Abstract

The SNR equation of a CW, monostatic, coherent laser radar system is examined for the case of a distributed aerosol target. General analytic equations are derived which explicitly describe the contribution to total SNR from each range interval along the optic axis, the range resolution of the measurement, and the atmospheric volume contributing to the measurement. Plots are presented showing the location in range and the volume of the laser radar measurement.

© 1991 Optical Society of America

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  1. R. M. Huffaker, “Laser Doppler Detection Systems for Gas Velocity Measurement,” Appl. Opt. 9, 1026–1039 (1970).
    [Crossref] [PubMed]
  2. A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
    [Crossref]
  3. T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
    [Crossref]
  4. R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).
  5. J. W. Bilbro, “Atmospheric Laser Doppler Velocimetry: an Overview,” Opt. Eng. 19, 533–542 (1980).
  6. F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
    [Crossref]
  7. R. M. Munoz, H. W. Mocker, L. Koehler, “Airborne Laser Doppler Velocimeter,” Appl. Opt. 13, 2890–2898 (1974).
    [Crossref]
  8. A. A. Woodfield, J. M. Vaughan, “Airspeed and Wind Shear Measurements with an Airborne CO2 CW Laser,” Int. J. Aviat. Safety 1, 207–224 (1983).
  9. R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
    [Crossref]
  10. L. Z. Kennedy, J. W. Bilbro, “Remote Measurement of the Transverse Wind Velocity Component Using a Laser Doppler Velocimeter,” Appl. Opt. 18, 3010–3013 (1979).
    [Crossref] [PubMed]
  11. R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
    [Crossref]
  12. F. Koepp, “Investigation of Aircraft Wake Vortices Using the DFVLR Infrared Doppler Lidar,” 3rd Topical Meeting on Coherent Laser Radar: Technology and Applications, paper VII.3, 1985.
  13. 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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).
  14. 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]
  15. J. L. Gras, W. D. Jones, “Australian Aerosol Backscatter Survey,” Appl. Opt. 28, 852–856 (1989).
    [Crossref] [PubMed]
  16. S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
    [Crossref]
  17. M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
    [Crossref]
  18. C. Werner, F. Koepp, R. L. Schwiesow, “Influence of Clouds and Fog on LDA Wind Measurements,” Appl. Opt. 23, 2482–2484 (1984).
    [Crossref] [PubMed]
  19. R. L. Schwiesow, R. F. Calfee, “Atmospheric Refractive Effects on Coherent Lidar Performance at 10.6 μm,” Appl. Opt. 18, 3911–3917 (1979).
    [Crossref] [PubMed]
  20. R. L. Schwiesow, R. E. Cupp, “Calibration of a cw Infrared Doppler Lidar,” Appl. Opt. 19, 3168–3172 (1980).
    [Crossref] [PubMed]
  21. J. M. Vaughan, Royal Signals & Radar Establishment, U.K.; private communication (1990), has also pointed out that for a reduced measurement volume the signal character may be largely dominated by the occasional passage of single larger particles. As a consequence, the signal would have non-Gaussian statistics and be subject to large fluctuations. Such fluctuations may exceed the dynamic range of the available signal processing leading to further measurement bias. Such effects have been observed in airborne lidar measurements in the atmosphere (Vaughan et al., unpublished work) and provide in principle a technique for determining whether the scattering is due to hosts of small particles or a few larger particles.
  22. R. G. Frehlich, M. J. Kavaya, “Coherent Laser Radar Performance for General Atmospheric Refractive Turbulence,” submitted to Appl. Opt.30, (1991).
    [Crossref] [PubMed]
  23. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), pp. 310–314.
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 61.
  25. 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). A list of unpublished errata for this paper can be obtained from the present authors.
    [Crossref] [PubMed]
  26. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), pp. 24, 49, and 68.
  27. J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

1990 (1)

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[Crossref]

1989 (1)

1987 (1)

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

1984 (2)

C. Werner, F. Koepp, R. L. Schwiesow, “Influence of Clouds and Fog on LDA Wind Measurements,” Appl. Opt. 23, 2482–2484 (1984).
[Crossref] [PubMed]

F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
[Crossref]

1983 (1)

A. A. Woodfield, J. M. Vaughan, “Airspeed and Wind Shear Measurements with an Airborne CO2 CW Laser,” Int. J. Aviat. Safety 1, 207–224 (1983).

1981 (2)

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (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]

1980 (2)

J. W. Bilbro, “Atmospheric Laser Doppler Velocimetry: an Overview,” Opt. Eng. 19, 533–542 (1980).

R. L. Schwiesow, R. E. Cupp, “Calibration of a cw Infrared Doppler Lidar,” Appl. Opt. 19, 3168–3172 (1980).
[Crossref] [PubMed]

1979 (3)

1978 (1)

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

1974 (1)

1972 (2)

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

1971 (1)

1970 (2)

R. M. Huffaker, “Laser Doppler Detection Systems for Gas Velocity Measurement,” Appl. Opt. 9, 1026–1039 (1970).
[Crossref] [PubMed]

R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
[Crossref]

Alejandro, S. B.

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[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.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

J. W. Bilbro, “Atmospheric Laser Doppler Velocimetry: an Overview,” Opt. Eng. 19, 533–542 (1980).

L. Z. Kennedy, J. W. Bilbro, “Remote Measurement of the Transverse Wind Velocity Component Using a Laser Doppler Velocimeter,” Appl. Opt. 18, 3010–3013 (1979).
[Crossref] [PubMed]

Calfee, R. F.

Clifton, T. H.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Craven, C. E.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Cupp, R. 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]

R. L. Schwiesow, R. E. Cupp, “Calibration of a cw Infrared Doppler Lidar,” Appl. Opt. 19, 3168–3172 (1980).
[Crossref] [PubMed]

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

Davies, P. H.

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[Crossref]

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.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

Foord, R.

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

Frehlich, R. G.

R. G. Frehlich, M. J. Kavaya, “Coherent Laser Radar Performance for General Atmospheric Refractive Turbulence,” submitted to Appl. Opt.30, (1991).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 61.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), pp. 24, 49, and 68.

Gras, J. L.

Hampton, D.

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

Haugen, D. A.

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

Horrigan, F. A.

Huffaker, R. M.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
[Crossref]

R. M. Huffaker, “Laser Doppler Detection Systems for Gas Velocity Measurement,” Appl. Opt. 9, 1026–1039 (1970).
[Crossref] [PubMed]

Hughes, A. J.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Jarzembski, M.

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

Jeffreys, H. B.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

Jelalian, A. V.

R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
[Crossref]

Johnson, S. C.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

Jones, I. P.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Jones, R.

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

Jones, W. D.

J. L. Gras, W. D. Jones, “Australian Aerosol Backscatter Survey,” Appl. Opt. 28, 852–856 (1989).
[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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

Kavaya, M. J.

R. G. Frehlich, M. J. Kavaya, “Coherent Laser Radar Performance for General Atmospheric Refractive Turbulence,” submitted to Appl. Opt.30, (1991).
[Crossref] [PubMed]

Keeler, R. J.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

Kennedy, L. Z.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

L. Z. Kennedy, J. W. Bilbro, “Remote Measurement of the Transverse Wind Velocity Component Using a Laser Doppler Velocimeter,” Appl. Opt. 18, 3010–3013 (1979).
[Crossref] [PubMed]

Koehler, L.

Koenig, G. G.

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[Crossref]

Koepp, F.

F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
[Crossref]

C. Werner, F. Koepp, R. L. Schwiesow, “Influence of Clouds and Fog on LDA Wind Measurements,” Appl. Opt. 23, 2482–2484 (1984).
[Crossref] [PubMed]

F. Koepp, “Investigation of Aircraft Wake Vortices Using the DFVLR Infrared Doppler Lidar,” 3rd Topical Meeting on Coherent Laser Radar: Technology and Applications, paper VII.3, 1985.

Lawrence, T. R.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Lee, R. W.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

Lenschow, D. H.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

McPherson, A.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Mocker, H. W.

Munoz, R. M.

Newman, J. T.

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

O’Shaughnessy, J.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Pike, E. R.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Pomeroy, W. R. M.

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

Post, M. J.

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

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]

Rothermel, J.

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), pp. 24, 49, and 68.

Schwiesow, R. L.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
[Crossref]

C. Werner, F. Koepp, R. L. Schwiesow, “Influence of Clouds and Fog on LDA Wind Measurements,” Appl. Opt. 23, 2482–2484 (1984).
[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]

R. L. Schwiesow, R. E. Cupp, “Calibration of a cw Infrared Doppler Lidar,” Appl. Opt. 19, 3168–3172 (1980).
[Crossref] [PubMed]

R. L. Schwiesow, R. F. Calfee, “Atmospheric Refractive Effects on Coherent Lidar Performance at 10.6 μm,” Appl. Opt. 18, 3911–3917 (1979).
[Crossref] [PubMed]

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

Serafin, R. J.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), pp. 310–314.

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]

Sonnenschein, C. M.

Spavins, C.

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Srivastava, V.

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

Thomson, J. A.

R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
[Crossref]

Thomson, J. A. L.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Vaughan, J. M.

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[Crossref]

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

A. A. Woodfield, J. M. Vaughan, “Airspeed and Wind Shear Measurements with an Airborne CO2 CW Laser,” Int. J. Aviat. Safety 1, 207–224 (1983).

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

J. M. Vaughan, Royal Signals & Radar Establishment, U.K.; private communication (1990), has also pointed out that for a reduced measurement volume the signal character may be largely dominated by the occasional passage of single larger particles. As a consequence, the signal would have non-Gaussian statistics and be subject to large fluctuations. Such fluctuations may exceed the dynamic range of the available signal processing leading to further measurement bias. Such effects have been observed in airborne lidar measurements in the atmosphere (Vaughan et al., unpublished work) and provide in principle a technique for determining whether the scattering is due to hosts of small particles or a few larger particles.

Werner, C.

F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
[Crossref]

C. Werner, F. Koepp, R. L. Schwiesow, “Influence of Clouds and Fog on LDA Wind Measurements,” Appl. Opt. 23, 2482–2484 (1984).
[Crossref] [PubMed]

Willetts, D. V.

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

Wilson, D. J.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Woodfield, A. A.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

A. A. Woodfield, J. M. Vaughan, “Airspeed and Wind Shear Measurements with an Airborne CO2 CW Laser,” Int. J. Aviat. Safety 1, 207–224 (1983).

Appl. Opt. (8)

Bull. Am. Meteorol. Soc. (1)

S. B. Alejandro, G. G. Koenig, J. M. Vaughan, P. H. Davies, “SABLE: A South Atlantic Aerosol Backscatter Measurement Program,” Bull. Am. Meteorol. Soc. 71, 281–287 (1990).
[Crossref]

Int. J. Aviat. Safety (1)

A. A. Woodfield, J. M. Vaughan, “Airspeed and Wind Shear Measurements with an Airborne CO2 CW Laser,” Int. J. Aviat. Safety 1, 207–224 (1983).

J. Appl. Meteorol. (2)

M. J. Post, R. L. Schwiesow, R. E. Cupp, D. A. Haugen, J. T. Newman, “A Comparison of Anemometer- and Lidar-Sensed Wind Velocity Data,” J. Appl. Meteorol. 17, 1179–1181 (1978).
[Crossref]

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. Atmos. Oceanic Technol. (1)

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An Airborne Laser Air Motion Sensing System. Part I: Concept and Preliminary Experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[Crossref]

J. Climate Appl. Meteorol. (1)

F. Koepp, R. L. Schwiesow, C. Werner, “Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar,” J. Climate Appl. Meteorol. 23, 148–154 (1984).
[Crossref]

Opt. Eng. (1)

J. W. Bilbro, “Atmospheric Laser Doppler Velocimetry: an Overview,” Opt. Eng. 19, 533–542 (1980).

Opto-electronics (1)

A. J. Hughes, J. O’Shaughnessy, E. R. Pike, A. McPherson, C. Spavins, T. H. Clifton, “Long Range Anemometry Using a CO2 Laser,” Opto-electronics 4, 379–384 (1972).
[Crossref]

Proc. IEEE (1)

R. M. Huffaker, A. V. Jelalian, J. A. Thomson, “Laser-Doppler System for Detection of Aircraft Trailing Vortices,” Proc. IEEE 58, 322–326 (1970).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. Foord, R. Jones, W. R. M. Pomeroy, J. M. Vaughan, D. V. Willetts, “Infrared Laser Velocimetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 197, 325–328 (1979).

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 66–71 (1981).

Rev. Sci. Instrum. (1)

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, “A Laser Velocimeter for Remote Wind Sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[Crossref]

Other (7)

F. Koepp, “Investigation of Aircraft Wake Vortices Using the DFVLR Infrared Doppler Lidar,” 3rd Topical Meeting on Coherent Laser Radar: Technology and Applications, paper VII.3, 1985.

J. M. Vaughan, Royal Signals & Radar Establishment, U.K.; private communication (1990), has also pointed out that for a reduced measurement volume the signal character may be largely dominated by the occasional passage of single larger particles. As a consequence, the signal would have non-Gaussian statistics and be subject to large fluctuations. Such fluctuations may exceed the dynamic range of the available signal processing leading to further measurement bias. Such effects have been observed in airborne lidar measurements in the atmosphere (Vaughan et al., unpublished work) and provide in principle a technique for determining whether the scattering is due to hosts of small particles or a few larger particles.

R. G. Frehlich, M. J. Kavaya, “Coherent Laser Radar Performance for General Atmospheric Refractive Turbulence,” submitted to Appl. Opt.30, (1991).
[Crossref] [PubMed]

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), pp. 310–314.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 61.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), pp. 24, 49, and 68.

J. Rothermel, W. D. Jones, V. Srivastava, M. Jarzembski, D. Hampton, “In Situ Backscatter Measurements Over the Pacific Ocean Using Two Coherent Focused CO2 Lidars,” in Technical Digest, Seventy-First AMS Annual Meeting, New Orleans, LA (13–18 Jan. 1991), paper J14.2.

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Figures (13)

Fig. 1
Fig. 1

Cumulative SNR vs normalized range as a function of normalized focal range.

Fig. 2
Fig. 2

Normalized percentile ranges vs normalized focal range. Note that R N (95%) is divided by 10 and shown as a dashed line.

Fig. 3
Fig. 3

Normalized range resolutions vs normalized focal range.

Fig. 4
Fig. 4

Relative SNR vs range as a function of focal range. The SNR is normalized to 1 at R = 0.

Fig. 5
Fig. 5

Cumulative SNR vs range as a function of focal range.

Fig. 6
Fig. 6

Percentile ranges vs focal range.

Fig. 7
Fig. 7

Range resolution widths vs focal range.

Fig. 8
Fig. 8

Range resolution widths vs beam diameter.

Fig. 9
Fig. 9

Percentile ranges vs beam diameter.

Fig. 10
Fig. 10

V(50%) vs focal range as a function of beam diameter.

Fig. 11
Fig. 11

V(90%) vs focal range as a function of beam diameter.

Fig. 12
Fig. 12

V(50%) vs diameter as a function of focal range.

Fig. 13
Fig. 13

V(90%) vs diameter as a function of focal range.

Equations (46)

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SNR = η π P C W β h ν B 0 d R 4 R 2 D 0 2 + ( 1 - R F ) 2 π 2 D 0 2 4 λ 2 = η P CW β λ h ν B 0 R R d R R 2 + ( 1 - R F ) 2 R R 2 ,
R R π D 0 2 4 λ ,
I ( R = F ) = R R F 2 = π D 0 2 4 λ F 2 ,
R P = F R R 2 R R 2 + F 2 = F 1 + F N 2 ,
F N F / R R
R P F ,
R P F F N 2 = R R 2 F ,
I ( R = R P ) = R R 2 + F 2 R R F 2 = 1 + F N 2 F F N .
SNR ( R = F ) SNR ( R = R P ) = R R 2 R R 2 + F 2 = 1 1 + F N 2 .
F P = R R .
R P ( F P ) = R R 2 .
SNR = η P CW β λ h ν B 0 d R N 1 - 2 R N F N + ( 1 + 1 F N 2 ) R N 2 ,
R N R / R R
d x a + b x + c x 2 = 2 Δ - 1 / 2 tan - 1 [ ( b + 2 c x ) Δ - 1 / 2 ]
SNR ( ) = η π P CW β λ 2 h ν B [ 1 + 2 π tan - 1 ( 1 F N ) ] ,
CUMSNR ( R N ) SNR ( R N ) SNR ( ) ,
SNR ( R N ) = η P CW β λ h ν B 0 R N d z 1 - 2 z F N + ( 1 + 1 F N 2 ) z 2 .
SNR ( R N ) = η P CW β λ h ν B { tan - 1 [ 1 F N + ( 1 + 1 F N 2 ) R N ] + tan - 1 ( 1 F N ) } .
tan - 1 x + tan - 1 y = α + tan - 1 ( x + y 1 - x y ) ,
x = 1 F N ,
y ( R N ) = ( 1 + 1 F N 2 ) R N - 1 F N ,
x y ( R N ) = ( 1 F N ) [ ( 1 + 1 F N 2 ) R N - 1 F N ] .
SNR ( R N ) = η P CW β λ h ν B × { α ( R N ) + tan - 1 [ ( 1 + 1 F N 2 ) R N 1 - ( 1 + 1 F N 2 ) ( R N F N ) + ( 1 F N ) 2 ] } = η P CW β λ h ν B { α ( R N α ( R N ) + tan - 1 [ R N 1 - ( R N F N ) ] } ,
CUMSNR ( R N ) = α ( R N ) + tan - 1 [ R N 1 - ( R N F N ) ] π 2 + tan - 1 ( 1 F N ) ;
tan - 1 ( - z ) = - π 2 + tan - 1 ( 1 z )
R N ( CUMSNR ) = F N tan γ F N + tan γ ,
γ = ( CUMSNR ) ( π - tan - 1 F N ) .
W N ( 50 % ) R N ( 75 % ) - R N ( 25 % ) ,
W N ( 90 % ) R N ( 95 % ) - R N ( 5 % ) .
W N ( 1 - 2 ) = 2 ( 1 + F N tan 2 δ ) ( F N + 1 F N ) ( 1 + tan δ F N ) ,
δ = ( π - tan - 1 F N ) ,
W N ( 1 - 2 ) 2 F N 2 tan ( π ) ,
W N ( 1 - 2 ) 2 tan ( π ) .
CUMSNR ( R N ) = π + tan - 1 [ F N R N F N - R N ] π - F N .
R N ( CUMSNR ) = F N tan ( π CUMSNR ) F N + tan ( π CUMSNR ) .
R ( 25 % ) F ( 1 - F N ) = F - F 2 R R ,
R ( 75 % ) F ( 1 + F N ) = F + F 2 R R .
W ( 50 % ) = R ( 75 % ) - R ( 25 % ) = 2 F F N = 2 F 2 R R = 8 λ F 2 π D 0 2 .
W ( 50 % ) = 2 π D min 2 4 λ ,
D ( R ) - D 0 [ ( 1 - R F ) 2 + R N 2 ] 1 / 2 .
D ( F ) = 4 λ F π D 0 = D 0 F R R = D 0 F N .
D ( R P ) = D min = D 0 [ 1 + ( 1 F N ) 2 ] 1 / 2 .
D min D 0 F N ,
D min D 0 ,
V = π 4 R L R U D 2 ( R ) d R = π D 0 2 4 R L R U [ ( 1 - R F ) 2 + ( R R R ) 2 ] d R = π D 0 2 4 [ ( R U - R L ) - 1 F ( R U 2 - R L 2 ) + 1 3 ( 1 F 2 + 1 R R 2 ) ( R U 3 - R L 3 ) ] .
V ( 50 % ) 32 π 2 λ 2 F 4 D 0 4 .

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