Abstract

We investigate the possibility of using the water-backscattered radiation from a bottom sounding airborne imaging light detection and ranging (lidar) system to determine the surface slope at the point where the laser beam intersects the surface. We show that the refraction angle of the beam can be determined using receivers whose sensitivities vary linearly over their field of view. Equations are derived to estimate the statistical mean and variance values of this refracted angle. We demonstrate that the proposed algorithm improves lidar imaging. Numerical examples with reference to typical marine conditions are given.

© 2008 Optical Society of America

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  1. R. E. Walker, Marine Light Field Statistics (Wiley, 1994).
  2. Yu.-A. R. Mullamaa, “Effect of wavy sea surface on the visibility of underwater objects,” Izv. Atmos. Ocean. Phys. 11, 199-205 (1975).
  3. A. G. Luchinin, “Some characteristics of the formation of a shelf image when it is observed through a wavy sea surface,” Izv. Atmos. Ocean. Phys. 17, 537-539 (1981).
  4. A. G. Luchinin, “Basic principles of imaging underwater objects observed through a rough surface,” Izv. Atmos. Ocean. Phys. 32, 273-279 (1996).
  5. V. L. Weber and A. G. Luchinin, “On the variance of the fluctuations of images viewed through wavy surface,” Izv. Atmos. Ocean. Phys. 19, 469-474 (1983).
  6. V. L. Weber and A. G. Luchinin, “Influence of correlation effects on the image characteristics of the reservoir bottom observed through the wavy surface,” Izv. Atmos. Ocean. Phys. 37, 239-246 (2001).
  7. W. J. McLean and J. D. Freemen, “Effects of ocean waves on airborne lidar images,” Appl. Opt. 35, 3261-3269 (1996).
    [CrossRef] [PubMed]
  8. E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).
  9. G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
    [CrossRef]
  10. Optika Okeana (Ocean Optics) (in Russian) A. S. Monin, ed. (Nauka, 1983)
  11. L. S. Dolin L. and I. M. Levin, Spravochnik po Teorii Podvodnogo Videniya (Handbook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).
  12. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
    [CrossRef]
  13. L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).
  14. G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
    [PubMed]
  15. G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
    [CrossRef]
  16. L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).
  17. A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).
  18. L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
    [CrossRef]
  19. I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).
  20. V. I. Weber, “New method for observation of underwater objects through rough sea surface,” in Proceedings of III International Conference: Current Problems in Optics of Natural Waters (ONW'2005) (D. S. Rozhdestvensky Optical Society, 2005), pp. 345-348.
    [PubMed]
  21. V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.
  22. A. G. Luchinin, “Effect of wind waves on characteristics of the light field backscattered from the bottom and the bulk of water,” Izv. Atmos. Ocean. Phys. 15, 513-534 (1979).
  23. D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).
  24. D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).
  25. W. Pierson and L. Moskovitz, “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).
  26. C. Cox and W. Munk, “Measurements of the roughness of the sea surface from photographs of the sun glitter,” J. Opt. Soc. Am. 44, 838-850 (1954).
    [CrossRef]
  27. D. I. Abrosimov and A. G. Luchinin, “Signal statistics of lidar sounding of the upper ocean through its rough surface,” Izv. Atmos. Ocean. Phys. 35, 266-273 (1999).
  28. A. G. Luchinin and L. S. Dolin, “Effect of wavy on the limiting resolution of aircraft oceanographic lidars,” Izv. Atmos. Ocean. Phys. 44, 660-669 (2008).
    [CrossRef]

2008 (1)

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

2007 (2)

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

2006 (1)

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

2005 (1)

A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).

2004 (1)

L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).

2001 (1)

V. L. Weber and A. G. Luchinin, “Influence of correlation effects on the image characteristics of the reservoir bottom observed through the wavy surface,” Izv. Atmos. Ocean. Phys. 37, 239-246 (2001).

2000 (1)

I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).

1999 (1)

D. I. Abrosimov and A. G. Luchinin, “Signal statistics of lidar sounding of the upper ocean through its rough surface,” Izv. Atmos. Ocean. Phys. 35, 266-273 (1999).

1996 (2)

W. J. McLean and J. D. Freemen, “Effects of ocean waves on airborne lidar images,” Appl. Opt. 35, 3261-3269 (1996).
[CrossRef] [PubMed]

A. G. Luchinin, “Basic principles of imaging underwater objects observed through a rough surface,” Izv. Atmos. Ocean. Phys. 32, 273-279 (1996).

1992 (1)

E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).

1983 (1)

V. L. Weber and A. G. Luchinin, “On the variance of the fluctuations of images viewed through wavy surface,” Izv. Atmos. Ocean. Phys. 19, 469-474 (1983).

1981 (1)

A. G. Luchinin, “Some characteristics of the formation of a shelf image when it is observed through a wavy sea surface,” Izv. Atmos. Ocean. Phys. 17, 537-539 (1981).

1979 (1)

A. G. Luchinin, “Effect of wind waves on characteristics of the light field backscattered from the bottom and the bulk of water,” Izv. Atmos. Ocean. Phys. 15, 513-534 (1979).

1975 (1)

Yu.-A. R. Mullamaa, “Effect of wavy sea surface on the visibility of underwater objects,” Izv. Atmos. Ocean. Phys. 11, 199-205 (1975).

1969 (2)

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

1954 (2)

W. Pierson and L. Moskovitz, “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 glitter,” J. Opt. Soc. Am. 44, 838-850 (1954).
[CrossRef]

Abrosimov, D. I.

D. I. Abrosimov and A. G. Luchinin, “Signal statistics of lidar sounding of the upper ocean through its rough surface,” Izv. Atmos. Ocean. Phys. 35, 266-273 (1999).

Bravo-Zhivotovsky, D. M.

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

Cox, C.

Dolin, L.

L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).

Dolin, L. S.

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

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).

L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

Dolin L., L. S.

L. S. Dolin L. and I. M. Levin, Spravochnik po Teorii Podvodnogo Videniya (Handbook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

Frantsuzov, O. N.

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

Freemen, J. D.

Gilbert, G.

L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).

Gilbert, G. D.

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Katsev, I. L.

I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).

E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Levin, I.

L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).

Levin, I. M.

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

L. S. Dolin L. and I. M. Levin, Spravochnik po Teorii Podvodnogo Videniya (Handbook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

Luchinin, A.

L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).

Luchinin, A. G.

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

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).

L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).

V. L. Weber and A. G. Luchinin, “Influence of correlation effects on the image characteristics of the reservoir bottom observed through the wavy surface,” Izv. Atmos. Ocean. Phys. 37, 239-246 (2001).

D. I. Abrosimov and A. G. Luchinin, “Signal statistics of lidar sounding of the upper ocean through its rough surface,” Izv. Atmos. Ocean. Phys. 35, 266-273 (1999).

A. G. Luchinin, “Basic principles of imaging underwater objects observed through a rough surface,” Izv. Atmos. Ocean. Phys. 32, 273-279 (1996).

V. L. Weber and A. G. Luchinin, “On the variance of the fluctuations of images viewed through wavy surface,” Izv. Atmos. Ocean. Phys. 19, 469-474 (1983).

A. G. Luchinin, “Some characteristics of the formation of a shelf image when it is observed through a wavy sea surface,” Izv. Atmos. Ocean. Phys. 17, 537-539 (1981).

A. G. Luchinin, “Effect of wind waves on characteristics of the light field backscattered from the bottom and the bulk of water,” Izv. Atmos. Ocean. Phys. 15, 513-534 (1979).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

McLean, W. J.

Moskovitz, L.

W. Pierson and L. Moskovitz, “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).

Mullamaa, Yu.-A. R.

Yu.-A. R. Mullamaa, “Effect of wavy sea surface on the visibility of underwater objects,” Izv. Atmos. Ocean. Phys. 11, 199-205 (1975).

Munk, W.

Osadchy, V. Ju.

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

Pierson, W.

W. Pierson and L. Moskovitz, “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).

Prikhach, A. S.

I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).

E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).

Rybalka, N. N.

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

Savchenko, V. V.

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

Savel'ev, V. A.

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

Stewart, S.

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

Titov, V. I.

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

Turlaev, D. G.

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).

L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).

Walker, R. E.

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

Weber, V. I.

V. I. Weber, “New method for observation of underwater objects through rough sea surface,” in Proceedings of III International Conference: Current Problems in Optics of Natural Waters (ONW'2005) (D. S. Rozhdestvensky Optical Society, 2005), pp. 345-348.
[PubMed]

Weber, V. L.

V. L. Weber and A. G. Luchinin, “Influence of correlation effects on the image characteristics of the reservoir bottom observed through the wavy surface,” Izv. Atmos. Ocean. Phys. 37, 239-246 (2001).

V. L. Weber and A. G. Luchinin, “On the variance of the fluctuations of images viewed through wavy surface,” Izv. Atmos. Ocean. Phys. 19, 469-474 (1983).

Zege, E. P.

I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).

E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Appl. Opt. (1)

Izv. Atmos. Ocean. Phys. (13)

L. S. Dolin, A. G. Luchinin and D. G. Turlaev, “Algorithm of recovering underwater object images distorted by surface waving,” Izv. Atmos. Ocean. Phys. 40, 756-764 (2004).

A. G. Luchinin, L. S. Dolin and D. G. Turlaev, “Correction of images of submerged objects on the basis of incomplete information about surface roughness,” Izv. Atmos. Ocean. Phys. 41, 247-252 (2005).

Yu.-A. R. Mullamaa, “Effect of wavy sea surface on the visibility of underwater objects,” Izv. Atmos. Ocean. Phys. 11, 199-205 (1975).

A. G. Luchinin, “Some characteristics of the formation of a shelf image when it is observed through a wavy sea surface,” Izv. Atmos. Ocean. Phys. 17, 537-539 (1981).

A. G. Luchinin, “Basic principles of imaging underwater objects observed through a rough surface,” Izv. Atmos. Ocean. Phys. 32, 273-279 (1996).

V. L. Weber and A. G. Luchinin, “On the variance of the fluctuations of images viewed through wavy surface,” Izv. Atmos. Ocean. Phys. 19, 469-474 (1983).

V. L. Weber and A. G. Luchinin, “Influence of correlation effects on the image characteristics of the reservoir bottom observed through the wavy surface,” Izv. Atmos. Ocean. Phys. 37, 239-246 (2001).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, and S. Stewart, “Influence of illumination conditions on the sea-bottom visibility,” Izv. Atmos. Ocean. Phys. 42, 115-123(2006).
[CrossRef]

A. G. Luchinin, “Effect of wind waves on characteristics of the light field backscattered from the bottom and the bulk of water,” Izv. Atmos. Ocean. Phys. 15, 513-534 (1979).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, and V. A. Savel'ev, “Some problems of the theory of visibility in turbid media,” Izv. Atmos. Ocean. Phys. 5, 388-393 (1969).

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin and V. A. Savel'ev, “Structure of a narrow light beam in sea water,” Izv. Atmos. Ocean. Phys. 5, 83-87 (1969).

D. I. Abrosimov and A. G. Luchinin, “Signal statistics of lidar sounding of the upper ocean through its rough surface,” Izv. Atmos. Ocean. Phys. 35, 266-273 (1999).

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

Izv. NANB Phys. Math. (1)

I. L. Katsev, E. P. Zege, A. S. Prikhach. “Image quality characteristics for observation of an object through a stochastic phase surface,” Izv. NANB Phys. Math. 4, 84-89(2000).

J. Geophys. Res. (1)

W. Pierson and L. Moskovitz, “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. (1)

Optika Atmos. Okeana (1)

E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Range of underwater objects vision,” Optika Atmos. Okeana 5, 789-811(1992).

Proc. SPIE (2)

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev, and S. Stewart, “Image transfer through rough sea surface: computer simulations,” Proc. SPIE 6615, 66150I(2007).
[CrossRef]

L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Correcting images of underwater objects distorted by sea surface roughness,” Proc. SPIE 6615, 66150K (2007).
[CrossRef]

Other (8)

V. I. Weber, “New method for observation of underwater objects through rough sea surface,” in Proceedings of III International Conference: Current Problems in Optics of Natural Waters (ONW'2005) (D. S. Rozhdestvensky Optical Society, 2005), pp. 345-348.
[PubMed]

V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov, and N. N. Rybalka, “Correction of image distorted by wavy water surface,” in Proceedings of the IV International Conference: Current Problems in Optics of Natural Waters (ONW'2007) (Institute of Applied Physics, Russian Academy of Sciences, 2007), pp. 91-93.

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

Optika Okeana (Ocean Optics) (in Russian) A. S. Monin, ed. (Nauka, 1983)

L. S. Dolin L. and I. M. Levin, Spravochnik po Teorii Podvodnogo Videniya (Handbook of the Theory of Underwater Vision) (in Russian) (Gidrometeoizdat, 1991).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Imaging through Wavy Sea Surface (Institute of Applied Physics, Russian Academy of Sciences, 2006).

G. D. Gilbert, L. S. Dolin, I. M. Levin, A. G. Luchinin, V. A. Savel'ev and S. Stewart, “Image transfer through rough sea surface,” in Proceedings of the International Conference on Current Problems in Optics of Natural Waters (ONW'2001), I. Levin and G. Gilbert, eds. (D. S. Rozhdestvensky Optical Society, 2001), pp. 24-31.
[PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of an imaging system.

Fig. 2
Fig. 2

Variance of the refraction angle estimate as a function of depth. Numbers near the curves show the near-water wind speed. The water-scattering coefficient is b = 0.1 / m .

Fig. 3
Fig. 3

Same as in Fig. 2. The water-scattering coefficient is b = 0.3 / m .

Fig. 4
Fig. 4

Logarithms of MTF, MTF , and Φ as functions of the spatial frequency. This calculation is carried out for the following parameter values: a water-scattering coefficient of b = 0.1 / m , a variance of surface wave slopes of σ η 2 = 0.0542 according to the data by Cox and Munk for a near-water wind speed V = 10 m / s , and a bottom depth z b = 20 m .

Fig. 5
Fig. 5

Same as in Fig. 4 for b = 0.3 / m .

Tables (1)

Tables Icon

Table 1 Width of MTF and MTF at Levels 0.1 and 0.01

Equations (28)

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P ( t ) = W 0 Σ Ω 2 π m 2 V b b ( z , r ) [ E r ( z , r , t t ) E s ( z , r , t ) d t ] d r d z ,
E s , r ( z , r , t ) = T δ ( t H / c m z / c ) × F s , r ( k 1 , k 1 H + k 2 z / m ) Φ ( k 2 , z ) × exp [ i k 1 · r s f i k 2 · ( r s f r ) + i k 2 · η ( r s f ) q z ] d k 1 d k 2 d r s f ,
F s , r ( k , p ) = ( 2 π ) 4 D s , r ( r , n ) exp ( i k · r i p · n ) d r d n
D s = δ ( r ) δ ( n ) , F s = ( 2 π ) 4 .
D 1 r = δ ( r ) , F 1 t = ( 2 π ) 2 δ ( p ) ,
D 2 r , x = δ ( r ) ( 1 + α n x ) , F 2 r , x = ( 2 π ) 2 [ δ ( p ) + i α δ ( p y ) δ ( p x ) ] ,
D 2 r , y = δ ( r ) ( 1 + α n y ) , F 2 r , y = ( 2 π ) 2 [ δ ( p ) + i α δ ( p x ) δ ( p y ) ] ,
P 1 ¯ = W 0 Σ Ω T 2 b b c 2 π m ( m H + z ) 2 Φ ( 0 , z ) ,
P ˜ 2 x = W 0 Σ Ω T 2 α ( m H ) 2 ( 2 π ) 4 b b c 2 π m × Φ ( k 1 , z ) Φ ( k 2 , z ) exp [ i r · ( k 1 + k 2 ) i k 2 · r s f γ i k 1 · η 0 q z i k 2 · η ( r s f ) q z ] r x , s f d r d r s f d k 1 d k 2 ,
P ˜ 2 x ¯ = W 0 Σ Ω T 2 ( m H + z ) 3 b b c 2 π Φ ( 0 , z ) q z η 0 x ¯ ,
η 0 x ¯ = P ˜ 2 x ¯ P 1 H + z / m α q z .
Δ η 0 x 2 ¯ = ( H + z / m α q z ) 2 ( P ˜ 2 x ¯ + Δ P ˜ 2 x P 1 ¯ + Δ P 1 P ˜ 2 x ¯ P 1 ¯ ) 2 , ¯
Δ η 0 x 2 ¯ = η 0 x ¯ 2 ( ( Δ P ˜ 2 x ) 2 ¯ P 2 ¯ 2 + ( Δ P 1 ) 2 ¯ P 1 ¯ 2 2 ( Δ P ˜ 2 x Δ P 1 ) ¯ P 1 P 2 ¯ ) .
Δ P ˜ 2 x = i q z W 0 Σ Ω T 2 α ( 2 π ) 2 m 3 H 3 b b c 2 ( η · k ) Φ 2 ( k , z ) exp ( i k · r s f γ i k · η 0 q z ) r x , s f d r s f d k .
Δ P 1 = i q z W 0 Σ Ω T 2 α ( 2 π ) 2 m 3 H 3 b b c 2 ( η · k ) Φ 2 ( k , z ) exp ( i k · r s f γ i k · η 0 q z ) r x , s f d r s f d k .
δ η 0 x 2 ¯ = 2 G ξ ( γ k ) [ | k | ( k x 2 + k 2 ) Φ ˜ 3 Φ ˜ k k 2 k x 2 ( Φ ˜ 3 2 Φ ˜ k 2 + Φ ˜ 2 ( Φ ˜ k ) 2 ) ] d k ,
( Δ P 1 ) 2 ¯ P 1 ¯ 2 = ( q z ) 2 ( Φ ˜ ( k , z ) ) 4 k 4 G ξ ( γ k ) d k .
δ η 0 , i 2 ¯ = 0 G ξ ( γ k ) [ 3 | k | 3 Φ ˜ 3 Φ ˜ k + k 4 ( Φ ˜ 3 2 Φ ˜ k 2 + Φ ˜ 2 ( Φ ˜ k ) 2 ) ] k d k .
Φ ˜ ( k , z ) = exp [ b z + ln ( k z / μ + 1 + ( k z / μ ) 2 ) μ b / k ] ,
G ξ ( k ) = β 0 k 4 exp ( 0.74 g 2 k 2 V w 4 ) ,
k 0 = 16.3 exp ( 0.63 V w ) / V w 2 .
Θ = exp ( σ η 2 q 2 z b 2 k 2 / 2 ) ,
Θ = exp ( σ η 2 δ η 0 2 ¯ q 2 z b 2 k 2 / 2 ) .
MTF = Θ ( k , z b ) Φ ( k , z b ) , MTF = Θ ( k , z b ) Φ ( k , z b ) .
Θ = exp ( ( σ 1 , η 2 δ η 0 2 ¯ + σ 2 , n 2 ) q 2 z b 2 k 2 / 2 ) ,
2 ϑ r > 2 z b z μ ( H + z / m ) ,
η 0 x ¯ = P ˜ 2 x ¯ P 1 ¯ H α q z z + Δ z ( Φ ( 0 , z ) 2 γ 2 d z ) z z + Δ z ( Φ ( 0 , z ) 2 γ 3 z d z ) ,
δ η 0 2 ¯ δ η 0 , Σ 2 ¯ = δ η 0 2 ¯ δ η 0 , s h 2 ¯ δ η 0 2 ¯ + δ η 0 , s h 2 ¯ .

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