Phys. Dokl.

L. S. Dolin, “Self-similar approximation of the multiple small-angle scattering theory,” Sov. Phys. Dokl. 26, 976–979 (1981).

Other

L. S. Dolin and I. M. Levin, Spravochnik po teorii podvodnogo videnya (Handboook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Parameter Q as a function of depth. Digits close to the curves here and in other figures indicate the effective radius of the area of the entrance pupil of the receiving aperture R in meters. The water scattering coefficient b = 0.1 m 1 .

Fig. 2
Fig. 2

Additional delay caused by surface elevations. The water scattering coefficient is b = 0.1 m 1 .

Fig. 3
Fig. 3

Total variation of delay due to waves. The water scattering coefficient is b = 0.1 m 1 .

Fig. 4
Fig. 4

Total pulse delay (with allowance for the medium). The water scattering coefficient is b = 0.1 m 1 . Dashed curves are calculated for a flat air–water interface.

Fig. 5
Fig. 5

The same as in Fig. 4. The water scattering coefficient is b = 0.3 m 1 .

Fig. 6
Fig. 6

Additive to pulse variance caused by waves. The water scattering coefficient is b = 0.1 m 1 .

Fig. 7
Fig. 7

Root-mean-square pulse length Δ l 2 as a function of depth. Dashed curves are calculated for a flat interface. The water scattering coefficient is b = 0.1 m 1 .

Fig. 8
Fig. 8

Same as in Fig. 7. The water scattering coefficient is b = 0.3 m 1 .

Fig. 9
Fig. 9

Delay of pulse and its effective width as a function of depth. V = 5 m / s , b = 0.1 m 1 , R = 0.1 m .

Equations (47)

Equations on this page are rendered with MathJax. Learn more.

P 0 ( t ) = W 0 δ ( t ) ,
I S ( r , n ) = W 0 D S ( r , n ) δ ( t ) ,
D S ( r , n ) d r d n = 1.
I ( r , n , t ) = W 0 D S ( r + n H , n ) δ ( t H / c ) ,
n m n ( m 1 ) η .
I ( r , n ) m 2 T I ( r , m n ( m 1 ) η ) .
I ( r , n , t ) = m 2 T W 0 D S ( r + ( m n ( m 1 ) η ( r ) ) H , m n ( m 1 ) η ( r ) ) δ ( t H / c ) ,
P ( z , t ) = D R ( r ) I ( z , n , r , t ) d r d n = D R ( r ) E ( z , r , t ) d r ,
E ( z , r , t ) = I ( z , n , r , t ) d n .
t ( z ) ¯ = t P ( z , t ) d t P ( z , t ) d t ,
Δ t ( z ) 2 ¯ = ( t t ( z ) ¯ ) 2 P ( z , t ) d t P ( z , t ) d t .
t ( z ) ¯ = i m c ( ln P ω ( z ) ) d ω | ω = 0 ,
Δ t ( z ) 2 ¯ = m 2 c 2 2 ( ln P ω ( z ) ) ω 2 | ω = 0 ,
P ω ( z ) = 2 π 1 P ( z , t ) exp ( i ω t ) d t .
I ω ( r , n ) = m 2 T W 0 D S ( r + ( m n ( m 1 ) η ( r ) ) H , m n ( m 1 ) η ( r ) ) exp ( H i ω / c ) .
E ω ( z , r ) = W 0 T m 2 ( 2 π ) 3 exp ( H i ω / c ) F S ( k 1 , k 1 H + k 2 z / m ) Φ ω ( k 2 , z ) × exp ( i k 1 r 1 i k 2 ( r 1 r ) i k 2 η ( r 1 ) q z ) d k 1 d k 2 d r 1 ,
F S ( k , p ) = ( 2 π ) 4 D S ( r , n ) exp ( i kr i pn ) d r d n ,
P ω ( z ) = ( 2 π ) 1 W 0 T m 2 exp ( H i ω / c ) F R ( k 2 ) F S ( k 1 , k 1 H + k 2 z / m ) Φ ω ( k 2 , z ) × exp ( i ( k 1 k 2 ) r 1 i k 2 η ( r 1 ) q z ) d k 1 d k 2 d r 1 ,
ξ ( r ) / z 1 , q η ( r ) 2 / 2 1 ,
t ( z ) ¯ = t ( z ) 0 ¯ + t ( z ) 1 ¯ ,
Δ t ( z ) 2 ¯ = Δ t ( z ) 0 2 ¯ + Δ t ( z ) 1 2 ¯ ,
t 0 ( z ) ¯ = i m c ( ln P ω 0 ( z ) ) ω | ω = 0 ,
Δ t ( z ) 0 2 ¯ = m 2 c 2 2 ( ln P ω 0 ( z ) ) ω 2 | ω = 0 ,
t 1 ( z ) ¯ = i m c 1 P ω 0 Δ P ω ω | ω = 0 Δ P ω ( P ω 0 ) 2 P ω 0 ω | ω = 0 ,
Δ t ( z ) 1 2 ¯ = m 2 c 2 1 P ω 0 2 Δ P ω ω 2 | ω = 0 + 2 Δ P ω ( P ω 0 ) 3 ( P ω 0 ω | ω = 0 ) 2 2 ( P ω 0 ) 2 P ω 0 ω | ω = 0 Δ P ω ω | ω = 0 Δ P ω ( P ω 0 ) 2 2 P ω 0 ω 2 | ω = 0 ,
P ω 0 ( z ) = 2 π W 0 T m 2 exp ( H i ω / c ) F R ( k ) F S ( k , k ( H + z / m ) ) Φ ω ( k , z ) Θ ( ) d k ,
Θ ( ) = Θ ( σ η x q z k x , σ η y q z k y ) .
t 1 ( z ) ¯ = t 1 ξ ( z ) ¯ + t 1 η ( z ) ¯ ,
t 0 ( z ) ¯ = m c ( ln P 0 ) a ,
t 1 ξ ( z ) ¯ = m σ ξ 2 2 c P ω = 0 0 ( 1 P 0 P 0 a 2 P 0 z 2 3 P 0 z 2 a 2 m P 0 z ) ,
t 1 ( z ) ¯ η = m z q 2 σ η 2 2 c P 0 ( 1 P 0 P 0 a P 0 z 2 P 0 z a ) ,
Δ t ( z ) 0 2 ¯ = m 2 c 2 2 ( ln P 0 ) a 2 ,
Δ t ( z ) 1 ξ 2 ¯ = m 2 σ ξ 2 c 2 2 P 0 ( 4 P 0 a 2 z 2 + 2 ( P 0 ) 2 ( P 0 a ) 2 2 P 0 z 2 2 P 0 P 0 a 3 P 0 a z 2 1 P 0 2 P 0 z 2 2 P 0 a 2 4 m P 0 P 0 a P 0 z + 4 m 2 P 0 a z + 2 P 0 m 2 ) ,
Δ t ( z ) 1 η 2 ¯ = m 2 q 2 σ η 2 z c 2 2 P 0 ( 3 P 0 a 2 z + 2 ( P 0 ) 2 ( P 0 a ) 2 P 0 z 1 P 0 P 0 z 2 P 0 a 2 2 P 0 2 P 0 a z P 0 a ) .
F S ( k , p ) = ( 2 π ) 4 exp ( α 2 k 2 / 2 β 2 p 2 / 2 ) ,
F R ( k ) = ( 2 π ) 2 π R 2 exp ( R 2 k 2 / 4 ) ,
Θ ( k , z ) = exp ( ( q z σ η k ) 2 / 4 ) ,
G ξ ( k ) = β 0 / 2 π k 4 exp ( 0.74 g 2 k 2 V 4 k 2 k 0 2 ) ,
ν = 10 ( 4.13 + 1.23 V ) β 0 1 .
Φ ( k , z ) = ( 1 + μ σ 1 / k ln ( k z / μ + ( 1 + ( k z / μ ) 2 ) 1 / 2 ) ) exp ( a z b z ) + Q ( z ) exp ( k 2 / S ( z ) a 1 z ) ,
X ( γ ) = 2 μ γ 1 exp ( μ γ ) .
Q ( z ) = ( cosh ( ν ) ) 1 ( 1 + b 1 z ) exp ( b 1 z ) ,
S ( z ) = z ( ν tanh ( ν ) ) ( ( cosh ( ν ) ) 1 exp ( b 1 z ) ) 2 a ν ( ( cosh ν ) 1 ( 1 + b 1 z ) exp ( b 1 z ) ) ,
l = t ¯ c / m , l 0 = t 0 ( z ) ¯ c / m , l 1 ξ = t 1 ξ ¯ c / m , l 1 η = t 1 η ¯ c / m , Δ l 2 = Δ t 2 ¯ ( c / m ) 2 , Δ l 0 2 = Δ t 0 2 ¯ ( c / m ) 2 , Δ l 1 ξ 2 = Δ t 1 ξ 2 ¯ ( c / m ) 2 , Δ l 1 η 2 = Δ t 1 η 2 ¯ ( c / m ) 2 .
l 1 ξ ( a 1 z 1 ) = q a 1 σ ξ 2 .
l 1 ξ ( a 1 z 1 ) = σ ξ 2 ( q + ( 2 μ ) 1 ( b 1 / a 1 ) 1 / 2 ) ( a 1 + ( b 1 a 1 ) 1 / 2 / μ ) .
P 0 ( a 1 z 1 ) exp ( ( a 1 + ( b 1 a 1 ) 1 / 2 / μ ) z ) .

Metrics