Abstract

A comparison is made of four prominent Doppler lidar systems, ranging in wavelength from the near UV to the middle IR, which are presently being studied for their potential in an earth-orbiting global tropospheric wind field measurement application. The comparison is restricted to relative photon efficiencies, i.e., the required number of transmitted photons per pulse is calculated for each system, for mid-tropospheric velocity estimate uncertainties ranging from :±1 to ±4 m/s. The results are converted to laser transmitter pulse energy and power requirements. The analysis indicates that a coherent CO2 Doppler lidar operating at 9.11-μm wavelength is the most efficient.

© 1986 Optical Society of America

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References

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  1. R. M. Huffaker, Ed., Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, NOAA TM ERL WPL-37 (1978).
  2. Global Wind Measuring Satellite System—WINDSAT, Final Report, NOAA contract NA79RA C00127, Lockheed Missiles & Space Co., with Perkin-Elmer Corp. and GTE Sylvania (Apr.1981).
  3. Feasibility Study of a Windsat Free Flyer, Final Report, contract NA82RAC00141, RCA Government Systems Division, Astro-Electronics, Princeton, NJ, with Perkin-Elmer Corp. and Math. Science Northwest, Inc. (July1983).
  4. R. T. Menzies, “A Comparison of Doppler Lidar Wind Sensors for Earth-Orbit Global Measurement Applications,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).
  5. M. J. Kavaya, R. T. Menzies, “Lidar Aerosol Backscatter Measurements: Systematic, Modeling, and Calibration Error Considerations,” Appl. Opt. 24, 3444 (1985).
    [CrossRef] [PubMed]
  6. V. J. Abreu, “Wind Measurements from an Orbiting Platform Using a Lidar System with Incoherent Detection: An Analysis,” Appl. Opt. 18, 2992 (1979).
    [CrossRef] [PubMed]
  7. P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).
  8. G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling Atmospheric Aerosol Backscatter at CO2 Laser Wavelengths. 1: Aerosol Properties, Modeling Techniques, and Associated Problems,” Appl. Opt. 22, 1655 (1983); also G. S. Kent, personal communication (1985).
    [CrossRef] [PubMed]
  9. T. S. Cress, “Airborne Measurement of Aerosol Size Distributions Over Northern Europe,” Vol. 1, Spring and Fall, 1976; Summer, 1977, AFGL, Hanscom Field, MA, Environmental Research Paper 702 (May1980).
  10. E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
    [CrossRef]
  11. M. J. Post, “Aerosol Backscattering Profiles at CO2 Wavelengths: the NOAA Data Base,” Appl. Opt. 23, 2507 (1984).
    [CrossRef] [PubMed]
  12. R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).
  13. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1982).
  14. Shuttle Atmospheric Lidar Research Program: Final Report of Atmospheric Lidar Working Group, NASA Spec. Publ. 433 (NTIS, Springfield, VA, 1979).
  15. P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).
  16. D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
    [CrossRef]
  17. I. S. McDermid, J. B. Laudenslager, D. Rees, “UV-Excimer Laser Based Incoherent Doppler Lidar System,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).
  18. D. S. Zrnik, “Estimation of Spectral Moments for Weather Echoes,” IEEE Trans. Geosci. Electron. GE-17, 113 (1979).
    [CrossRef]
  19. T. J. Kane, B. Zhou, R. L. Byer, “Potential for Coherent Doppler Wind Velocity Lidar Using Neodymium Lasers,” Appl. Opt. 23, 2477 (1984).
    [CrossRef] [PubMed]
  20. G. J. Hernandez, “Analytical Description of a Fabry-Perot Photoelectric Spectrometer,” Appl. Opt. 5, 1745 (1966); “Analytical Description of a Fabry-Perot Photoelectric Spectrometer: 2. Numerical Results,” Appl. Opt. 9, 1591 (1970).
    [CrossRef] [PubMed]
  21. G. Megie, R. T. Menzies, “Complementarity of UV and IR Differential Absorption Lidar for Global Measurements of Atmospheric Species,” Appl. Opt. 19, 1173 (1980).
    [CrossRef] [PubMed]
  22. W. E. Baker, “Objective Analysis and Assimilation of Observational Data from FGGE,” Mon. Weather Rev. 111, 328 (1983).
    [CrossRef]
  23. R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
    [CrossRef]
  24. R. M. Atlas, “Observing System Simulation Experiments at GSFC,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).
  25. G. D. Emmitt, “Doppler Lidar Sampling Strategies and Accuracies—Regional Scale,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

1985 (2)

M. J. Kavaya, R. T. Menzies, “Lidar Aerosol Backscatter Measurements: Systematic, Modeling, and Calibration Error Considerations,” Appl. Opt. 24, 3444 (1985).
[CrossRef] [PubMed]

R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
[CrossRef]

1984 (2)

1983 (2)

1982 (1)

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

1981 (1)

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).

1980 (2)

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

G. Megie, R. T. Menzies, “Complementarity of UV and IR Differential Absorption Lidar for Global Measurements of Atmospheric Species,” Appl. Opt. 19, 1173 (1980).
[CrossRef] [PubMed]

1979 (2)

1966 (1)

Abreu, V. J.

V. J. Abreu, “Wind Measurements from an Orbiting Platform Using a Lidar System with Incoherent Detection: An Analysis,” Appl. Opt. 18, 2992 (1979).
[CrossRef] [PubMed]

P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).

Atlas, R.

R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
[CrossRef]

Atlas, R. M.

R. M. Atlas, “Observing System Simulation Experiments at GSFC,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

Baker, W. E.

W. E. Baker, “Objective Analysis and Assimilation of Observational Data from FGGE,” Mon. Weather Rev. 111, 328 (1983).
[CrossRef]

Byer, R. L.

Cress, T. S.

T. S. Cress, “Airborne Measurement of Aerosol Size Distributions Over Northern Europe,” Vol. 1, Spring and Fall, 1976; Summer, 1977, AFGL, Hanscom Field, MA, Environmental Research Paper 702 (May1980).

Deepak, A.

Delany, A. C.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

Emmitt, G. D.

G. D. Emmitt, “Doppler Lidar Sampling Strategies and Accuracies—Regional Scale,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

Farrukh, U. O.

Greenaway, A. H.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Halem, M.

R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
[CrossRef]

Hays, P. B.

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).

P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).

Hernandez, G. J.

Heubert, B. J.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

Huffaker, R. M.

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Kalnay, E.

R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
[CrossRef]

Kane, T. J.

Kavaya, M. J.

Keeler, R. J.

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Kennedy, B. C.

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).

Kent, G. S.

Kiang, C. S.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

Killeen, T. L.

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).

Korrell, J. A.

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Laudenslager, J. B.

I. S. McDermid, J. B. Laudenslager, D. Rees, “UV-Excimer Laser Based Incoherent Doppler Lidar System,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

Lawrence, T. R.

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Leslie, A. C. D.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

McDermid, I. S.

I. S. McDermid, J. B. Laudenslager, D. Rees, “UV-Excimer Laser Based Incoherent Doppler Lidar System,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

McWhirter, I.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Megie, G.

Menzies, R. T.

Patterson, E. M.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

Post, M. J.

M. J. Post, “Aerosol Backscattering Profiles at CO2 Wavelengths: the NOAA Data Base,” Appl. Opt. 23, 2507 (1984).
[CrossRef] [PubMed]

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Priestly, J. T.

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

Rees, D.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

I. S. McDermid, J. B. Laudenslager, D. Rees, “UV-Excimer Laser Based Incoherent Doppler Lidar System,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

Rosenberg, A.

P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).

Rounce, P. A.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Scott, A. F. D.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1982).

Sroga, J.

P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).

Towlson, W.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Wartburg, A. F.

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1982).

Yue, G. K.

Zhou, B.

Zrnik, D. S.

D. S. Zrnik, “Estimation of Spectral Moments for Weather Echoes,” IEEE Trans. Geosci. Electron. GE-17, 113 (1979).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Geosci. Electron. (1)

D. S. Zrnik, “Estimation of Spectral Moments for Weather Echoes,” IEEE Trans. Geosci. Electron. GE-17, 113 (1979).
[CrossRef]

J. Geophys. Res. (1)

E. M. Patterson, C. S. Kiang, A. C. Delany, A. F. Wartburg, A. C. D. Leslie, B. J. Heubert, “Global Measurements of Aerosols in Remote Continental and Marine Regions: Concentrations, Size Distributions, and Optical Properties,” J. Geophys. Res. 85, 7361 (1980).
[CrossRef]

J. Phys. E (1)

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of Atmospheric Absorption Lines from a Stabilized Balloon Platform and Measurements of Stratospheric Winds,” J. Phys. E 15, 191 (1982).
[CrossRef]

Mon. Weather Rev. (1)

W. E. Baker, “Objective Analysis and Assimilation of Observational Data from FGGE,” Mon. Weather Rev. 111, 328 (1983).
[CrossRef]

Opt. Eng. (1)

R. Atlas, E. Kalnay, M. Halem, “Impact on Satellite Temperature Sounding and Wind Data on Numerical Weather Prediction,” Opt. Eng. 24, 341 (1985).
[CrossRef]

Space Sci. Instrum. (1)

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395 (1981).

Other (12)

I. S. McDermid, J. B. Laudenslager, D. Rees, “UV-Excimer Laser Based Incoherent Doppler Lidar System,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

R. M. Atlas, “Observing System Simulation Experiments at GSFC,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

G. D. Emmitt, “Doppler Lidar Sampling Strategies and Accuracies—Regional Scale,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T. Priestly, J. A. Korrell, Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, Part II, NOAA TM ERL WPL-63 (1980).

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1982).

Shuttle Atmospheric Lidar Research Program: Final Report of Atmospheric Lidar Working Group, NASA Spec. Publ. 433 (NTIS, Springfield, VA, 1979).

R. M. Huffaker, Ed., Feasibility Study of Satellite-Borne Lidar Global Wind Monitoring System, NOAA TM ERL WPL-37 (1978).

Global Wind Measuring Satellite System—WINDSAT, Final Report, NOAA contract NA79RA C00127, Lockheed Missiles & Space Co., with Perkin-Elmer Corp. and GTE Sylvania (Apr.1981).

Feasibility Study of a Windsat Free Flyer, Final Report, contract NA82RAC00141, RCA Government Systems Division, Astro-Electronics, Princeton, NJ, with Perkin-Elmer Corp. and Math. Science Northwest, Inc. (July1983).

R. T. Menzies, “A Comparison of Doppler Lidar Wind Sensors for Earth-Orbit Global Measurement Applications,” in Global Wind Measurements, W. E. Baker, R. J. Curran, Eds. (A. Deepak, Hampton, VA, 1985).

P. B. Hays, V. J. Abreu, J. Sroga, A. Rosenberg, “Analysis of a 0.5 Micron Spaceborne Wind Sensor,” presented at the AMS Conference on Satellite Remote Sensing, Clearwater, FL (June 1984).

T. S. Cress, “Airborne Measurement of Aerosol Size Distributions Over Northern Europe,” Vol. 1, Spring and Fall, 1976; Summer, 1977, AFGL, Hanscom Field, MA, Environmental Research Paper 702 (May1980).

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Figures (3)

Fig. 1
Fig. 1

Number of photons per joule of transmitted energy per unit area of receiver telescope (1 m2) received from the backscatter of a 1-km aerosol layer as a function of altitude.

Fig. 2
Fig. 2

Dependence of required transmitter pulse energy on radial velocity estimate uncertainty, assuming a 1.75-km slant range resolution corresponding to a 1-km vertical resolution. The earth-orbiting platform height is 800 km.

Fig. 3
Fig. 3

Altitude dependence of single-pulse radial velocity estimate accuracy for three lidar systems with transmitter pulse energies indicated in the inset.

Tables (3)

Tables Icon

Table I Doppler Lidar System Descriptions

Tables Icon

Table II Receiver Doppler Shift Measurement Efficiency: Coherent Lidars(±1-m/s Accuracy)

Tables Icon

Table III Receiver Doppler Shift Measurement Efficiency: Direct Detection F. P. Etalon Lidars (±1-m/s Accuracy)

Equations (3)

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

P b ( t ) = c ( t - τ p ) / 2 c t / 2 P T ( t - 2 R c ) · β ( R ) · A R 2 · η · O ( R ) · τ ( R ) d R ,
δ v = λ 4 π ( f L t ) 1 / 2 [ π 3 / 2 W + 8 π 2 W 2 SNR + π 3 ( SNR ) 2 ] 1 / 2 ,
S k = N k ( N k + N B k + N D ) 1 / 2 ,

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