Abstract

We investigate the signal-to-noise ratio (SNR) for a bistatic coherent laser radar (CLR) system. With a bistatic configuration, the spatial resolution is determined by the overlap of the transmit beam and the virtual backpropagated local oscillator beam. This eliminates the trade-off between range resolution and the bandwidth of the transmitted pulse inherent in monostatic systems. The presented analysis is completely general in that the expressions can be applied to both monostatic and bistatic CLR systems. The heterodyne SNR is computed under the assumption of untruncated Gaussian optics and untruncated Gaussian beam profiles. The analysis also includes the effects of refractive turbulence. The results show that, for maximum SNR, small transmit and local oscillator beam profiles (e -1 intensity radius) are desired.

© 2002 Optical Society of America

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  1. J. G. Hawley, R. Targ, S. W. Henderson, C. P. Hale, M. J. Kavaya, D. Moerder, “Coherent launch-site atmospheric wind sounder: theory and experiment,” Appl. Opt. 32, 4557–4568 (1993).
    [CrossRef] [PubMed]
  2. S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
    [CrossRef]
  3. A. V. Jelalian, Laser Radar Systems (Artech House, Norwood, Mass., 1992).
  4. M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
    [CrossRef]
  5. R. M. Huffaker, “Laser Doppler detection systems for gas velocity measurement,” Appl. Opt. 9, 1026–1039 (1970).
    [CrossRef] [PubMed]
  6. E. P. Magee, “Performance analysis of a multistatic coherent Doppler lidar,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1998).
  7. B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
    [CrossRef] [PubMed]
  8. T. J. Kane, W. J. Kozlovsky, R. L. Byer, C. E. Byvik, “Coherent laser radar at 1.06 µm using Nd:YAG lasers,” Opt. Lett. 12, 239–241 (1987).
    [CrossRef] [PubMed]
  9. R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
    [CrossRef]
  10. R. G. Frehlich, “Conditions for optimal performance of monostatic coherent laser radar,” Opt. Lett. 15, 643–645 (1990).
    [CrossRef] [PubMed]
  11. S. W. Henderson, C. P. Hale, J. R. Magee, M. J. Kavaya, A. V. Huffaker, “Eye-safe coherent laser radar system at 2.1 µm using Tm,Ho:YAG lasers,” Opt. Lett. 16, 773–775 (1991).
    [CrossRef] [PubMed]
  12. R. Targ, M. J. Kavaya, R. M. Huffaker, R. L. Bowles, “Coherent lidar airborne windshear sensor: performance evaluation,” Appl. Opt. 30, 2013–2026 (1991).
    [CrossRef] [PubMed]
  13. M. J. Kavaya, P. J. M. Suni, “Continuous wave coherent laser radar: calculation of measurement location and volume,” Appl. Opt. 30, 2634–2642 (1991).
    [CrossRef] [PubMed]
  14. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
  15. R. G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
    [CrossRef] [PubMed]
  16. R. G. Frehlich, “Optimal local oscillator field for a monostatic coherent laser radar with a circular aperture,” Appl. Opt. 32, 4569–4577 (1993).
    [CrossRef] [PubMed]
  17. R. G. Frehlich, “Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets,” J. Mod. Opt. 41, 2115–2129 (1994).
    [CrossRef]
  18. M. C. Jackson, “The geometry of bistatic radar systems,” IEE Proc. F 133, 604–612 (1986).
  19. N. J. Willis, Bistatic Radar (Artech House, Boston, Mass., 1991).
  20. M. Fogiel, ed., Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphs, Transforms (Research & Education Association, Piscataway, N.J., 1994).
  21. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966).
    [CrossRef] [PubMed]
  22. B. J. Rye, “Refractive-turbulence contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. 71, 687–691 (1981).
    [CrossRef]
  23. K. P. Chan, D. K. Killinger, N. Sugimoto, “Heterodyne Doppler 1-µm lidar measurement of reduced effective telescope aperture due to atmospheric turbulence,” Appl. Opt. 30, 2617–2627 (1991).
    [CrossRef] [PubMed]
  24. J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
    [CrossRef]
  25. R. G. Frehlich, “Space-time fourth moments of waves propagating in random media,” Radio Sci. 22, 481–490 (1987).
    [CrossRef]
  26. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).
  27. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Dedham, Mass., 1987).
  28. R. G. Frehlich, “Intensity covariance of a point source in a random medium with a Kolmogorov spectrum and an inner scale of turbulence,” J. Opt. Soc. Am. A 4, 360–366 (1987).
    [CrossRef]
  29. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
    [CrossRef]
  30. C. Y. Young, L. C. Andrews, “Effects of a modified spectral model on the spatial coherence of a laser beam,” Waves Random Media 4, 385–397 (1994).
    [CrossRef]
  31. L. C. Andrews, Laser Beam Propagation through Random Media (SPIE, Bellingham, Wash., 1998).
  32. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  33. L. D. Dickson, “Characteristics of a propagating Gaussian beam,” Appl. Opt. 9, 1854–1861 (1970).
    [CrossRef] [PubMed]
  34. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  35. P. Koepke, M. Hess, “Scattering functions of tropospheric aerosols: the effects of nonspherical particles,” Appl. Opt. 27, 2422–2430 (1988).
    [CrossRef] [PubMed]
  36. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, New York, 1984).
  37. W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, Colo., 1979); updated version available at ftp://climate.gsfc.nasa.gov/pub/wiscombe/Single_Scatt/Homogen_Sphere/Exact_Mie/ ).
  38. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef] [PubMed]
  39. E. P. Shettle, R. W. Fenn, “Models for the aerosol of the lower atmosphere and the effects of humidity variations on their optical properties,” Tech. Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  40. E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley, New York, 1976).
  41. K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
    [CrossRef]
  42. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  43. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II: Correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
    [CrossRef]
  44. R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
    [CrossRef]

2001 (1)

1994 (4)

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

R. G. Frehlich, “Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets,” J. Mod. Opt. 41, 2115–2129 (1994).
[CrossRef]

C. Y. Young, L. C. Andrews, “Effects of a modified spectral model on the spatial coherence of a laser beam,” Waves Random Media 4, 385–397 (1994).
[CrossRef]

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
[CrossRef]

1993 (4)

1991 (5)

1990 (1)

1989 (1)

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

1988 (1)

1987 (3)

1986 (2)

M. C. Jackson, “The geometry of bistatic radar systems,” IEE Proc. F 133, 604–612 (1986).

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

1984 (1)

K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
[CrossRef]

1981 (1)

1980 (1)

1979 (2)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
[CrossRef] [PubMed]

1970 (2)

1966 (1)

Andrews, L. C.

C. Y. Young, L. C. Andrews, “Effects of a modified spectral model on the spatial coherence of a laser beam,” Waves Random Media 4, 385–397 (1994).
[CrossRef]

L. C. Andrews, Laser Beam Propagation through Random Media (SPIE, Bellingham, Wash., 1998).

Banakh, V. A.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Dedham, Mass., 1987).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bowles, R. L.

Byer, R. L.

Byvik, C. E.

Chan, K. P.

Clifford, S. F.

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

Codona, J. L.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Constant, G.

Creamer, D. B.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Dickson, L. D.

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosol of the lower atmosphere and the effects of humidity variations on their optical properties,” Tech. Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Flatté, S. M.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Frehlich, R. G.

R. G. Frehlich, “Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets,” J. Mod. Opt. 41, 2115–2129 (1994).
[CrossRef]

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
[CrossRef]

R. G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
[CrossRef] [PubMed]

R. G. Frehlich, “Optimal local oscillator field for a monostatic coherent laser radar with a circular aperture,” Appl. Opt. 32, 4569–4577 (1993).
[CrossRef] [PubMed]

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, “Conditions for optimal performance of monostatic coherent laser radar,” Opt. Lett. 15, 643–645 (1990).
[CrossRef] [PubMed]

R. G. Frehlich, “Space-time fourth moments of waves propagating in random media,” Radio Sci. 22, 481–490 (1987).
[CrossRef]

R. G. Frehlich, “Intensity covariance of a point source in a random medium with a Kolmogorov spectrum and an inner scale of turbulence,” J. Opt. Soc. Am. A 4, 360–366 (1987).
[CrossRef]

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Goodman, J. W.

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

Hale, C. P.

Hardesty, R. M.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II: Correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

Harris, M.

Hawley, J. G.

Henderson, S. W.

Henyey, F. S.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Hess, M.

Huffaker, A. V.

Huffaker, R. M.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jackson, M. C.

M. C. Jackson, “The geometry of bistatic radar systems,” IEE Proc. F 133, 604–612 (1986).

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech House, Norwood, Mass., 1992).

Kaimal, J. C.

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

Kane, T. J.

Kavaya, M. J.

Killinger, D. K.

Koepke, P.

Kozlovsky, W. J.

Lataitis, R. J.

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

Magee, E. P.

E. P. Magee, “Performance analysis of a multistatic coherent Doppler lidar,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1998).

Magee, J. R.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley, New York, 1976).

Measures, R. M.

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

Menzies, R. T.

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

Mironov, V. L.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Dedham, Mass., 1987).

Moerder, D.

Murthy, B. V. K.

K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
[CrossRef]

Parameswaran, K.

K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
[CrossRef]

Rose, K. D.

K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
[CrossRef]

Rye, B. J.

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the aerosol of the lower atmosphere and the effects of humidity variations on their optical properties,” Tech. Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Siegman, A. E.

Strauch, R. G.

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

Sugimoto, N.

Suni, P. J. M.

Targ, R.

Tatarski, V. I.

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Ward, C.

Willis, N. J.

N. J. Willis, Bistatic Radar (Artech House, Boston, Mass., 1991).

Wiscombe, W. J.

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, Colo., 1979); updated version available at ftp://climate.gsfc.nasa.gov/pub/wiscombe/Single_Scatt/Homogen_Sphere/Exact_Mie/ ).

Yadlowsky, M. J.

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
[CrossRef]

Young, C. Y.

C. Y. Young, L. C. Andrews, “Effects of a modified spectral model on the spatial coherence of a laser beam,” Waves Random Media 4, 385–397 (1994).
[CrossRef]

Yura, H. T.

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Appl. Opt. (14)

J. G. Hawley, R. Targ, S. W. Henderson, C. P. Hale, M. J. Kavaya, D. Moerder, “Coherent launch-site atmospheric wind sounder: theory and experiment,” Appl. Opt. 32, 4557–4568 (1993).
[CrossRef] [PubMed]

M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
[CrossRef]

R. M. Huffaker, “Laser Doppler detection systems for gas velocity measurement,” Appl. Opt. 9, 1026–1039 (1970).
[CrossRef] [PubMed]

B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
[CrossRef] [PubMed]

R. Targ, M. J. Kavaya, R. M. Huffaker, R. L. Bowles, “Coherent lidar airborne windshear sensor: performance evaluation,” Appl. Opt. 30, 2013–2026 (1991).
[CrossRef] [PubMed]

M. J. Kavaya, P. J. M. Suni, “Continuous wave coherent laser radar: calculation of measurement location and volume,” Appl. Opt. 30, 2634–2642 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
[CrossRef] [PubMed]

R. G. Frehlich, “Optimal local oscillator field for a monostatic coherent laser radar with a circular aperture,” Appl. Opt. 32, 4569–4577 (1993).
[CrossRef] [PubMed]

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966).
[CrossRef] [PubMed]

K. P. Chan, D. K. Killinger, N. Sugimoto, “Heterodyne Doppler 1-µm lidar measurement of reduced effective telescope aperture due to atmospheric turbulence,” Appl. Opt. 30, 2617–2627 (1991).
[CrossRef] [PubMed]

L. D. Dickson, “Characteristics of a propagating Gaussian beam,” Appl. Opt. 9, 1854–1861 (1970).
[CrossRef] [PubMed]

P. Koepke, M. Hess, “Scattering functions of tropospheric aerosols: the effects of nonspherical particles,” Appl. Opt. 27, 2422–2430 (1988).
[CrossRef] [PubMed]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

IEE Proc. F (1)

M. C. Jackson, “The geometry of bistatic radar systems,” IEE Proc. F 133, 604–612 (1986).

IEEE Trans. Geosci. Remote Sens. (1)

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II: Correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
[CrossRef]

J. Geophys. Res. (1)

K. Parameswaran, K. D. Rose, B. V. K. Murthy, “Aerosol characteristics from bistatic lidar observations,” J. Geophys. Res. 89, 2541–2552 (1984).
[CrossRef]

J. Mod. Opt. (1)

R. G. Frehlich, “Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets,” J. Mod. Opt. 41, 2115–2129 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (2)

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

S. F. Clifford, J. C. Kaimal, R. J. Lataitis, R. G. Strauch, “Ground-based remote profiling in atmospheric studies: an overview,” Proc. IEEE 82, 313–355 (1994).
[CrossRef]

Radio Sci. (2)

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in a random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

R. G. Frehlich, “Space-time fourth moments of waves propagating in random media,” Radio Sci. 22, 481–490 (1987).
[CrossRef]

Waves Random Media (1)

C. Y. Young, L. C. Andrews, “Effects of a modified spectral model on the spatial coherence of a laser beam,” Waves Random Media 4, 385–397 (1994).
[CrossRef]

Other (14)

L. C. Andrews, Laser Beam Propagation through Random Media (SPIE, Bellingham, Wash., 1998).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Dedham, Mass., 1987).

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

E. P. Shettle, R. W. Fenn, “Models for the aerosol of the lower atmosphere and the effects of humidity variations on their optical properties,” Tech. Rep. AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley, New York, 1976).

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

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, Colo., 1979); updated version available at ftp://climate.gsfc.nasa.gov/pub/wiscombe/Single_Scatt/Homogen_Sphere/Exact_Mie/ ).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

A. V. Jelalian, Laser Radar Systems (Artech House, Norwood, Mass., 1992).

E. P. Magee, “Performance analysis of a multistatic coherent Doppler lidar,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1998).

N. J. Willis, Bistatic Radar (Artech House, Boston, Mass., 1991).

M. Fogiel, ed., Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphs, Transforms (Research & Education Association, Piscataway, N.J., 1994).

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Figures (11)

Fig. 1
Fig. 1

Geometry for a bistatic coherent detection laser radar system.

Fig. 2
Fig. 2

Schematic for a bistatic coherent detection laser radar system. The dotted lines represent the BPLO field.

Fig. 3
Fig. 3

Pulse SNR (s-polarization) plots for various aperture sizes. Refractive turbulence effects are not included. σ R = 100 mm (solid curve); σ R = 50 mm (dotted curve); σ R = 10 mm (dashed curve); σ R = 5 mm (dashed-dotted curve); σ R = 1 mm (dashed-double-dotted curve).

Fig. 4
Fig. 4

Coherent responsivity for various aperture sizes. σ R = 100 mm (solid curve); σ R = 50 mm (dotted curve); σ R = 10 mm (dashed curve); σ R = 5 mm (dashed-dotted curve); σ R = 1 mm (dashed-double-dotted curve). As can be seen, the optimum aperture size is approximately 5 mm.

Fig. 5
Fig. 5

Pulsed SNR (s-polarization) plots for various beam sizes and infinite apertures. Refractive turbulence effects are not included. σ L = 100 mm (solid curve); σ L = 50 mm (dotted curve); σ L = 10 mm (dashed curve); σ L = 5 mm (dashed-dotted curve); σ L = 1 mm (dashed-double-dotted curve). Again, the optimum aperture size is approximately 5 mm.

Fig. 6
Fig. 6

SNR reduction factor for various beam sizes. σ L = 100 mm (solid curve); σ L = 50 mm (dotted curve); σ L = 10 mm (dashed curve); σ L = 5 mm (dashed-dotted curve); σ L = 1 mm (dashed-double-dotted curve).

Fig. 7
Fig. 7

SNR reduction factor for a fixed beam size (σ L = 5 mm) and various turbulence strengths.

Fig. 8
Fig. 8

Monostatic SNR for a pulsed coherent lidar system for various aperture sizes. σ R = 100 mm (solid curve); σ R = 50 mm (dotted curve); σ R = 10 mm (dashed curve); σ R = 5 mm (dashed-dotted curve); σ R = 1 mm (dashed-double-dotted curve).

Fig. 9
Fig. 9

Coherent responsivity for the monostatic case and various aperture sizes. σ R = 100 mm (solid curve); σ R = 50 mm (dotted curve); σ R = 10 mm (dashed curve); σ R = 5 mm (dashed-dotted curve); σ R = 1 mm (dashed-double-dotted curve).

Fig. 10
Fig. 10

Scattering volumes for various beam sizes. σ L = 100 mm (solid curve); σ L = 50 mm (dotted curve); σ L = 10 mm (dashed curve); σ L = 5 mm (dashed-dotted curve); σ L = 1 mm (dashed-double-dotted curve).

Fig. 11
Fig. 11

Effective scattering volume for the monostatic configuration and various aperture sizes. The 1/e pulse width is 250 ns. σ R = 100 mm (solid curve); σ R = 50 mm (dotted curve); σ R = 10 mm (dashed curve); σ R = 5 mm (dashed-dotted curve); σ R = 1 mm (dashed-double-dotted curve).

Tables (1)

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Table 1 System Parameters

Equations (54)

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SNRt=is2tiN2,
xryrzr=cos θS0sin θS010-sin θS0cos θSxpypzp+00RR,
xtytzt=xpypzp+RT.
SNRt=1hνBwPLODDDηQw1ηQw2×MSw1, w2, L, tMLO*w1, w2, Ld2w1d2w2,
MSv1, v2, L, t=ESv1, L, tES*v2, L, t
SNRt=ηQhνBw-RTK2zpPLt-zt/c×βzp, θSCzp, tdzp,
Czp, t=λ2-jTp, zt, t-zt/cjBPLOp, zrd2p
ELu, z, t=PLteLu, z, t, ELOv, z=PLOeLOv, z,
jTp, zt, t=|eTp, zt, t|2, jBPLOp, zr=|eBPLOp, zr|2.
EBPLOv, 0=ηQELO*v, 0WRv,
Γ4p; u1, u2, v1, v2, zt, zr =Gp; u1, ztG*p; u2, zt×Gp; v1, zrG*p; v2, zr.
Γ4=Gp; u1, ztG*p; u2, ztGp; v1, zrG*p; v2, zr,
Gp1; u1, RG*p2; u2, R=k22πR2 ×expik2Rp1-u12-p2-u22 ×exp-120RDu1-u21-zR+p1-p2zR, zdz,
Dx, z=4πk2-1-cosκ · x ×Φnκ, κz=0, zd2κ
0RDu1-u21-z/R, zdz=|u1-u2|ρ0R5/3,
ρ0R=2.91438k20RCn2z1-z/R5/3dz-3/5
eLu, 0, t=1σLπexp-u22σL2-iku22FL,
WTu=exp-u22σT2-iku22FT,
eTu, 0=1σLπexp-u22σTE2-iku22FTE,
1σTE2=1σL2+1σT2,
1FTE=1FL+1FT,
jTxt, yt, zt=σTE2πσL2σBT2ztexpxt2+yt2σBT2zt,
σBT2zt=σTE21-ztFTE2+zt2k2σTE2+2zt2k2ρ02zt.
jBPLOxr, yr, zr=σRE2πσLO2σBR2zrexpxr2+yr2σBR2zr,
σBR2zr=σRE21-zrFRE2+zr2k2σRE2+2zr2k2ρ02zr
TT=σTE2σL2, TR=σRE2σLO2,
jTxp, yp, zp, RT=TTπσBT2zp, RT×exp-xp2+yp2σBT2zp, RT,
jBPLOxp, yp, zp, RR=TRπσBR2xp, zp, RR×exp-xp cos θS+zp sin θS2+yp2σBR2xp, zp, RR,
σBT2zp, RT=σTE21-zp+RTFTE2+zp+RT2k2σTE2+2zp+RT2k2ρ0T2σTE21-RTFTE2+RT2k2σTE2+2RT2k2ρ02RT,
σBR2xp, zp, RR=σRE21--xp sin θS+zp cos θS+RRFRE2+-xp sin θS+zp cos θS+RR2k2σRE2+2-xp sin θS+zp cos θS+RR2k2ρ0R2 σRE21-RRFRE2+RR2k2σRE2+2RR2k2ρ02RR,
Czp, RT, RR=λ2TTTRπσBR02RT+σBT02RRσBR02RR+σBT02RTcos2 θS1/2×exp-zp2sin2 θSσBR02RR+σBT02RTcos2 θS,
CR=λ2TTTRπσBT2R+σBR2R,
PLt=ULτpπexp-t2τp2,
K2zp=KRTKRR, βzp, θS=βRT, θS,
SNRRT, RR, t=ULηQK2RT, RRβRT, θsλ3TTTRπhBwσeff2RT, RR×exp-t-RT/c2τp2×1-RT, RR,
σeff2RT, RR=σBR2RR+σBT2RTτp2c2 sin2 θsσBR2RR+σBT2RTcos2 θs1/2,
εRT, RR=σBR2RR+σBT2RTcos2 θsτp2c2 sin2 θs+σBR2RR+σBT2RTcos2 θs.
SNRRT, RR=PLηQK2RT, RRβRT, θsλ2TTTRhνBw sin θSπσBR2RR+σBT2RT1/2,
β,θS=1k2r1r2i,θSNrdr,
Nzz=N0 exp-zH,
Cn2z=Cn2z=1 mz-4/3,
ρ0RT=2.91438k2Cn2z=1 m0RTzt cos θnt+5-4/31-zt/Rt5/3dzt-3/5,
ρ0RR=2.91438k2Cn2z=1 m×0RRzr cos θnr+5-4/31-zr/Rr5/3dzr-3/5,
SNRρ01σeff2RT, RR,
σˆBR2RRσRE21-RRFRE2+RR2k2σRE2, σˆBT2RTσTE21-RTFTE2+RT2k2σTE2.
FP=SNRρ0SNRρ0=σˆBR2+σˆBT2τp2c2 sin2 θs+σˆBR2+σˆBT2 cos2 θsσBR2+σBT2(τp2c2 sin2 θs+σBR2+σBT2 cos2 θs]1/2
Fcw=σˆBR2+σˆBT2σBR2+σBT21/2.
σeff2=τpc sin θsσBR2+σBT21+Δ1/2,
Δ=σBR2RR+σBT2RTcos2 θsτp2c2 sin2 θs.
σRopt=92RT2+B22k21/4=1.45652RT2+B2k21/4.
σBT2zp, RT=σL2+RT2k2σL2+2RT2k2ρ02RT, σBR2xp, zp, RR=σLO2+RR2k2σLO2+2RR2k2ρ02RR.
σLopt=2RT2+B22k21/4 =0.8412RT2+B2k21/4.
V---exp-xp2+yp2σBT2×exp-zp2 sin2 θSσBR2dxpdypdzp =π3σBRσBT2sin θS.
V=πσBT2cΔt2 =πσBT2cτpln 2,

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