Abstract

Laser speckle can influence lidar measurements from a diffuse hard target. Atmospheric optical turbulence will also affect the lidar return signal. We present a numerical simulation that models the propagation of a lidar beam and accounts for both reflective speckle and atmospheric turbulence effects. Our simulation is based on implementing a Huygens–Fresnel approximation to laser propagation. A series of phase screens, with the appropriate atmospheric statistical characteristics, are used to simulate the effect of atmospheric turbulence. A single random phase screen is used to simulate scattering of the entire beam from a rough surface. We compare the output of our numerical model with separate CO2 lidar measurements of atmospheric turbulence and reflective speckle. We also compare the output of our model with separate analytical predictions for atmospheric turbulence and reflective speckle. Good agreement was found between the model and the experimental data. Good agreement was also found with analytical predictions. Finally, we present results of a simulation of the combined effects on a finite-aperture lidar system that are qualitatively consistent with previous experimental observations of increasing rms noise with increasing turbulence level.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley-Interscience, New York, 1984).
  2. R. M. Measures, Laser Remote Chemical Analysis (Wiley, New York, 1988).
  3. E. D. Hinkley, ed., Laser Monitoring of the Atmosphere (Springer-Verlag, New York, 1976).
    [CrossRef]
  4. W. B. Grant, R. H. Kagann, W. A. McClenny, “Optical remote measurements of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
    [CrossRef] [PubMed]
  5. W. B. Grant, J. S. Margolis, A. M. Brothers, D. M. Tratt, “CO2 DIAL measurements of water vapor,” Appl. Opt. 26, 3033–3042 (1987).
    [CrossRef] [PubMed]
  6. The reader is encouraged to explore the web site compiled by W. B. Grant on lidar publications at http://w3.osa.org/HOMES/GENERAL/BIBLIO/lidar97.html .
  7. E. R. Murray, J. E. van der Laan, “Remote measurement of ethylene using a CO2 differential-absorption lidar,” Appl. Opt. 17, 814–817 (1978).
    [CrossRef] [PubMed]
  8. W. B. Grant, “He–Ne and cw CO2 laser long-path systems for gas detection,” Appl. Opt. 25, 709–719 (1986).
    [CrossRef] [PubMed]
  9. A. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
    [CrossRef] [PubMed]
  10. R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
    [CrossRef]
  11. S. R. Murty, “Aerosol speckle effects on atmospheric pulsed lidar backscattered signals,” Appl. Opt. 28, 875–878 (1989).
    [CrossRef] [PubMed]
  12. V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill, New York, 1961).
  13. R. R. Beland, “Propagation through atmospheric turbulence,” in The Infrared Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs Series (SPIE, Bellingham, Wash., 1993), pp. 157–232.
  14. R. L. Fante, “Electromagnetic beam propagation in a turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997).
  16. A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 129–170.
    [CrossRef]
  17. T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. 10, 2456–2461 (1971).
    [CrossRef] [PubMed]
  18. G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
    [CrossRef]
  19. D. L. Fried, G. E. Mevers, M. P. Keister, “Measurements of laser beam scintillation in the atmosphere,” J. Opt. Soc. Am. 57, 787–797 (1967).
    [CrossRef]
  20. J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
    [CrossRef]
  21. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.
  22. P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for speckle effects on pulsed CO2 lidar signal returns from remote targets,” Appl. Opt. 23, 1412–1417 (1984).
    [CrossRef]
  23. R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
    [CrossRef]
  24. D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
    [CrossRef]
  25. E. Durieux, L. Fiorani, “Measurement of the lidar signal fluctuation with a shot-per-shot instrument,” Appl. Opt. 37, 7128–7131 (1998).
    [CrossRef]
  26. J. F. Holmes, “Speckle propagation through turbulence: its characteristics and effects,” in Laser Beam Propagation in the Atmosphere, J. C. Leader, ed., Proc. SPIE410, 89–97 (1983).
    [CrossRef]
  27. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
    [CrossRef] [PubMed]
  28. M. J. T. Milton, P. T. Woods, “Pulse averaging methods for a laser remote monitoring system using atmospheric backscatter,” Appl. Opt. 26, 2598–2603 (1987).
    [CrossRef] [PubMed]
  29. E. P. MacKerrow, M. J. Schmitt, D. C. Thompson, “Effect of speckle on lidar pulse-pair ratio statistics,” Appl. Opt. 36, 8650–8669 (1997).
    [CrossRef]
  30. N. Menyuk, D. K. Killinger, C. R. Menyuk, “Error reduction in laser remote sensing: combined effects of cross correlation and signal averaging,” Appl. Opt. 24, 118–131 (1985).
    [CrossRef] [PubMed]
  31. C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
    [CrossRef] [PubMed]
  32. J. M. Martin, S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990).
    [CrossRef]
  33. M. Z. M. Jenu, D. H. O. Bebbingtion, “Intensity scintillation index of finite beam optical propagation in a turbulent atmosphere,” Electron. Lett. 30, 582–583 (1994).
    [CrossRef]
  34. M. Tur, “Numerical solutions for the fourth moment of a finite beam propagating in a random medium,” J. Opt. Soc. Am. A 2, 2161–2170 (1985).
    [CrossRef]
  35. G. Welch, R. Phillips, “Simulation of enhanced backscatter by a phase screen,” J. Opt. Soc. Am. A 7, 578–584 (1990).
    [CrossRef]
  36. D. G. Youmans, G. A. Hart, “Numerical evaluation of the “M” parameter for direct detection ladar,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 176–187 (1998).
    [CrossRef]
  37. H. Fujii, J. Uozumi, T. Asakura, “Computer simulation study of image speckle patterns with relation to object surface profile,” J. Opt. Soc. Am. 66, 1222–1236 (1976).
    [CrossRef]
  38. D. G. Youmans, V. S. R. Gudimetla, “Round-trip turbulence scintillation effects on laser radar: Monte Carlo simulation results for unresolved targets,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 71–83 (1997).
    [CrossRef]
  39. C. A. Davis, “Computer simulation of wave propagation through turbulent media,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1994).
  40. M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).
  41. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  42. D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
    [CrossRef]
  43. J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  44. R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1985), pp. 6-1–6-56.
  45. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  46. S. M. Flatté, C. Bracher, G. Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994).
    [CrossRef]
  47. F. G. Gebhard, “High power laser propagation,” Appl. Opt. 15, 1479–1493 (1976).
    [CrossRef]
  48. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  49. D. L. Walters, “Atmospheric modulation transfer function for desert and mountain locations: r0 measurements,” J. Opt. Soc. Am. 71, 406–409 (1981).
    [CrossRef]
  50. T. Wang, G. R. Ochs, S. F. Clifford, “A saturation-resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
    [CrossRef]
  51. H. T. Yura, “Atmospheric turbulence induced laser beam spread,” Appl. Opt. 10, 2771–2773 (1971).
    [CrossRef] [PubMed]
  52. W. B. Miller, J. C. Ricklin, L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
    [CrossRef]
  53. E. P. MacKerrow, M. J. Schmitt, “Measurement of integrated speckle statistics for CO2 lidar returns from a moving, nonuniform, hard target,” Appl. Opt. 36, 6921–6937 (1997).
    [CrossRef]
  54. J. C. Russ, The Image Processing Handbook (CRC Press, Boca Raton, Fla., 1992).
  55. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

1998

1997

1994

1993

1992

W. B. Grant, R. H. Kagann, W. A. McClenny, “Optical remote measurements of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

1991

1990

1989

1988

1987

1986

1985

1984

1983

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

1981

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

D. L. Walters, “Atmospheric modulation transfer function for desert and mountain locations: r0 measurements,” J. Opt. Soc. Am. 71, 406–409 (1981).
[CrossRef]

1978

1976

1975

R. L. Fante, “Electromagnetic beam propagation in a turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1974

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

1971

1967

1966

1965

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[CrossRef]

Andrews, L. C.

Asakura, T.

Bebbingtion, D. H. O.

M. Z. M. Jenu, D. H. O. Bebbingtion, “Intensity scintillation index of finite beam optical propagation in a turbulent atmosphere,” Electron. Lett. 30, 582–583 (1994).
[CrossRef]

Beland, R. R.

R. R. Beland, “Propagation through atmospheric turbulence,” in The Infrared Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs Series (SPIE, Bellingham, Wash., 1993), pp. 157–232.

Bevington, P. R.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

Bracher, C.

Brothers, A. M.

Chiba, T.

Churnside, J. H.

Clifford, S. F.

Dabas, A.

Davis, C. A.

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

C. A. Davis, “Computer simulation of wave propagation through turbulent media,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1994).

Durieux, E.

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in a turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Fiorani, L.

Flamant, P. H.

Flatté, S. M.

Fried, D. L.

Fujii, H.

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

Gebhard, F. G.

Goodman, J. W.

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.

Grant, W. B.

Gudimetla, V. S. R.

D. G. Youmans, V. S. R. Gudimetla, “Round-trip turbulence scintillation effects on laser radar: Monte Carlo simulation results for unresolved targets,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 71–83 (1997).
[CrossRef]

Hart, G. A.

D. G. Youmans, G. A. Hart, “Numerical evaluation of the “M” parameter for direct detection ladar,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 176–187 (1998).
[CrossRef]

Holmes, J. F.

J. F. Holmes, “Speckle propagation through turbulence: its characteristics and effects,” in Laser Beam Propagation in the Atmosphere, J. C. Leader, ed., Proc. SPIE410, 89–97 (1983).
[CrossRef]

Hufnagel, R. E.

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1985), pp. 6-1–6-56.

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 129–170.
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997).

Jenu, M. Z. M.

M. Z. M. Jenu, D. H. O. Bebbingtion, “Intensity scintillation index of finite beam optical propagation in a turbulent atmosphere,” Electron. Lett. 30, 582–583 (1994).
[CrossRef]

Kagann, R. H.

W. B. Grant, R. H. Kagann, W. A. McClenny, “Optical remote measurements of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

Kavaya, M. J.

Keister, M. P.

Killinger, D. K.

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

Knepp, D. L.

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

MacKerrow, E. P.

E. P. MacKerrow, M. J. Schmitt, “Measurement of integrated speckle statistics for CO2 lidar returns from a moving, nonuniform, hard target,” Appl. Opt. 36, 6921–6937 (1997).
[CrossRef]

E. P. MacKerrow, M. J. Schmitt, D. C. Thompson, “Effect of speckle on lidar pulse-pair ratio statistics,” Appl. Opt. 36, 8650–8669 (1997).
[CrossRef]

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Margolis, J. S.

Martin, J. M.

McClenny, W. A.

W. B. Grant, R. H. Kagann, W. A. McClenny, “Optical remote measurements of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

Measures, R. M.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley-Interscience, New York, 1984).

R. M. Measures, Laser Remote Chemical Analysis (Wiley, New York, 1988).

Menyuk, C. R.

Menyuk, N.

Menzies, R. T.

Mevers, G. E.

Miller, W. B.

Milton, M. J. T.

Murray, E. R.

Murty, S. R.

Nelson, D. H.

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

Ochs, G. R.

Parry, G.

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Petrin, R. R.

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Phillips, R.

Porch, W. M.

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Quick, C. R.

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

Ricklin, J. C.

Robinson, D. K.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

Russ, J. C.

J. C. Russ, The Image Processing Handbook (CRC Press, Boca Raton, Fla., 1992).

Salamitou, P.

Schmitt, M. J.

E. P. MacKerrow, M. J. Schmitt, “Measurement of integrated speckle statistics for CO2 lidar returns from a moving, nonuniform, hard target,” Appl. Opt. 36, 6921–6937 (1997).
[CrossRef]

E. P. MacKerrow, M. J. Schmitt, D. C. Thompson, “Effect of speckle on lidar pulse-pair ratio statistics,” Appl. Opt. 36, 8650–8669 (1997).
[CrossRef]

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Schotland, R. M.

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill, New York, 1961).

Thompson, D. C.

Tiee, J. J.

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

Tratt, D. M.

Tur, M.

Uozumi, J.

van der Laan, J. E.

Walters, D. L.

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

D. L. Walters, “Atmospheric modulation transfer function for desert and mountain locations: r0 measurements,” J. Opt. Soc. Am. 71, 406–409 (1981).
[CrossRef]

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Wang, G. Y.

Wang, T.

Welch, G.

Whitehead, M. C.

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

Woods, P. T.

Youmans, D. G.

D. G. Youmans, V. S. R. Gudimetla, “Round-trip turbulence scintillation effects on laser radar: Monte Carlo simulation results for unresolved targets,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 71–83 (1997).
[CrossRef]

D. G. Youmans, G. A. Hart, “Numerical evaluation of the “M” parameter for direct detection ladar,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 176–187 (1998).
[CrossRef]

Yura, H. T.

Zardecki, A.

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

Appl. Opt.

F. G. Gebhard, “High power laser propagation,” Appl. Opt. 15, 1479–1493 (1976).
[CrossRef]

E. R. Murray, J. E. van der Laan, “Remote measurement of ethylene using a CO2 differential-absorption lidar,” Appl. Opt. 17, 814–817 (1978).
[CrossRef] [PubMed]

P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for speckle effects on pulsed CO2 lidar signal returns from remote targets,” Appl. Opt. 23, 1412–1417 (1984).
[CrossRef]

N. Menyuk, D. K. Killinger, C. R. Menyuk, “Error reduction in laser remote sensing: combined effects of cross correlation and signal averaging,” Appl. Opt. 24, 118–131 (1985).
[CrossRef] [PubMed]

W. B. Grant, “He–Ne and cw CO2 laser long-path systems for gas detection,” Appl. Opt. 25, 709–719 (1986).
[CrossRef] [PubMed]

M. J. T. Milton, P. T. Woods, “Pulse averaging methods for a laser remote monitoring system using atmospheric backscatter,” Appl. Opt. 26, 2598–2603 (1987).
[CrossRef] [PubMed]

W. B. Grant, J. S. Margolis, A. M. Brothers, D. M. Tratt, “CO2 DIAL measurements of water vapor,” Appl. Opt. 26, 3033–3042 (1987).
[CrossRef] [PubMed]

S. R. Murty, “Aerosol speckle effects on atmospheric pulsed lidar backscattered signals,” Appl. Opt. 28, 875–878 (1989).
[CrossRef] [PubMed]

J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
[CrossRef] [PubMed]

A. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
[CrossRef] [PubMed]

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

E. P. MacKerrow, M. J. Schmitt, “Measurement of integrated speckle statistics for CO2 lidar returns from a moving, nonuniform, hard target,” Appl. Opt. 36, 6921–6937 (1997).
[CrossRef]

E. Durieux, L. Fiorani, “Measurement of the lidar signal fluctuation with a shot-per-shot instrument,” Appl. Opt. 37, 7128–7131 (1998).
[CrossRef]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
[CrossRef] [PubMed]

E. P. MacKerrow, M. J. Schmitt, D. C. Thompson, “Effect of speckle on lidar pulse-pair ratio statistics,” Appl. Opt. 36, 8650–8669 (1997).
[CrossRef]

T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. 10, 2456–2461 (1971).
[CrossRef] [PubMed]

H. T. Yura, “Atmospheric turbulence induced laser beam spread,” Appl. Opt. 10, 2771–2773 (1971).
[CrossRef] [PubMed]

Electron. Lett.

M. Z. M. Jenu, D. H. O. Bebbingtion, “Intensity scintillation index of finite beam optical propagation in a turbulent atmosphere,” Electron. Lett. 30, 582–583 (1994).
[CrossRef]

J. Air Waste Manage. Assoc.

W. B. Grant, R. H. Kagann, W. A. McClenny, “Optical remote measurements of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

J. Appl. Meteorol.

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Proc. IEEE

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in a turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

Other

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1985), pp. 6-1–6-56.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

D. G. Youmans, G. A. Hart, “Numerical evaluation of the “M” parameter for direct detection ladar,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 176–187 (1998).
[CrossRef]

J. C. Russ, The Image Processing Handbook (CRC Press, Boca Raton, Fla., 1992).

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997).

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 129–170.
[CrossRef]

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley-Interscience, New York, 1984).

R. M. Measures, Laser Remote Chemical Analysis (Wiley, New York, 1988).

E. D. Hinkley, ed., Laser Monitoring of the Atmosphere (Springer-Verlag, New York, 1976).
[CrossRef]

The reader is encouraged to explore the web site compiled by W. B. Grant on lidar publications at http://w3.osa.org/HOMES/GENERAL/BIBLIO/lidar97.html .

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill, New York, 1961).

R. R. Beland, “Propagation through atmospheric turbulence,” in The Infrared Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs Series (SPIE, Bellingham, Wash., 1993), pp. 157–232.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.

R. R. Petrin, D. H. Nelson, M. J. Schmitt, C. R. Quick, J. J. Tiee, M. C. Whitehead, “Atmospheric effects on CO2 differential absorption lidar sensitivity,” in Gas and Chemical Lasers, R. Sze, ed., Proc. SPIE2702, 28–39 (1996).
[CrossRef]

D. H. Nelson, R. R. Petrin, E. P. MacKerrow, M. J. Schmitt, C. R. Quick, A. Zardecki, W. M. Porch, M. C. Whitehead, D. L. Walters, “Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 differential absorption LIDAR (DIAL),” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 147–158 (1998).
[CrossRef]

J. F. Holmes, “Speckle propagation through turbulence: its characteristics and effects,” in Laser Beam Propagation in the Atmosphere, J. C. Leader, ed., Proc. SPIE410, 89–97 (1983).
[CrossRef]

D. G. Youmans, V. S. R. Gudimetla, “Round-trip turbulence scintillation effects on laser radar: Monte Carlo simulation results for unresolved targets,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 71–83 (1997).
[CrossRef]

C. A. Davis, “Computer simulation of wave propagation through turbulent media,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1994).

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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 (14)

Fig. 1
Fig. 1

Propagation scheme of lidar highlighting effects of the atmosphere and the target on the return signal.

Fig. 2
Fig. 2

(a) Phase screen for a 200-m step, turbulence level C n 2 = 10-14 m-2/3, and wavelength 10.6 µm. Each pixel in the array is square and is 0.0046 m wide. Considering the phase for each of the 512 × 512 (262,144) pixels, the phase ranges from -1.0671 to 0.9490 rad. The mean phase is zero radians with a standard deviation of 0.3402 rad. (b) Slice of the phase screen indicated by the white line in (a).

Fig. 3
Fig. 3

Computer images of a 10.6-µm Gaussian beam intensity on target. Propagation distance is 7300 m and the diffraction-limited beam divergence is 0.290 mrad. Axis values are in meters. The simulation used 10 propagation steps of 730 m each with a 512 × 512 array: (a) with zero turbulence and (b) a uniform turbulence level of C n 2 = 10-14 m-2/3. The modeled beam path is horizontal and ∼3 m above the ground.

Fig. 4
Fig. 4

Comparison of experimental and simulation data of the beam-profiling experiment with analytical theory. Beam profile measurements of CO2 lidar were for a propagation path of 3300 m. Measurements were taken by scanning the beam across a pole and determining the best-fit Gaussian profile. In the simulation, a total of 100 pulses were summed to obtain the long-term beam-spreading effect. Columns of pixels in the resulting pattern were then summed to mimic the effect of scanning a pole, resulting in a one-dimensional profile. A best-fit Gaussian to this resulting profile was determined to obtain the beam size. Laser 0 and laser 1 are the designations used for the two lasers in our system. The simulation used five propagation steps and a 512 × 512 array. The beam divergence was normalized by its diffraction-limited value. LANL, Los Alamos National Laboratory.

Fig. 5
Fig. 5

Scintillation of a 10.6-µm lidar beam for a point (one pixel) detector after a 2-km propagation through different levels of optical turbulence. The error bars are estimated from the 100 samples in each simulation.

Fig. 6
Fig. 6

Off-axis variation of scintillation as a function of radius from the center of a 10.6-µm Gaussian beam. The beam had an angular divergence of 500 µrad and propagated 1 km through a turbulence level of C n 2 = 10-13 m-2/3. The error bars are estimated from the 100 samples in the simulation.

Fig. 7
Fig. 7

Transverse coherence length of a 10.6-µm Gaussian beam after a propagation of 1 km for different amounts of optical turbulence. The beam had a 500-µrad angular divergence. Simulation values were obtained from the long-term atmospheric modulation transfer function and are compared with the analytical theory for plane wave, spherical wave, and Gaussian beam. The error bars are estimated from the resolution of the simulation grid.

Fig. 8
Fig. 8

Simulated reflective speckle pattern at the receiver for the case shown in Fig. 3(a) except that the beam divergence has been changed to 0.160 mrad. This smaller beam divergence provides for a better illustration with a larger speckle correlation diameter.

Fig. 9
Fig. 9

Comparison of simulated speckle correlation diameter in zero turbulence with that predicted by theory as a function of beam diameter on target. A single-pulse simulation was used with five propagation steps on a 512 × 512 array. The 1/e value of the normalized autocovariance rendered the speckle correlation diameter. The simulated value errors bars represent one pixel width which is the resolution of the simulation. The analytical values are given by Eq. (20). Propagation range is 1000 m and the lidar wavelength is 10.6 µm.

Fig. 10
Fig. 10

Probability density function for measuring a speckled lidar return of intensity I, relation (22). M is approximately the number of speckle integrated by the receiver aperture on an average pulse. For M > 10 this function approaches a Gaussian pdf.

Fig. 11
Fig. 11

(a) Simulated pdf for a receiver of radius ∼1.4 cm with independent speckle realizations and zero turbulence (C n 2 = 0). The diffraction-limited diameter of the beam on target ∼0.20 m and z = 1000 m. The inverted triangles represent the distribution of simulated received intensity for 1000 pulses. The solid curve represents the best-fit Gamma distribution. This figure compares favorably with the M = 1 curve in Fig. 10. The simulation used five propagation steps on a 512 × 512 array. (b) Same simulation parameters as (a) except the receiver radius is ∼2.3 cm. Note the similarity with the M = 2 curve in Fig. 10. (c) Same simulation parameters as (a) and (b) except the receiver radius is ∼18.2 cm. The transition to a more Gaussian shape is apparent as with the M = 10 curve in Fig. 10.

Fig. 12
Fig. 12

Comparison of fitted values of M, M fit versus ratio of the aperture area to the estimated correlation area from simulation and theory. The theoretical plots of M, M circ-Gauss are those predicted for Gaussian target illumination with a circular receiver aperture. S M is the area of the receiver aperture and S C is the average area of a speckle. We simulated 1000 pulses for a transmitter to a target distance of 1000 m. Five propagation steps on a 512 × 512 array were used. The beam diameter on target ∼0.20 m. Curve fits were performed to determine the simulated M factor M fit. The data points represent receiver apertures of different radii.

Fig. 13
Fig. 13

Comparison of signal-to-noise ratio versus fitted M values, M fit, from simulation and theory for the same data as shown in Fig. 12.

Fig. 14
Fig. 14

(a) Shown are rms intensity fluctuations for a 0.075-m diameter, 10.6-µm Gaussian lidar beam scattered from a diffuse target for two-way propagation along a 1-km propagation path for different amounts of optical turbulence. The beam had a 500-µrad divergence. The error bars are estimated from the 100 samples in each simulation. (b) Same as (a) except the propagation path is 2 km and the angular divergence is 200 µrad.

Tables (1)

Tables Icon

Table 1 Sample M fit Parameters for Different Receiver Aperture Sizes

Equations (38)

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

Ui=WiπL2 fTi, Ri, Qi exp-2Calαi,
Erˆ, z=-iλ A Eρˆ, zexpikz2+|rˆ-ρˆ|21/2z2+|rˆ-ρˆ|21/2dA.
Erˆ, zIFTexp-iπλz|fˆ|2FTEρˆ, 0,
Eρˆ, Δz=IFTexp-iπλΔz|fˆ|2FTEρˆ, 0expiθρˆ,
θρˆ=0.0984k0Cn2zΔzNδx5/6×FTnx2+ny2-11/6Θ0nx, ny,
σI¯2Δz<0.1σI¯2L.
σI¯2Δz<0.1.
σI¯=exp4σχ2-11/2,
σχ2=0.124Cn2k07/6L11/6,
Enx, nyreflected=Enx, nytarget×expi2π randomnx, ny,
D2=8αd2+αt2,
αt=λLπρ0,
ρ0-plane=1.46k020L Cn2zdz-3/5,
ρ0-spherical=1.46k020L Cn2zzL5/3dz-3/5,
ρ0-Gaussian=ρ0-plane1-Lfl2+4L2k02Dx41+13Dxρ0-plane21-133Lfl+113Lfl2+4L23k02Dx41+14Dxρ0-plane21/2,
σχ2=0.0675Cn2k07/6L11/6,
MTFatmosphere=exp-3.44rˆr05/3,
RIx1, y1; x2, y2=Ix1, y1I*x2, y2,
RIΔx, Δy=I21+exp-π2wT2λ2z2Δx2+Δy2,
dc=2λLπwT,
CIN=I1-II2-IσI2.
pI0I01ΓMMIMI0M-1 exp-M I0I,if I0>00,otherwise
signalnoisermsI0σI0=Mexact1/2,
signalnoisermsM1/2,
Mcirc-Gauss=π1601dyy cos-1y-y21-y2×exp-4SMSCy2-1,
SC=π dC22=λ2z2πwT2.
χ2=j=1nbinhxj-NtotPxj2σjh2.
χν2=χ2νf,
Mexact=signalnoiserms2,
Erˆ, z=-iλA Eρˆ, zexpikz2+|rˆ-ρˆ|21/2z2+|rˆ-ρˆ|21/2dA.
Erˆ, z-iλz  Eρˆ, 0×expi2πzλ1+rˆ-ρˆz21/2dρˆ.
Erˆ, z-iλzexpi2πzλ  Eρˆ, 0×expiπλz|rˆ-ρˆ|2dρˆ.
Eρˆ, 0= dfˆ exp2πi fˆρˆ  dρˆ×exp-2πifˆρˆEρˆ, 0.
Erˆ, z- iλz   dfˆ exp2πifˆρˆ dρˆ×exp-2πifˆρˆEρˆ, 0expiπλz|rˆ-ρˆ|2dρˆ.
Erˆ, ziλz  dfˆ exp2πifˆrˆ dρˆ×exp-2πifˆρˆEρˆ, 0× drˆ exp-2πifˆrˆexpiπλz|rˆ|2.
 drˆ exp-2πifˆrˆexpiπλz|rˆ|2=iλz exp-iπλz|fˆ|2.
Erˆ, z dfˆ exp2πifˆrˆ×exp-iπλz|fˆ|2  dρˆEρˆ, 0exp-2πifˆρˆ.
Erˆ, zIFTexp-iπλz|fˆ|2FTEρˆ, 0,

Metrics