Abstract

A simple analytic model is developed for the shot-noise-limited measurement precision of Doppler wind lidars based on the fringe imaging technique by use of either molecular or aerosol atmospheric backscatter. The model leads to etalon design parameters for an instrument optimized for precision. The ultimate measurement precision possible is two to four times the limit for a perfect, lossless receiver. The corresponding result for the double-edge Doppler analyzer was a ratio of 2.5, showing that the two methods are little different in this respect. For aerosol backscatter instruments, the wind speed dynamic range of the fringe imager is substantially greater than that for the edge detector. The etalon aperture needed to meet system etendue requirements is derived and shown to be approximately half that of each of the two etalons required by the double-edge technique. A comparison with more detailed modeling of fringe imaging Doppler-shift analyzers shows good agreement for the Rayleigh model and fair for the aerosol version, confirming the validity of this simpler technique for analyzer design and performance prediction.

© 1998 Optical Society of America

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References

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  1. J. A. McKay, “Modeling of direct detection Doppler wind lidar. I. The edge technique,” Appl. Opt. 37, 6480–6486 (1998).
    [Crossref]
  2. K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
    [Crossref]
  3. M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng.37, (October1998).
  4. P. B. Hays, R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
    [Crossref] [PubMed]
  5. J.-M. Gagné, J.-P. Saint-Dizier, M. Picard, “Méthode d’echantillonage des fonctions déterministes en spectroscopie: application à un spectromètre multicanal par comptage photonique,” Appl. Opt. 13, 581–588 (1974).
    [Crossref]
  6. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
    [Crossref]
  7. G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1988), Eq. 2.2.2b.
  8. C. S. Gardner, “Optical remote sensing techniques for measuring winds: a comparison of theoretical performance capabilities,” viewgraph presentation at Winds ’97, the Third Workshop on Wind Measurements in the Middle Atmosphere, Ann Arbor, Mich., 6–9 October 1997; C. Gardner, University of Illinois, Urbana, Ill. 61801 (personal communication, 1997).
  9. J. A. McKay, “The edge filter and fringe imaging for laser Doppler wind speed measurement,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 420–427 (1997).
    [Crossref]
  10. J. A. McKay, T. D. Wilkerson, “Direct detection wind speed Doppler lidar systems,” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 42–52 (1997).
    [Crossref]
  11. G. Hernandez, “Analytical description of a Fabry-Perot spectrometer. 4: Signal noise limitations in data retrieval; winds, temperature, and emission rate,” Appl. Opt. 17, 2967–2972 (1978).
    [Crossref] [PubMed]
  12. W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
    [Crossref]
  13. T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Symanow, D. H. Ceckowski, “Image plane detector for the Dynamics Explorer Fabry-Perot interferometer,” Appl. Opt. 22, 3503–3513 (1983).
    [Crossref]
  14. T. L. Killeen, P. B. Hays, “Doppler line profile analysis for a multichannel Fabry-Perot interferometer,” Appl. Opt. 23, 612–620 (1984).
    [Crossref] [PubMed]
  15. W. R. Skinner, P. B. Hays, “A comparative study of coherent and incoherent Doppler lidar techniques,” Marshall Space Flight Center Study Report, contract NAS8-38775 (University of Michigan, Ann Arbor, Mich., 1994). The equation in this publication is in error by a factor √2 [confirmed by W. R. Skinner, University of Michigan, Ann Arbor, Mich. 48109 (personal communication, 1997)].
  16. D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
    [Crossref]
  17. D. Rees, Hovemere Ltd., Keston, Kent BR2 6AN United Kingdom (personal communication, 1997).

1998 (2)

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng.37, (October1998).

J. A. McKay, “Modeling of direct detection Doppler wind lidar. I. The edge technique,” Appl. Opt. 37, 6480–6486 (1998).
[Crossref]

1996 (1)

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

1995 (1)

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

1993 (1)

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[Crossref]

1984 (1)

1983 (1)

1978 (1)

1974 (1)

1971 (1)

P. B. Hays, R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
[Crossref] [PubMed]

Abreu, V. J.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

Barnes, J. E.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

Ceckowski, D. H.

Fischer, K. F.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

Fricke, K.-H.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

Gagné, J.-M.

Gardner, C. S.

C. S. Gardner, “Optical remote sensing techniques for measuring winds: a comparison of theoretical performance capabilities,” viewgraph presentation at Winds ’97, the Third Workshop on Wind Measurements in the Middle Atmosphere, Ann Arbor, Mich., 6–9 October 1997; C. Gardner, University of Illinois, Urbana, Ill. 61801 (personal communication, 1997).

Hardesty, R. M.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[Crossref]

Hays, P. B.

T. L. Killeen, P. B. Hays, “Doppler line profile analysis for a multichannel Fabry-Perot interferometer,” Appl. Opt. 23, 612–620 (1984).
[Crossref] [PubMed]

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Symanow, D. H. Ceckowski, “Image plane detector for the Dynamics Explorer Fabry-Perot interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[Crossref]

P. B. Hays, R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
[Crossref] [PubMed]

W. R. Skinner, P. B. Hays, “A comparative study of coherent and incoherent Doppler lidar techniques,” Marshall Space Flight Center Study Report, contract NAS8-38775 (University of Michigan, Ann Arbor, Mich., 1994). The equation in this publication is in error by a factor √2 [confirmed by W. R. Skinner, University of Michigan, Ann Arbor, Mich. 48109 (personal communication, 1997)].

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[Crossref]

Hernandez, G.

Irgang, T. D.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

Kennedy, B. C.

Killeen, T. L.

Lloyd, N. D.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

McGill, M. J.

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng.37, (October1998).

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

McKay, J. A.

J. A. McKay, “Modeling of direct detection Doppler wind lidar. I. The edge technique,” Appl. Opt. 37, 6480–6486 (1998).
[Crossref]

J. A. McKay, “The edge filter and fringe imaging for laser Doppler wind speed measurement,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 420–427 (1997).
[Crossref]

J. A. McKay, T. D. Wilkerson, “Direct detection wind speed Doppler lidar systems,” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 42–52 (1997).
[Crossref]

Nelke, G.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

Picard, M.

Rees, D.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

D. Rees, Hovemere Ltd., Keston, Kent BR2 6AN United Kingdom (personal communication, 1997).

Roble, R. G.

P. B. Hays, R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
[Crossref] [PubMed]

Rye, B. J.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[Crossref]

Saint-Dizier, J.-P.

Singer, W.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

Skinner, W. R.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

W. R. Skinner, P. B. Hays, “A comparative study of coherent and incoherent Doppler lidar techniques,” Marshall Space Flight Center Study Report, contract NAS8-38775 (University of Michigan, Ann Arbor, Mich., 1994). The equation in this publication is in error by a factor √2 [confirmed by W. R. Skinner, University of Michigan, Ann Arbor, Mich. 48109 (personal communication, 1997)].

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[Crossref]

Spinhirne, J. D.

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng.37, (October1998).

Symanow, D. A.

von Cossart, G.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

von Zahn, U.

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

Wilkerson, T. D.

J. A. McKay, T. D. Wilkerson, “Direct detection wind speed Doppler lidar systems,” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 42–52 (1997).
[Crossref]

Appl. Opt. (1)

P. B. Hays, R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
[Crossref] [PubMed]

Appl. Opt. (5)

IEEE Trans. Geosci. Remote Sensing (1)

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[Crossref]

J. Atmos. Terr. Phys. (1)

D. Rees, G. Nelke, K.-H. Fricke, U. von Zahn, W. Singer, G. von Cossart, N. D. Lloyd, “The Doppler wind and temperature system of the Alomar lidar,” J. Atmos. Terr. Phys. 58, 1827–1842 (1996).
[Crossref]

Opt. Eng. (2)

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[Crossref]

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng.37, (October1998).

Other (7)

D. Rees, Hovemere Ltd., Keston, Kent BR2 6AN United Kingdom (personal communication, 1997).

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1988), Eq. 2.2.2b.

C. S. Gardner, “Optical remote sensing techniques for measuring winds: a comparison of theoretical performance capabilities,” viewgraph presentation at Winds ’97, the Third Workshop on Wind Measurements in the Middle Atmosphere, Ann Arbor, Mich., 6–9 October 1997; C. Gardner, University of Illinois, Urbana, Ill. 61801 (personal communication, 1997).

J. A. McKay, “The edge filter and fringe imaging for laser Doppler wind speed measurement,” in Laser Radar Technology and Applications II, G. W. Kamerman, ed., Proc. SPIE3065, 420–427 (1997).
[Crossref]

J. A. McKay, T. D. Wilkerson, “Direct detection wind speed Doppler lidar systems,” in Application of Lidar to Current Atmospheric Topics II, A. J. Sedlacek, K. W. Fischer, eds., Proc. SPIE3127, 42–52 (1997).
[Crossref]

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[Crossref]

W. R. Skinner, P. B. Hays, “A comparative study of coherent and incoherent Doppler lidar techniques,” Marshall Space Flight Center Study Report, contract NAS8-38775 (University of Michigan, Ann Arbor, Mich., 1994). The equation in this publication is in error by a factor √2 [confirmed by W. R. Skinner, University of Michigan, Ann Arbor, Mich. 48109 (personal communication, 1997)].

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Figures (3)

Fig. 1
Fig. 1

Calculated Doppler measurement uncertainty, as a ratio to the Cramer–Rao limit for a perfect receiver. Each contour is for a specified ratio of Gaussian (G) source width (1/e) to etalon free spectral range. Contours of constant finesse and the operating point selected by McGill and Spinhirne’s optimization of the Rayleigh analyzer R are shown.

Fig. 2
Fig. 2

Calculated measurement uncertainty (standard deviation) for a fringe imaging Doppler analyzer using Rayleigh backscatter, with etalon parameters proposed by McGill and Spinhirne. The dependence on source signal amplitude is merely the 1/√N characteristic of Poisson statistics. The modeling technique presented in this research agrees closely with McGill’s previous research. LOS, line of sight.

Fig. 3
Fig. 3

Calculated Doppler measurement uncertainty for a fringe imaging aerosol backscatter analyzer for McGill and Spinhirne’s FPI parameters and 1000 potential photocounts versus the ratio of aerosol-to-Rayleigh backscatter coefficients. The Rayleigh noise is large for the backscatter ratios assumed here. The modeling of this research yields uncertainty estimates somewhat higher than obtained by McGill and Spinhirne. LOS, line of sight.

Tables (1)

Tables Icon

Table 1 Etalon Parameters Assumed by McGill and Spinhirne for Aerosol and Rayleigh Fringe Imager Doppler Uncertainty Modelinga

Equations (12)

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δ ν 2 = - ν i 2 S ν i -   S ν i 2 ,
δ ν = Δ ν e 2 N 1 / 2 ,
S i = T 0 N 0 1 + 2   k = 1   R k exp - π k Δ ν e / Δ ν fsr 2 × cos 2 π k ν cos   θ i / Δ ν fsr Δ ν Δ ν fsr ,
T 0 = 1 - A 1 - R 2 1 - R 1 + R ,
S i = T 0 N 0 1 + 2   k = 1   R k exp - π k Δ ν e / Δ ν fsr 2 × cos 2 π k Δ m i Δ m ,
Δ m i = ν - ν 0 Δ ν fsr - ν 0 Δ ν fsr θ i 2 2 + m 0 ,
δ ν 2 = Δ m T 0 2 N 0 2 i ν i 2 S i .
S i = N 0 π Δ ν fsr Δ ν e exp - ν i - ν 0 2 / Δ ν e 2 Δ m ,
δ ν = Δ ν e 2 N 0 1 / 2 ,
δ ν - ν 0 = c λ 2 j = 1 K SNR j 2 1 N d N d λ j 2 - 1 / 2 ,
A Ω = π D FPI 2 2 λ e 0 ,
F ap = π D FPI 2 2 λ e 0 1 A Ω ,

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