Abstract

A theoretical model for simulation of airborne depth-sounding lidar is presented with the purpose of analyzing the influence from water surface waves on the ability to detect 1-m3 targets placed on the sea bottom. Although water clarity is the main limitation, sea surface waves can significantly affect the detectability. The detection probability for a target at a 9-m depth can be above 90% at 1-m/s wind and below 80% at 6-m/s wind for the same water clarity. The simulation model contains both numerical and analytical components. Simulated data are compared with measured data and give realistic results for bottom depths between 3 and 10 m.

© 2004 Optical Society of America

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  1. J. L. Irish, W. J. Lillycrop, “Scanning laser mapping of the coastal zone: the SHOALS system,” ISPRS J. Photogramm. Remote Sensing 54, 123–129 (1999).
    [Crossref]
  2. M. F. Penny, R. H. Abbot, D. M. Phillips, B. Billard, D. Rees, D. W. Faulkner, D. G. Cartwright, B. Woodcock, G. J. Perry, P. J. Wilsen, T. R. Adams, J. Richards, “Airborne laser hydrography in Australia,” Appl. Opt. 25, 2046–2058 (1986).
    [Crossref] [PubMed]
  3. K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Airborne laser depth sounding: system aspects and performance,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 392–412 (1994).
    [Crossref]
  4. K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
    [Crossref]
  5. H. M. Tulldahl, K. O. Steinvall, “Analytical waveform generation from small objects in lidar bathymetry,” Appl. Opt. 38, 1021–1039 (1999).
    [Crossref]
  6. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).
  7. J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
    [Crossref]
  8. A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
    [Crossref]
  9. G. W. Kattawar, C. N. Adams, “Errors in radiance calculations induced by using scalar rather than Stokes vector theory in a realistic atmosphere-ocean system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 2–12 (1990).
    [Crossref]
  10. G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. II. Polarization characteristics of signals,” Appl. Opt. 37, 1596–1601 (1998).
    [Crossref]
  11. A. P. Vasilkov, Y. A. Goldin, B. A. Gureev, F. E. Hoge, R. N. Swift, C. W. Wright, “Airborne polarized lidar detection of scattering layers in the ocean,” Appl. Opt. 40, 4353–4364 (2001).
    [Crossref]
  12. K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Experimental evaluation of an airborne depth-sounding lidar,” Opt. Eng. 32, 1307–1321 (1993).
    [Crossref]
  13. G. C. Guenther, R. W. L. Thomas, “Prediction and correction of propagation-induced depth measurement biases plus signal attenuation and beam spreading for airborne laser hydrography,” NOAA Tech. Rep. NOS 106, Charting and Geodetic Services Series CGS 2 (National Oceanic and Atmospheric Administration, Rockville, Md., 1984).
  14. G. C. Guenther, “Airborne laser hydrography, system design and performance factors,” NOAA Professional Paper Ser. NOS 1 (National Oceanic and Atmospheric Administration, Rockville, Md., 1985).
  15. G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of the atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
    [Crossref]
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    [Crossref]
  18. J. W. McLean, J. D. Freeman, “Effects of ocean waves on airborne lidar imaging,” Appl. Opt. 35, 3261–3269 (1996).
    [Crossref] [PubMed]
  19. V. J. Feigels, “Lidars for oceanological research: criteria for comparison, main limitations, perspectives,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 473–484 (1992).
    [Crossref]
  20. R. E. Walker, Marine Light Field Statistics (John Wiley & Sons, New York, 1994).
  21. C.-C. Liu, K. L. Carder, R. L. Miller, J. E. Ivey, “Fast and accurate model of underwater scalar irradiance,” Appl. Opt. 41, 4962–4974 (2002).
    [Crossref] [PubMed]
  22. C. Cox, W. Munk, Slopes of the Sea Surface Deduced from Photographs of Sun Glitter (University of California Press, Berkeley, Calif., 1956).
  23. P. Koepke, “Effective reflectance of oceanic whitecaps,” Appl. Opt. 23, 1816–1824 (1984).
    [Crossref] [PubMed]
  24. R. F. Lutomirski, A. P. Ciervo, G. J. Hall, “Moments of multiple scattering,” Appl. Opt. 34, 7125–7136 (1995).
    [Crossref] [PubMed]
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  27. L. B. Stotts, “Closed form expression for optical pulse broadening in multiple-scattering media,” Appl. Opt. 17, 504–505 (1978).
    [Crossref] [PubMed]
  28. H. C. van de Hulst, 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]
  29. J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1994).
    [Crossref]
  30. A. B. Fraser, R. E. Walker, F. C. Jurgens, “Spatial and temporal correlation of underwater sunlight fluctuations in the sea,” IEEE J. Oceanic Eng. OE-5, 195–198 (1980).
    [Crossref]
  31. J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
    [Crossref]
  32. R. F. Lutomirski, “An analytic model for optical beam propagation through the marine boundary layer,” in Ocean Optics V, M. B. White, ed., Proc. SPIE160, 110–122 (1978).
    [Crossref]
  33. L. R. Thebaud, S. J. Gayer, “Calculation of lidar beam spread in stratified media,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE489, 236–246 (1984).
    [Crossref]
  34. R. E. Walker, J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
    [Crossref]
  35. H. M. Tulldahl, B. Knuthammar, K. O. Steinvall, “Shoal detection in laser depth sounding,” Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998, Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).
  36. H. M. Tulldahl, M. Andersson, K. O. Steinvall, “Experimental results of small target detection in airborne laser depth sounding,” presented at the Ocean Optics XV Conference, Monaco, France, 16–20 October 2000, available from the Office of Naval Research, Washington, D.C.
  37. G. C. Guenther, T. J. Eisler, J. L. Riley, S. W. Perez, “Obstruction detection and data decimation for airborne laser hydrography,” in Proceedings of the Canadian Hydrographic Conference (Canadian Hydrographic Service, Halifax, Nova Scotia, 1996).

2002 (1)

2001 (3)

1999 (3)

1998 (3)

1997 (1)

1996 (1)

1995 (1)

1994 (1)

1993 (1)

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Experimental evaluation of an airborne depth-sounding lidar,” Opt. Eng. 32, 1307–1321 (1993).
[Crossref]

1988 (1)

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

1986 (1)

1984 (1)

1980 (1)

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

1979 (1)

A. G. Luchinin, “Influence of wind waves on the characteristics of the light field backscattered by the bottom and the intervening water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 531–534 (1979).

1978 (1)

Abbot, R. H.

Adams, C. N.

G. W. Kattawar, C. N. Adams, “Errors in radiance calculations induced by using scalar rather than Stokes vector theory in a realistic atmosphere-ocean system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 2–12 (1990).
[Crossref]

Adams, T. R.

Andersson, M.

H. M. Tulldahl, M. Andersson, K. O. Steinvall, “Experimental results of small target detection in airborne laser depth sounding,” presented at the Ocean Optics XV Conference, Monaco, France, 16–20 October 2000, available from the Office of Naval Research, Washington, D.C.

Barnard, A.

Billard, B.

Boss, E.

Carder, K. L.

Cartwright, D. G.

Ciervo, A. P.

Cox, C.

C. Cox, W. Munk, Slopes of the Sea Surface Deduced from Photographs of Sun Glitter (University of California Press, Berkeley, Calif., 1956).

Dolin, L. S.

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

Eisler, T. J.

G. C. Guenther, T. J. Eisler, J. L. Riley, S. W. Perez, “Obstruction detection and data decimation for airborne laser hydrography,” in Proceedings of the Canadian Hydrographic Conference (Canadian Hydrographic Service, Halifax, Nova Scotia, 1996).

Ellsén, R.

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

Faulkner, D. W.

Feigels, V. I.

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

Feigels, V. J.

V. J. Feigels, “Lidars for oceanological research: criteria for comparison, main limitations, perspectives,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 473–484 (1992).
[Crossref]

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. OE-5, 195–198 (1980).
[Crossref]

Freeman, J. D.

Gayer, S. J.

L. R. Thebaud, S. J. Gayer, “Calculation of lidar beam spread in stratified media,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE489, 236–246 (1984).
[Crossref]

Gjellan, E.

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

Goldin, Y. A.

Guenther, G. C.

G. C. Guenther, R. W. L. Thomas, “Prediction and correction of propagation-induced depth measurement biases plus signal attenuation and beam spreading for airborne laser hydrography,” NOAA Tech. Rep. NOS 106, Charting and Geodetic Services Series CGS 2 (National Oceanic and Atmospheric Administration, Rockville, Md., 1984).

G. C. Guenther, “Airborne laser hydrography, system design and performance factors,” NOAA Professional Paper Ser. NOS 1 (National Oceanic and Atmospheric Administration, Rockville, Md., 1985).

G. C. Guenther, T. J. Eisler, J. L. Riley, S. W. Perez, “Obstruction detection and data decimation for airborne laser hydrography,” in Proceedings of the Canadian Hydrographic Conference (Canadian Hydrographic Service, Halifax, Nova Scotia, 1996).

Gureev, B. A.

Hall, G. J.

Hoge, F. E.

Irish, J. L.

J. L. Irish, W. J. Lillycrop, “Scanning laser mapping of the coastal zone: the SHOALS system,” ISPRS J. Photogramm. Remote Sensing 54, 123–129 (1999).
[Crossref]

Ishimaru, A.

Ivey, J. E.

Jaruwatanadilok, S.

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. OE-5, 195–198 (1980).
[Crossref]

Karlsson, U. C. M.

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Experimental evaluation of an airborne depth-sounding lidar,” Opt. Eng. 32, 1307–1321 (1993).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Airborne laser depth sounding: system aspects and performance,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 392–412 (1994).
[Crossref]

Katsev, I. L.

Kattawar, G. W.

H. C. van de Hulst, 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]

G. W. Kattawar, C. N. Adams, “Errors in radiance calculations induced by using scalar rather than Stokes vector theory in a realistic atmosphere-ocean system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 2–12 (1990).
[Crossref]

Kirk, J. T. O.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1994).
[Crossref]

Knuthammar, B.

H. M. Tulldahl, B. Knuthammar, K. O. Steinvall, “Shoal detection in laser depth sounding,” Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998, Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Koepke, P.

Kopelevich, O. V.

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

Koppari, K. R.

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Experimental evaluation of an airborne depth-sounding lidar,” Opt. Eng. 32, 1307–1321 (1993).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Airborne laser depth sounding: system aspects and performance,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 392–412 (1994).
[Crossref]

Krekov, G. M.

Krekova, M. M.

Kuga, Y.

Lejdebrink, U.

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

Levin, I. M.

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

Lillycrop, W. J.

J. L. Irish, W. J. Lillycrop, “Scanning laser mapping of the coastal zone: the SHOALS system,” ISPRS J. Photogramm. Remote Sensing 54, 123–129 (1999).
[Crossref]

Liu, C.-C.

Luchinin, A. G.

A. G. Luchinin, “Influence of wind waves on the characteristics of the light field backscattered by the bottom and the intervening water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 531–534 (1979).

Lutomirski, R. F.

R. F. Lutomirski, A. P. Ciervo, G. J. Hall, “Moments of multiple scattering,” Appl. Opt. 34, 7125–7136 (1995).
[Crossref] [PubMed]

R. F. Lutomirski, “An analytic model for optical beam propagation through the marine boundary layer,” in Ocean Optics V, M. B. White, ed., Proc. SPIE160, 110–122 (1978).
[Crossref]

McLean, J. W.

Miller, R. L.

Mobley, C. D.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, San Diego, Calif., 1994).

Munk, W.

C. Cox, W. Munk, Slopes of the Sea Surface Deduced from Photographs of Sun Glitter (University of California Press, Berkeley, Calif., 1956).

Nilsson, M.

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

Penny, M. F.

Perez, S. W.

G. C. Guenther, T. J. Eisler, J. L. Riley, S. W. Perez, “Obstruction detection and data decimation for airborne laser hydrography,” in Proceedings of the Canadian Hydrographic Conference (Canadian Hydrographic Service, Halifax, Nova Scotia, 1996).

Perry, G. J.

Phillips, D. M.

Polonsky, I. N.

Prikhach, A. S.

Rees, D.

Richards, J.

Riley, J. L.

G. C. Guenther, T. J. Eisler, J. L. Riley, S. W. Perez, “Obstruction detection and data decimation for airborne laser hydrography,” in Proceedings of the Canadian Hydrographic Conference (Canadian Hydrographic Service, Halifax, Nova Scotia, 1996).

Shamanaev, V. S.

Steinvall, K. O.

H. M. Tulldahl, K. O. Steinvall, “Analytical waveform generation from small objects in lidar bathymetry,” Appl. Opt. 38, 1021–1039 (1999).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Experimental evaluation of an airborne depth-sounding lidar,” Opt. Eng. 32, 1307–1321 (1993).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. C. M. Karlsson, “Airborne laser depth sounding: system aspects and performance,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 392–412 (1994).
[Crossref]

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

H. M. Tulldahl, M. Andersson, K. O. Steinvall, “Experimental results of small target detection in airborne laser depth sounding,” presented at the Ocean Optics XV Conference, Monaco, France, 16–20 October 2000, available from the Office of Naval Research, Washington, D.C.

H. M. Tulldahl, B. Knuthammar, K. O. Steinvall, “Shoal detection in laser depth sounding,” Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998, Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Stotts, L. B.

Swift, R. N.

Thebaud, L. R.

L. R. Thebaud, S. J. Gayer, “Calculation of lidar beam spread in stratified media,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE489, 236–246 (1984).
[Crossref]

Thomas, R. W. L.

G. C. Guenther, R. W. L. Thomas, “Prediction and correction of propagation-induced depth measurement biases plus signal attenuation and beam spreading for airborne laser hydrography,” NOAA Tech. Rep. NOS 106, Charting and Geodetic Services Series CGS 2 (National Oceanic and Atmospheric Administration, Rockville, Md., 1984).

Tulldahl, H. M.

H. M. Tulldahl, K. O. Steinvall, “Analytical waveform generation from small objects in lidar bathymetry,” Appl. Opt. 38, 1021–1039 (1999).
[Crossref]

H. M. Tulldahl, M. Andersson, K. O. Steinvall, “Experimental results of small target detection in airborne laser depth sounding,” presented at the Ocean Optics XV Conference, Monaco, France, 16–20 October 2000, available from the Office of Naval Research, Washington, D.C.

H. M. Tulldahl, B. Knuthammar, K. O. Steinvall, “Shoal detection in laser depth sounding,” Ocean Optics XIV Conference, Kailua-Kona, Hawaii, 10–13 November 1998, Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

van de Hulst, H. C.

Vasilkov, A. P.

Walker, R. E.

R. E. Walker, J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
[Crossref]

J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
[Crossref]

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

R. E. Walker, Marine Light Field Statistics (John Wiley & Sons, New York, 1994).

Wilsen, P. J.

Winell, J.

K. O. Steinvall, K. R. Koppari, U. Lejdebrink, J. Winell, M. Nilsson, R. Ellsén, E. Gjellan, “Depth-sounding lidar: performance and models,” in Laser Radar Technology and Applications, G. W. Kamerman, ed., Proc. SPIE2748, 18–38 (1996).
[Crossref]

Woodcock, B.

Wright, C. W.

Zaneveld, J. R. V.

Zege, E. P.

Appl. Opt. (15)

M. F. Penny, R. H. Abbot, D. M. Phillips, B. Billard, D. Rees, D. W. Faulkner, D. G. Cartwright, B. Woodcock, G. J. Perry, P. J. Wilsen, T. R. Adams, J. Richards, “Airborne laser hydrography in Australia,” Appl. Opt. 25, 2046–2058 (1986).
[Crossref] [PubMed]

H. M. Tulldahl, K. O. Steinvall, “Analytical waveform generation from small objects in lidar bathymetry,” Appl. Opt. 38, 1021–1039 (1999).
[Crossref]

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. II. Polarization characteristics of signals,” Appl. Opt. 37, 1596–1601 (1998).
[Crossref]

A. P. Vasilkov, Y. A. Goldin, B. A. Gureev, F. E. Hoge, R. N. Swift, C. W. Wright, “Airborne polarized lidar detection of scattering layers in the ocean,” Appl. Opt. 40, 4353–4364 (2001).
[Crossref]

J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
[Crossref]

A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
[Crossref]

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of the atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
[Crossref]

J. W. McLean, J. D. Freeman, “Effects of ocean waves on airborne lidar imaging,” Appl. Opt. 35, 3261–3269 (1996).
[Crossref] [PubMed]

C.-C. Liu, K. L. Carder, R. L. Miller, J. E. Ivey, “Fast and accurate model of underwater scalar irradiance,” Appl. Opt. 41, 4962–4974 (2002).
[Crossref] [PubMed]

P. Koepke, “Effective reflectance of oceanic whitecaps,” Appl. Opt. 23, 1816–1824 (1984).
[Crossref] [PubMed]

R. F. Lutomirski, A. P. Ciervo, G. J. Hall, “Moments of multiple scattering,” Appl. Opt. 34, 7125–7136 (1995).
[Crossref] [PubMed]

L. B. Stotts, “Closed form expression for optical pulse broadening in multiple-scattering media,” Appl. Opt. 17, 504–505 (1978).
[Crossref] [PubMed]

H. C. van de Hulst, 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]

J. R. V. Zaneveld, E. Boss, A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001).
[Crossref]

R. E. Walker, J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
[Crossref]

IEEE J. Oceanic Eng. (1)

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Figures (27)

Fig. 1
Fig. 1

Schematic illustration of the depth-sounding lidar system and the (x 0, y 0, z 0) coordinate system. The coordinate system is right oriented, with its origin in the hit on the mean water surface level of the optical axis of the collocated, collinear transmitter and receiver. The laser inclination angle θ0 is always in the x 0-z 0 plane.

Fig. 2
Fig. 2

Part of the gravity-wave surface model and its associated coordinate system (x 1, y 1, z 1). (a) The center of each triangular wave facet (x c , y c , z c ) (marked by a dot in one triangle) is at one third of the distance G s along the y 1 axis from the triangle base. The triangle vertices have constant (x 1, y 1) coordinates, and their z 1 coordinates are assigned values for each surface realization. (b) The (x 2, y 2, z 2) coordinate system is shown, which has its x 2-y 2 plane in the plane of the gravity-wave facet.

Fig. 3
Fig. 3

Lower hemisphere of the (x 2, y 2, z 2) coordinate system partitioned into quads. There are 39 quads and a polar cap in the θ2 direction, and 96 quads in the ϕ2 direction.

Fig. 4
Fig. 4

Simulation of capillary wave reflectances for point sources and upwind (ϕ2 = 0) rays. Simulation with 3000 rays for each wind speed and ray direction.

Fig. 5
Fig. 5

Monte Carlo simulations of a collimated laser beam transmitted through an air-water interface covered with capillary waves. Standard deviation σCap of beam directional distribution versus angle of incidence after air-incident transmission through the capillary wave surface. Simulations are implemented with the algorithms described by Mobley.6

Fig. 6
Fig. 6

(x 3, y 3, z 3) coordinate system used for definition of the in-water propagation model. The coordinate system origin is in the center of the triangular gravity-wave facet. The z 3 axis is along the mean direction 〈 t 〉 of the transmitted beam. The downward normal to the gravity-wave facet is denoted G and the vertical downward normal in .

Fig. 7
Fig. 7

Part of the triangular bottom grid model and its associated coordinate system (x 4, y 4, z 4). The bottom grid side is denoted G b . A cube target is modeled as an elevation of grid facets above the bottom.

Fig. 8
Fig. 8

Geometry for calculation of the in-water beam propagation, where 〈 t [k]〉 is the mean beam direction from surface facet k, variable r w [i, k] is the vector from the center of surface facet k to the center of bottom facet i, and is the downward normal to the bottom facet i. Variable r a [k] is the vector from the sensor to surface facet k. Depth z 0 = D is the vertical depth from the mean water surface.

Fig. 9
Fig. 9

Simulated downwelling attenuation coefficient d as a function of depth for vertically incident light and water types according to Table 2. Values are calculated for a flat water surface (0-m/s wind) and compared with numerical simulations of K d (z m ) by Kirk.29 The triangle symbols for Kirk data are placed at depth z m at which the irradiance has been reduced to 10% of the subsurface value.

Fig. 10
Fig. 10

Simulation of horizontal plane irradiance profiles at different vertical depths below the sea surface for a flat sea surface (0-m/s wind). The figure illustrates the McLean et al.7 analytical beam spread function. Parameter values are σ s = 0.5 m, θ0 = 0, and the water type is clear.

Fig. 11
Fig. 11

Examples of simulated horizontal irradiance profiles at depths of 1, 5, and 10 m for wind speeds of 0 m/s (solid curves) and 6 m/s (pluses). Each value is presented relative to the maximum value within each beam. For a 6-m/s wind speed, data from fifteen simulated profiles are shown. The wind direction is parallel to the lidar plane of incidence. Parameter values are σ s = 1 m, θ0 = 20, and the water type is clear.

Fig. 12
Fig. 12

Estimated mean beam center position b as a function of vertical depth for three water types. The lidar optical axis hit on the water surface is at x 4 = 0; see Fig. 7. Both the wind direction and the lidar inclination angle are parallel to the x 4 axis, and the thin dashed curve represents the lidar optical axis in the water for a flat water surface. Parameter values are σ s = 1 m, θ0 = 20, and the water type is clear. The same result was obtained for all the simulated wind speeds of 0, 3, 6, and 9 m/s.

Fig. 13
Fig. 13

Estimated upwind mean beam diameter 2σ̅ xb as a function of vertical depth for three water types. Lidar parameters are the same as in Fig. 12. The same results were obtained for all the simulated wind speeds of 0, 3, 6, and 9 m/s.

Fig. 14
Fig. 14

Estimated upwind standard deviations for beam center position and beam diameter for (a), (d) clear; (b), (e) average; (c), (f) turbid water types. Lidar parameters are the same as in Fig. 12. Results for 3, 6, and 9 m/s are shown.

Fig. 15
Fig. 15

Transmitter and receiver (inverse transmitter) beam paths for volume-backscatter calculation.

Fig. 16
Fig. 16

Simulated waveforms of the volume-backscattered power for clear and average coastal water types and FOV diameters of 3 and 9 m at the water surface. Sensor altitude H = 300 m, θ0 = 0, and beam radius on surface σ s = 0.15 m.

Fig. 17
Fig. 17

Effect of the receiver FOV on the lidar attenuation coefficient. Our calculations for nonconservative (circles) and conservative scattering (pluses) are compared with measurements by Steinvall et al.3 (mean and standard deviation) and to theoretical values from Walker and McLean.34 The lidar attenuation coefficient was averaged over the depth range z 0 = 3–5 m. The water optical properties used for simulations are a = 0.3 m-1 and b = 0.7 m-1, consistent with measured values. Sensor altitude H = 300 m, θ0 = 20°, and a narrow beam radius on surface σ s = 0.016 m.

Fig. 18
Fig. 18

Examples of the FOV inner blocking influence on simulated waveforms for a flat bottom at depths of 3, 5, and 9 m. The y axis shows the received optical power in log scale. Waveforms are shown for no inner blocking (0 mrad) and for inner blockings (full angle) of 8 and 12 mrad. The FOV (outer) is 17 mrad. Wind U = 6 m/s, H = 200 m, θ0 = 20°, σ s = 1 m, and receiver channel is PMT slow.

Fig. 19
Fig. 19

Comparison of measured and model waveforms from a flat bottom at 4.5-m depth. The depth axis shows the elapsed time from the mean water surface multiplied by c w /2. A noticeable difference in the surface echo is caused by the limited angular resolution (quad partitioning) of the simulated reflected power; see Subsection 2.A. The different start times of the surface echoes can be explained by different wave elevations on the sounding position. Wind U = 6 m/s, H = 200 m, θ0 = 20°; σ s = 1 m, receiver channel is an APD, and FOV is 15 mrad.

Fig. 20
Fig. 20

Zoom of measured and model waveforms in linear scale from a flat bottom at 4.5-m depth. The depth axis shows the elapsed time from the surface hit multiplied by c w /2. Wind U = 6 m/s, H = 200 m, θ0 = 20°, σ s = 1 m, receiver channel is an APD, and FOV is 15 mrad. Both (a) and (b) show one measured and two simulated waveforms; all six are different waveforms.

Fig. 21
Fig. 21

Comparison of measured and model waveforms from a 1-m3 cube target on a flat bottom at a 5-m depth. Other simulation parameters as in Fig. 20. The exact (x 0, y 0) positions of the target are not known from measurements but are given as intervals. In both (a) and (b) the same measured waveform is shown. All four simulated waveforms are different and are generated from two different target positions within the beam.

Fig. 22
Fig. 22

Simulated waveform from a 1-m3 cube target on a flat bottom at a 5-m depth. Laser pulse width t 0 = 5 ns. Other simulation parameters as in Fig. 20.

Fig. 23
Fig. 23

Definition of the width characteristics of the bottom pulses in the received waveforms.

Fig. 24
Fig. 24

Comparison of bottom pulse widths of measured and model waveforms at vertical depths of 3, 5, and 9 m (25%, 50%, and 75% widths are defined in Fig. 23). Error bars specify standard deviation. Parameters for simulations and measurements: At 3 m, wind is 5 m/s, receiver channel is an APD, and FOV is 15 mrad. At 5 m, wind is 6 m/s, receiver channel is PMT slow, and FOV is 17 mrad. At 9 m, wind is 7 m/s, receiver channel is PMT fast, and FOV is 25 mrad. Other simulation parameters as in Fig. 20.

Fig. 25
Fig. 25

Number of shots per flight passage where the target was detected with double echoes (bold curves) or a combination of double echoes and single echoes (thin curves). Mean and standard deviation of simulated data from 30 flight passages over the target at four different bottom depths and at four wind speeds. Clear water, 5-mJ pulse energy, 5-ns pulse length, and receiver channel is PMT fast. Other simulation parameters as in Fig. 20. The wind direction is parallel to the lidar plane of incidence.

Fig. 26
Fig. 26

Estimated detection probability of the cube target as a function of depth for clear and average water types. Simulation parameters as in Fig. 25.

Fig. 27
Fig. 27

Estimated detection probability of the cube target at 9-m depth as a function of receiver FOV for clear water type, 6-m/s wind, and pulse energies of 5 and 7 mJ. Other simulation parameters as in Fig. 25.

Tables (3)

Tables Icon

Table 1 Parameters for Simulation Unless Otherwise Quantified in Text

Tables Icon

Table 2 Water Optical Properties

Tables Icon

Table 3 Detector Parameters for Comparison with Measured Data

Equations (67)

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P=Pb+Pbsc+Ps+Pbg+Pn,
Pbg=LsAsΔληopt,RxARH/cos θ02,
As=πH2 tan2FOV/2cos2 θ0.
rˆ=sin θ2 cos ϕ2xˆ2+sin θ2 sin ϕ2ŷ2+cos θ2zˆ2.
ta,wθ2, ϕ2, U=1Φq Φtq
ra,wθ2, ϕ2, U=1Φq Φrq,
rˆt=1ta,wΦqrˆtqΦtq,
σCap2θ2, ϕ2, U=1ta,wΦqrˆt-rˆtq2Φtq.
ηu,G=dz1/dx1,
ηc,G=dz1/dy1.
σu,G2=1Mk=1M ηu,G2k,
σc,G2=1Mk=1M ηc,G2k.
σu2=auU,
σc2=acU,
σu,Cap2=σu2-σu,G2,
σc,Cap2=σc2-σc,G2,
Escρ3, z3=Φscz312πσsc2exp-ρ322σsc2,
σsc2=σρ2+z32σCap2+σGrid2,
σρ2z32=43μτz3/cw11+a2cwστ2/μτ,
μτz3/cw=1-1-exp-bz3νbz3ν 14 bz3Θ2-124bz32Θ22+,
στ2z3/cw2=23w2-3wνexp-bz3ν-1+bz3ν+2ν2exp-bz3w-1+bz3wb2z32wν2w-ν-1-exp-bz3νbz3ν2 112 bz3Θ4+124bz32Θ22+,
σGrid2=nˆG·rˆtnˆ·nˆGx1,y1Δ1AGx1-xc2+y1-yc2dx1dy1,
x1,y1Δ1AGx1-xc2+y1-yc2dx1dy1=772 Gs2.
Eunscρ3, z3=Φunscz312πσunsc2exp-ρ322σunsc2,
σunsc2=z32σCap2+σGrid2,
Φscz3=Φt1-exp-bz3exp-az31+a2cwστ2/μτμτ2/στ2,
Φunscz3=Φt exp-bz3exp-az3.
Φsci=k Φsci, k,
Φsci, k=Esci, kGb22rˆtk·nˆi
Φunsc=k Φunsci, k,
Φunsci, k=Eunsci, kGb22rˆtk·nˆi
K¯scz0=-z0lnΦscz0/Φt,sc,
Φt,sc=1-exp-bz0/cos θwk Φtk
Φscz0=i Φsci.
K¯unscz0=-z0lnΦunscz0/Φt,unsc,
Φt,unsc=exp-bz0/cos θwk Φtk
Φunscz0=i Φunsci
K¯dz0=-z0lnΦscz0+Φunscz0/Φt,sc+Φt,unsc.
Kdzm=a2+Gab1/2,
G=-2.401cos θ+2.430
xb=1Θsc+Θunsci x4iΦsci+Φunsci,
σxb=1Θsc+Θunscix4i-xb2×Φsci+Φunsci1/2,
ti, k=|rak|c0+|rwi, k|cw,
hsc,sct=g*g*C1ikl Φsc,Txi, k×Φsc,Rxi, lρiδt-tDi, k, l,
gt=μσ2Γμ2/σ2μσ2μ2/σ2-1 exp-μtσ2,
μ=μτ11+a2cwστ2/μτ,
σ=στ11+a2cwστ2/μτ,
hsc,unsct=g*C2 ,
hunsc,sct=g*C3 ,
hunsc,unsct=C4 .
Pbt=QbWsc,schsc,sct+Wsc,unschsc,unsct +Wunsc,schunsc,sct+Wunsc,unschunsc,unsct.
Qb=ARπnwH/cos θ0+z0/cos θw2 ×E0ηopt,Txηopt,RxTatm21-ra,wU, θ0×1-rw,aU, θwρb.
Wsc,sc=1-exp-bz0/cos θw2×exp-2z0K¯sc,
Wsc,unsc=Wunsc,sc =1-exp-bz0/cos θwexp-bz0/cos θw×exp-z0K¯sc+K¯unsc,
Wunsc,unsc=exp-bz0/cos θw2 exp-2z0K¯unsc,
Pbsct=Qbschbsct,
Qbsc=ARnwH/cos θ02 ×0.5t0cwβπP0ηopt,Txηopt,RxTatm2 ×1-ra,wU, θ01-rw,aU, θw ×0τ=2Dcw cos θwexp-2K¯sc cos θwcwτ2dτ
0τ=2Dcw cos θwexp-2K¯sc cos θwcwτ2dτ=1-exp-2DK¯sccwK¯sc cos θw.
hbsct=C5kl hbsck, l
tsk, l=|rak|+|ral|c0.
hbsck, lt=ΦtkΦtl12πσsc2×exp-rk, l+rˆtk-rˆtl×t-tsk, lcw222σsc2
tbotk, l=tsk, l+|rtk|+|rtl|cw.
Pst=AR cos2 θ0H2l Islδt-tsl,
tsl=2|ral|/c0
Isl=Φrq, lΩq,
P=Pb+Pbsc+Ps+Pbg+Pn=Pext+Pn.
σnt=Pextt2eBFRλ1/2,

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