Abstract

Two continuous-wave (CW) focused CO2 Doppler lidars (9.1 and 10.6 μm) were developed for airborne in situ aerosol backscatter measurements. The complex path of reliably calibrating these systems, with different signal processors, for accurate derivation of atmospheric backscatter coefficients is documented. Lidar calibration for absolute backscatter measurement for both lidars is based on range response over the lidar sample volume, not solely at focus. Both lidars were calibrated with a new technique using well-characterized aerosols as radiometric standard targets and related to conventional hard-target calibration. A digital signal processor (DSP), a surface acoustic wave spectrum analyzer, and manually tuned spectrum analyzer signal analyzers were used. The DSP signals were analyzed with an innovative method of correcting for systematic noise fluctuation; the noise statistics exhibit the chi-square distribution predicted by theory. System parametric studies and detailed calibration improved the accuracy of conversion from the measured signal-to-noise ratio to absolute backscatter. The minimum backscatter sensitivity is ~3 × 10−12 m−1 sr−1 at 9.1 μm and ~9 × 10−12 m−1 sr−1 at 10.6 μm. Sample measurements are shown for a flight over the remote Pacific Ocean in 1990 as part of the NASA Global Backscatter Experiment (GLOBE) survey missions, the first time to our knowledge that 9.1–10.6-μm lidar intercomparisons were made. Measurements at 9.1 μm, a potential wavelength for space-based lidar remote-sensing applications, are to our knowledge the first based on the rare isotope 12C 18O2 gas.

© 1996 Optical Society of America

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    [CrossRef] [PubMed]
  2. D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
    [CrossRef]
  3. J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
    [CrossRef]
  4. R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
    [CrossRef]
  5. W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  12. The mention of brand names in this paper is for information purposes only and does not constitute an endorsement of the product by the authors, their institutions, or sponsors.
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  20. Hereafter, with obvious exceptions, total lidar system efficiency η is referenced to the type of target (HT, SPM, or VM), measurement coverage (at focus F or over the focal volume at different ranges L), and signal analyzer (DSP, SA, or SAW).
  21. M. J. Kavaya, S. W. Henderson, R. G. Frehlich, “Theory of CW lidar aerosol backscatter measurements and development of a 2.1 μm solid-state pulsed laser radar for aerosol backscatter profiling,” NASA Contr. Rep. CR-4347 (NASA, Washington, D.C., 1991).
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  23. M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
    [CrossRef] [PubMed]
  24. V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
    [CrossRef]
  25. D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).
  26. M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
    [CrossRef]

1995

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

M. A. Jarzembski, V. Srivastava, D. M. Chambers, “Lidar calibration technique using laboratory-generated aerosols,” Appl. Opt. 35, 2096–2108 (1995).
[CrossRef]

1991

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 2. Algorithm performance,” J. Geophys. Res. 96, 5299–5305 (1991).
[CrossRef]

1990

1989

1986

1985

1984

1981

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

1971

Alejandro, S. B.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

Anderson, J. R.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Arnold, J. E.

D. A. Bowdle, J. Rothermel, J. E. Arnold, S. F. Williams, “The GLObal backscatter experiment Pacific survey mission: results and implications for LAWS,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 290–292.

Atlas, R. M.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Baker, W. E.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Barrett, E. W.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

Bilbro, J. W.

J. W. Bilbro, C. A. DiMarzio, D. E. Fitzjarrald, S. C. Johnson, W. D. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 3952–3960 (1986).
[CrossRef] [PubMed]

W. D. Jones, L. Z. Kennedy, J. W. Bilbro, H. B. Jeffreys, “Coherent focal volume mapping of a continuous-wave CO2 Doppler lidar,” Appl. Opt. 23, 730–733 (1984).
[CrossRef] [PubMed]

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Bowdle, D. A.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 2. Algorithm performance,” J. Geophys. Res. 96, 5299–5305 (1991).
[CrossRef]

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, M. J. Post, “Evidence of a tropospheric aerosol backscatter background mode,” Appl. Opt. 28, 1040–1042 (1989).
[CrossRef] [PubMed]

J. M. Vaughan, R. D. Callan, D. A. Bowdle, J. Rothermel, “Spectral analysis, digital integration and measurement of low backscatter in coherent laser radar,” Appl. Opt. 28, 3008–3014 (1989).
[CrossRef] [PubMed]

D. A. Bowdle, J. Rothermel, J. E. Arnold, S. F. Williams, “The GLObal backscatter experiment Pacific survey mission: results and implications for LAWS,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 290–292.

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Brown, D. W.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

Brown, R. A.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Callan, R. D.

Chambers, D. M.

M. A. Jarzembski, V. Srivastava, D. M. Chambers, “Lidar calibration technique using laboratory-generated aerosols,” Appl. Opt. 35, 2096–2108 (1995).
[CrossRef]

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

Clarke, A. D.

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Cupp, R. E.

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[CrossRef] [PubMed]

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

Cutten, D. R.

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Derr, V. E.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

DiMarzio, C. A.

J. W. Bilbro, C. A. DiMarzio, D. E. Fitzjarrald, S. C. Johnson, W. D. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 3952–3960 (1986).
[CrossRef] [PubMed]

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Emmitt, G. D.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Fitzjarrald, D. E.

Frehlich, R. G.

M. J. Kavaya, S. W. Henderson, R. G. Frehlich, “Theory of CW lidar aerosol backscatter measurements and development of a 2.1 μm solid-state pulsed laser radar for aerosol backscatter profiling,” NASA Contr. Rep. CR-4347 (NASA, Washington, D.C., 1991).

Gras, J. L.

Hardesty, R. M.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Harris, M.

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

Henderson, S. W.

M. J. Kavaya, S. W. Henderson, R. G. Frehlich, “Theory of CW lidar aerosol backscatter measurements and development of a 2.1 μm solid-state pulsed laser radar for aerosol backscatter profiling,” NASA Contr. Rep. CR-4347 (NASA, Washington, D.C., 1991).

Hill, C. A.

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

Horrigan, F. A.

Jarzembski, M. A.

M. A. Jarzembski, V. Srivastava, D. M. Chambers, “Lidar calibration technique using laboratory-generated aerosols,” Appl. Opt. 35, 2096–2108 (1995).
[CrossRef]

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

Jeffreys, H. B.

W. D. Jones, L. Z. Kennedy, J. W. Bilbro, H. B. Jeffreys, “Coherent focal volume mapping of a continuous-wave CO2 Doppler lidar,” Appl. Opt. 23, 730–733 (1984).
[CrossRef] [PubMed]

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Johnson, S. C.

J. W. Bilbro, C. A. DiMarzio, D. E. Fitzjarrald, S. C. Johnson, W. D. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 3952–3960 (1986).
[CrossRef] [PubMed]

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Jones, W. D.

J. L. Gras, W. D. Jones, “Australian aerosol backscatter survey,” Appl. Opt. 28, 852–856 (1989).
[CrossRef] [PubMed]

J. W. Bilbro, C. A. DiMarzio, D. E. Fitzjarrald, S. C. Johnson, W. D. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 3952–3960 (1986).
[CrossRef] [PubMed]

W. D. Jones, L. Z. Kennedy, J. W. Bilbro, H. B. Jeffreys, “Coherent focal volume mapping of a continuous-wave CO2 Doppler lidar,” Appl. Opt. 23, 730–733 (1984).
[CrossRef] [PubMed]

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

W. D. Jones, L. Z. Kennedy, R. W. Lee, “Determination of atmospheric backscatter at 10.6 μm,” in Coherent Infrared Radar Systems and Applications II, R. C. Harney, ed., Soc. Photo-Opt. Instrum. Eng. 415, 77–84 (1983).

Kavaya, M. J.

M. J. Kavaya, S. W. Henderson, R. G. Frehlich, “Theory of CW lidar aerosol backscatter measurements and development of a 2.1 μm solid-state pulsed laser radar for aerosol backscatter profiling,” NASA Contr. Rep. CR-4347 (NASA, Washington, D.C., 1991).

M. J. Kavaya, “The JPL lidar target calibration facility,” in Third Topical Meeting on Coherent Laser Radar: Technology and Applications (Optical Society of America, Washington, D.C., 1985), p. II.1.

Kennedy, L. Z.

W. D. Jones, L. Z. Kennedy, J. W. Bilbro, H. B. Jeffreys, “Coherent focal volume mapping of a continuous-wave CO2 Doppler lidar,” Appl. Opt. 23, 730–733 (1984).
[CrossRef] [PubMed]

W. D. Jones, L. Z. Kennedy, R. W. Lee, “Determination of atmospheric backscatter at 10.6 μm,” in Coherent Infrared Radar Systems and Applications II, R. C. Harney, ed., Soc. Photo-Opt. Instrum. Eng. 415, 77–84 (1983).

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Koenig, G. G.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

Krishnamurti, T. N.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Lee, R. W.

W. D. Jones, L. Z. Kennedy, R. W. Lee, “Determination of atmospheric backscatter at 10.6 μm,” in Coherent Infrared Radar Systems and Applications II, R. C. Harney, ed., Soc. Photo-Opt. Instrum. Eng. 415, 77–84 (1983).

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

Lorenc, A. C.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

McElroy, J.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Menzies, R. T.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Miller, T. L.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Molinari, J. E.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Nash, C.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

Paegle, J.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Pearson, G. N.

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

Post, M. J.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[CrossRef] [PubMed]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, M. J. Post, “Evidence of a tropospheric aerosol backscatter background mode,” Appl. Opt. 28, 1040–1042 (1989).
[CrossRef] [PubMed]

Pueschel, R. F.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Robertson, P.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Rothermel, J.

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 2. Algorithm performance,” J. Geophys. Res. 96, 5299–5305 (1991).
[CrossRef]

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, M. J. Post, “Evidence of a tropospheric aerosol backscatter background mode,” Appl. Opt. 28, 1040–1042 (1989).
[CrossRef] [PubMed]

J. M. Vaughan, R. D. Callan, D. A. Bowdle, J. Rothermel, “Spectral analysis, digital integration and measurement of low backscatter in coherent laser radar,” Appl. Opt. 28, 3008–3014 (1989).
[CrossRef] [PubMed]

D. A. Bowdle, J. Rothermel, J. E. Arnold, S. F. Williams, “The GLObal backscatter experiment Pacific survey mission: results and implications for LAWS,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 290–292.

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Schwiesow, R. L.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

Shapiro, J. H.

Sinclair, P. C.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962).

Sonnenschein, C. M.

Spinhirne, J. D.

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Srivastava, V.

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

M. A. Jarzembski, V. Srivastava, D. M. Chambers, “Lidar calibration technique using laboratory-generated aerosols,” Appl. Opt. 35, 2096–2108 (1995).
[CrossRef]

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Vaughan, J. M.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 2. Algorithm performance,” J. Geophys. Res. 96, 5299–5305 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

J. M. Vaughan, R. D. Callan, D. A. Bowdle, J. Rothermel, “Spectral analysis, digital integration and measurement of low backscatter in coherent laser radar,” Appl. Opt. 28, 3008–3014 (1989).
[CrossRef] [PubMed]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, M. J. Post, “Evidence of a tropospheric aerosol backscatter background mode,” Appl. Opt. 28, 1040–1042 (1989).
[CrossRef] [PubMed]

Williams, S. F.

D. A. Bowdle, J. Rothermel, J. E. Arnold, S. F. Williams, “The GLObal backscatter experiment Pacific survey mission: results and implications for LAWS,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 290–292.

Woodfield, A. A.

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

Appl. Opt.

W. D. Jones, L. Z. Kennedy, J. W. Bilbro, H. B. Jeffreys, “Coherent focal volume mapping of a continuous-wave CO2 Doppler lidar,” Appl. Opt. 23, 730–733 (1984).
[CrossRef] [PubMed]

J. W. Bilbro, C. A. DiMarzio, D. E. Fitzjarrald, S. C. Johnson, W. D. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 3952–3960 (1986).
[CrossRef] [PubMed]

J. L. Gras, W. D. Jones, “Australian aerosol backscatter survey,” Appl. Opt. 28, 852–856 (1989).
[CrossRef] [PubMed]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, M. J. Post, “Evidence of a tropospheric aerosol backscatter background mode,” Appl. Opt. 28, 1040–1042 (1989).
[CrossRef] [PubMed]

J. M. Vaughan, R. D. Callan, D. A. Bowdle, J. Rothermel, “Spectral analysis, digital integration and measurement of low backscatter in coherent laser radar,” Appl. Opt. 28, 3008–3014 (1989).
[CrossRef] [PubMed]

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[CrossRef] [PubMed]

M. A. Jarzembski, V. Srivastava, D. M. Chambers, “Lidar calibration technique using laboratory-generated aerosols,” Appl. Opt. 35, 2096–2108 (1995).
[CrossRef]

C. M. Sonnenschein, F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10, 1600–1604 (1971).
[CrossRef] [PubMed]

J. H. Shapiro, “Precise comparison of experimental and theoretical SNRs in CO2 laser heterodyne systems: comments,” Appl. Opt. 24, 1245–1247 (1985).
[CrossRef] [PubMed]

Bull. Am. Meteorol. Soc.

W. E. Baker, G. D. Emmitt, P. Robertson, R. M. Atlas, J. E. Molinari, D. A. Bowdle, J. Paegle, R. M. Hardesty, R. T. Menzies, T. N. Krishnamurti, R. A. Brown, M. J. Post, J. R. Anderson, A. C. Lorenc, T. L. Miller, J. McElroy, “Lidar measured winds from space: a key component for weather and climate prediction,” Bull. Am. Meteorol. Soc. 76, 869–888 (1995).
[CrossRef]

Geophys. Res. Lett.

V. Srivastava, D. A. Bowdle, M. A. Jarzembski, J. Rothermel, D. M. Chambers, D. R. Cutten, “High-resolution remote sensing of sulfate aerosols from CO2 lidar backscatter,” Geophys. Res. Lett. 22, 2373–2376 (1995).
[CrossRef]

J. Appl. Meteorol.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, P. C. Sinclair, “Aerosol backscatter coefficient profiles measured at 10.6 μm,” J. Appl. Meteorol. 20, 184–194 (1981).
[CrossRef]

J. Geo-phys. Res.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains 2. Backscatter structure,” J. Geo-phys. Res. 96, 5337–5344 (1991).
[CrossRef]

J. Geophys. Res.

J. M. Vaughan, D. W. Brown, C. Nash, S. B. Alejandro, G. G. Koenig, “Atlantic atmospheric aerosol studies. 2. Compendium of airborne backscatter measurements at 10.6 μm,” J. Geophys. Res. 100, 1043–1065 (1995).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, D. W. Brown, A. A. Woodfield, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 1. Algorithm description,” J. Geophys. Res. 96, 5293–5298 (1991).
[CrossRef]

J. Rothermel, D. A. Bowdle, J. M. Vaughan, “Calculation of aerosol backscatter from airborne continuous-wave focused CO2 Doppler lidar measurements 2. Algorithm performance,” J. Geophys. Res. 96, 5299–5305 (1991).
[CrossRef]

Opt. Commun.

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “The fractal character of Gaussian–Lorentzian light,” Opt. Commun. 116, 15–19 (1995).
[CrossRef]

Other

D. R. Cutten, R. F. Pueschel, D. A. Bowdle, V. Srivastava, A. D. Clarke, J. Rothermel, J. D. Spinhirne, R. T. Menzies, “Multi-wavelength comparison of modeled and measured remote tropospheric backscatter over the Pacific Ocean,” J. Geophys. Res. (to be published).

Hereafter, with obvious exceptions, total lidar system efficiency η is referenced to the type of target (HT, SPM, or VM), measurement coverage (at focus F or over the focal volume at different ranges L), and signal analyzer (DSP, SA, or SAW).

M. J. Kavaya, S. W. Henderson, R. G. Frehlich, “Theory of CW lidar aerosol backscatter measurements and development of a 2.1 μm solid-state pulsed laser radar for aerosol backscatter profiling,” NASA Contr. Rep. CR-4347 (NASA, Washington, D.C., 1991).

M. J. Kavaya, “The JPL lidar target calibration facility,” in Third Topical Meeting on Coherent Laser Radar: Technology and Applications (Optical Society of America, Washington, D.C., 1985), p. II.1.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962).

D. A. Bowdle, J. Rothermel, J. E. Arnold, S. F. Williams, “The GLObal backscatter experiment Pacific survey mission: results and implications for LAWS,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 290–292.

The mention of brand names in this paper is for information purposes only and does not constitute an endorsement of the product by the authors, their institutions, or sponsors.

W. D. Jones, J. W. Bilbro, S. C. Johnson, H. B. Jeffreys, L. Z. Kennedy, R. W. Lee, C. A. DiMarzio, “Design and calibration of a coherent lidar for measurement of atmospheric backscatter,” in The Human in the Photo-Optical System (New York), R. L. Minter, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 5, 66–71 (1982).

W. D. Jones, L. Z. Kennedy, R. W. Lee, “Determination of atmospheric backscatter at 10.6 μm,” in Coherent Infrared Radar Systems and Applications II, R. C. Harney, ed., Soc. Photo-Opt. Instrum. Eng. 415, 77–84 (1983).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the NASA Marshall Space Flight Center (MSFC) 9.1-μm CW focused coherent Doppler lidar. The dots and two-headed arrows along optical path indicate perpendicular and parallel polarization, respectively. The 10.6-μm CW lidar has a similar configuration; differences are noted in the text.

Fig. 2
Fig. 2

Intercomparison measurements of SNR with DSP and SAW signal analyzers: (a) scatterplot of the laboratory study using combined output from signal and random noise generators and using stepped attenuation of the signal to simulate the range of the SNR from atmospheric targets (the dashed curve represents nonlinear correction function for SAW, as described in the text), (b) scatterplot of SNRDSP and SNRSAW for atmospheric measurements from GLOBE II, based on 11,500 (5-s) and 65,536 (1-s) integrations, respectively. Note the similarity in trends.

Fig. 3
Fig. 3

Total system efficiency η as a function of average laser output power for the 9.1-μm CW Doppler lidar using both HT and well-characterized, artificially generated aerosols.

Fig. 4
Fig. 4

Intercomparisons of the aerosol backscatter coefficient β(π) (in m−1 sr−1) at 9.1 and 10.6 μm, as estimated from SA, SAW, and DSP signal analyzer measurements during GLOBE II, flight 13, 3 June 1990, over the remote northwestern Pacific Ocean: (a) time series of β(π, 10.6 μm) from SA and DSP, with altitude (alt) superimposed, (b) scatterplot of β(π, 9.1 μm) estimates from DSP and SAW, (c) scatterplot of β(π, 9.1 μm) and β(π, 10.6 μm) from DSP. DSP and SAW estimates are based on 11,500 (5-s) and 65,536 (1-s) integrations, respectively.

Tables (3)

Tables Icon

Table 1 Significant Data System Features

Tables Icon

Table 2 Lidar Parameter, Signal, and Backscatter Estimation Uncertaintiesa

Tables Icon

Table 3 Lidar System SNR and Backscatter Sensitivity (×m−1 sr−1) as a Function of Signal Analyzer Type and Wavelengtha

Equations (13)

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

e = k = k l k u [ S p ( k ) - G M p ( k ) ] 2 ,
G = k = k l k u S p ( k ) M p ( k ) k l k u [ M p ( k ) ] 2 ,
SNR DSP = k = k 0 k 1 [ S p ( k ) - G M p ( k ) ] k = k 0 k = k 1 G M p ( k ) / n ,
S p ( k ) - G M p ( k ) > 2 σ ,
SNR SAW = C k = k 0 k 1 [ S V 2 ( k ) - N V 2 ( k ) ] [ k = k 0 k 1 N V 2 ( k ) ] / n ,
S V 2 ( k ) - N V 2 ( k ) > 2 σ ,
SNR SA = S V 2 - N V 2 N V 2 .
C = 0.953 - 0.249 ( log SNR SAW ) - 0.071 ( log SNR SAW ) 2 + 0.028 ( log SNR SAW ) 3 ,
β ( π ) = SNR K B P T ,
K = { ( η λ h ν ) [ π 2 + tan - 1 ( π R 2 λ F ) ] } - 1 ,
η HT , F , SA η HT , L , SA η HT , F , SA η HT , L , DSP η HT , L , SA η VM , L , DSP η HT , L , DSP = η VM , L , DSP .
SNR HT ( L ) = η P T π R 2 ρ * B h ν L 2 [ 1 + ( π R 2 λ L ) 2 ( 1 - L F ) 2 ] ,
SNR HT ( F ) = η P T π R 2 ρ * B h ν F 2 .

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