Abstract

The theoretical performance of a Mach–Zehnder interferometer used as a spectral analyzer for wind-speed measurement by direct-detection Doppler lidar is presented. The interferometer is optimized for measurement of wind velocity from the signal backscattered by the molecules. Two arrangements are proposed, involving two detection channels (DMZ) or four detection channels (QMZ). Using the assumption of a pure molecular signal with a Gaussian spectral profile, we derive an analytic expression for the standard deviation of the measurement error for each arrangement. They are then compared with the ideal spectral analyzer (ISA) and with the double-edge Fabry–Perot (DFP) in the case of a shot-noise-limited signal. The DMZ measurement error is shown to be only 1.65 times that of the ISA and is 1.4 times lower than that given by the DFP. The QMZ arrangement provides a measurement that is insensitive to the aerosol scattering contribution but gives a measurement error that is 1.4 times higher than that of the DMZ.

© 2001 Optical Society of America

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References

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  1. M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
    [CrossRef]
  2. R. T. Menzies, “Doppler lidar atmospheric wind sensors: a comparative performance evaluation for global measurement applications from earth orbit,” Appl. Opt. 25, 2546–2553 (1986).
    [CrossRef] [PubMed]
  3. B. J. Rye, “Comparative precision of distributed-backscatter Doppler lidars,” Appl. Opt. 34, 8341–8344 (1995).
    [CrossRef] [PubMed]
  4. European Space Agency/Earth Sciences Division, P. Ingman, “The four candidate Earth explorer core missions—atmospheric dynamics,” , B. Battrick, ed. (ESA Publication Division, European Space Research and Technology Center, Noordwijk, The Netherlands, July1999).
  5. V. J. Abreu, J. E. Barnes, P. B. Hays, “Observations of winds with an incoherent lidar detector,” Appl. Opt. 31, 4509–4514 (1992).
    [CrossRef] [PubMed]
  6. D. Rees, I. S. McDermid, “Doppler lidar atmospheric wind sensor: reevaluation of a 355-nm incoherent Doppler lidar,” Appl. Opt. 29, 4133–4144 (1990).
    [CrossRef] [PubMed]
  7. S. H. Bloom, R. Kremer, P. A. Searcy, M. Rivers, J. Menders, E. Korevaar, “Long-range, noncoherent laser Doppler velocimeter,” Opt. Lett. 16, 1794–1796 (1991).
    [CrossRef] [PubMed]
  8. A. Garnier, M.-L. Chanin, “Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere,” Appl. Phys. B 55, 35–40 (1992).
    [CrossRef]
  9. C. L. Korb, B. M. Gentry, C. Y. Weng, “Edge technique: theory and application to the lidar measurement of atmospheric wind,” Appl. Opt. 31, 4202–4213 (1992).
    [CrossRef] [PubMed]
  10. B. M. Gentry, C. L. Korb, “Edge technique for high-accuracy Doppler velocimetry,” Appl. Opt. 33, 5770–5777 (1994).
    [CrossRef] [PubMed]
  11. C. L. Korb, B. M. Gentry, S. X. Xingfu Li, “Edge technique Doppler lidar wind measurements with high vertical resolution,” Appl. Opt. 36, 5976–5983 (1997).
    [CrossRef] [PubMed]
  12. C. Souprayen, A. Garnier, A. Hertzog, A. Hauchecorne, J. Porteneuve, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. I. Instrumental setup, validation, and first climatological results,” Appl. Opt. 38, 2410–2421 (1999).
    [CrossRef]
  13. C. Souprayen, A. Garnier, A. Hertzog, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. II. Mie scattering effect, theory, and calibration,” Appl. Opt. 38, 2422–2431 (1999).
    [CrossRef]
  14. C. Flesia, C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
    [CrossRef]
  15. M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng. 37, 2675–2686 (1998).
    [CrossRef]
  16. J. A. McKay, “Modeling of direct detection Doppler wind lidar. I. The edge technique,” Appl. Opt. 37, 6480–6486 (1998).
    [CrossRef]
  17. J. A. McKay, “Modeling of direct detection Doppler wind lidar. II. The fringe imaging technique,” Appl. Opt. 37, 6487–6493 (1998).
    [CrossRef]
  18. J. M. Vaughan, “Wind lidar: fundamental review of heterodyne and direct detection methods,” (Defense Evaluation and Research Agency, Farnborough, Hamphire, UK, 1999).
  19. Z. Liu, T. Kobayashi, “Differential discrimination technique for incoherent Doppler lidar to measure atmospheric wind and backscatter ratio,” Opt. Rev. 3, 47–52 (1996).
    [CrossRef]
  20. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]
  21. J.-M. Gagné, J.-P. Saint-Dizier, M. Picard, “Méthode d’échantillonnage des fonctions déterministes en spectroscopie: application à un spectromètre multicanal par comptage photonique,” Appl. Opt. 13, 581–588 (1974).
    [CrossRef]
  22. 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 Sens. 31, 16–27 (1993).
    [CrossRef]
  23. R. Chabbal, “Finesse limite d’un Fabry–Perot formé de lames imparfaites,” J. Phys. Rad. 19, 295–299 (1958).
    [CrossRef]
  24. P. Jacquinot, “The luminosity of spectrometers with prisms, gratings or Fabry–Perot etalons,” J. Opt. Soc. Am. 44, 761–765 (1954).
    [CrossRef]

1999 (3)

1998 (3)

1997 (1)

1996 (1)

Z. Liu, T. Kobayashi, “Differential discrimination technique for incoherent Doppler lidar to measure atmospheric wind and backscatter ratio,” Opt. Rev. 3, 47–52 (1996).
[CrossRef]

1995 (1)

1994 (1)

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 Sens. 31, 16–27 (1993).
[CrossRef]

1992 (3)

1991 (1)

1990 (1)

1989 (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

1986 (1)

1981 (1)

1974 (1)

1958 (1)

R. Chabbal, “Finesse limite d’un Fabry–Perot formé de lames imparfaites,” J. Phys. Rad. 19, 295–299 (1958).
[CrossRef]

1954 (1)

Abreu, V. J.

Barnes, J. E.

Bloom, S. H.

Chabbal, R.

R. Chabbal, “Finesse limite d’un Fabry–Perot formé de lames imparfaites,” J. Phys. Rad. 19, 295–299 (1958).
[CrossRef]

Chanin, M. L.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Chanin, M.-L.

A. Garnier, M.-L. Chanin, “Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere,” Appl. Phys. B 55, 35–40 (1992).
[CrossRef]

Flesia, C.

Gagné, J.-M.

Garnier, A.

C. Souprayen, A. Garnier, A. Hertzog, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. II. Mie scattering effect, theory, and calibration,” Appl. Opt. 38, 2422–2431 (1999).
[CrossRef]

C. Souprayen, A. Garnier, A. Hertzog, A. Hauchecorne, J. Porteneuve, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. I. Instrumental setup, validation, and first climatological results,” Appl. Opt. 38, 2410–2421 (1999).
[CrossRef]

A. Garnier, M.-L. Chanin, “Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere,” Appl. Phys. B 55, 35–40 (1992).
[CrossRef]

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Gentry, B. M.

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 Sens. 31, 16–27 (1993).
[CrossRef]

Hauchecorne, A.

Hays, P. B.

Hertzog, A.

Ingman, P.

European Space Agency/Earth Sciences Division, P. Ingman, “The four candidate Earth explorer core missions—atmospheric dynamics,” , B. Battrick, ed. (ESA Publication Division, European Space Research and Technology Center, Noordwijk, The Netherlands, July1999).

Jacquinot, P.

Klett, J. D.

Kobayashi, T.

Z. Liu, T. Kobayashi, “Differential discrimination technique for incoherent Doppler lidar to measure atmospheric wind and backscatter ratio,” Opt. Rev. 3, 47–52 (1996).
[CrossRef]

Korb, C. L.

Korevaar, E.

Kremer, R.

Liu, Z.

Z. Liu, T. Kobayashi, “Differential discrimination technique for incoherent Doppler lidar to measure atmospheric wind and backscatter ratio,” Opt. Rev. 3, 47–52 (1996).
[CrossRef]

McDermid, I. S.

McGill, M. J.

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng. 37, 2675–2686 (1998).
[CrossRef]

McKay, J. A.

Menders, J.

Menzies, R. T.

Picard, M.

Porteneuve, J.

Rees, D.

Rivers, M.

Rye, B. J.

B. J. Rye, “Comparative precision of distributed-backscatter Doppler lidars,” Appl. Opt. 34, 8341–8344 (1995).
[CrossRef] [PubMed]

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 Sens. 31, 16–27 (1993).
[CrossRef]

Saint-Dizier, J.-P.

Searcy, P. A.

Souprayen, C.

Spinhirne, J. D.

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng. 37, 2675–2686 (1998).
[CrossRef]

Vaughan, J. M.

J. M. Vaughan, “Wind lidar: fundamental review of heterodyne and direct detection methods,” (Defense Evaluation and Research Agency, Farnborough, Hamphire, UK, 1999).

Weng, C. Y.

Xingfu Li, S. X.

Appl. Opt. (14)

J.-M. Gagné, J.-P. Saint-Dizier, M. Picard, “Méthode d’échantillonnage des fonctions déterministes en spectroscopie: application à un spectromètre multicanal par comptage photonique,” Appl. Opt. 13, 581–588 (1974).
[CrossRef]

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef] [PubMed]

R. T. Menzies, “Doppler lidar atmospheric wind sensors: a comparative performance evaluation for global measurement applications from earth orbit,” Appl. Opt. 25, 2546–2553 (1986).
[CrossRef] [PubMed]

D. Rees, I. S. McDermid, “Doppler lidar atmospheric wind sensor: reevaluation of a 355-nm incoherent Doppler lidar,” Appl. Opt. 29, 4133–4144 (1990).
[CrossRef] [PubMed]

C. L. Korb, B. M. Gentry, C. Y. Weng, “Edge technique: theory and application to the lidar measurement of atmospheric wind,” Appl. Opt. 31, 4202–4213 (1992).
[CrossRef] [PubMed]

V. J. Abreu, J. E. Barnes, P. B. Hays, “Observations of winds with an incoherent lidar detector,” Appl. Opt. 31, 4509–4514 (1992).
[CrossRef] [PubMed]

B. M. Gentry, C. L. Korb, “Edge technique for high-accuracy Doppler velocimetry,” Appl. Opt. 33, 5770–5777 (1994).
[CrossRef] [PubMed]

C. L. Korb, B. M. Gentry, S. X. Xingfu Li, “Edge technique Doppler lidar wind measurements with high vertical resolution,” Appl. Opt. 36, 5976–5983 (1997).
[CrossRef] [PubMed]

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

J. A. McKay, “Modeling of direct detection Doppler wind lidar. II. The fringe imaging technique,” Appl. Opt. 37, 6487–6493 (1998).
[CrossRef]

B. J. Rye, “Comparative precision of distributed-backscatter Doppler lidars,” Appl. Opt. 34, 8341–8344 (1995).
[CrossRef] [PubMed]

C. Flesia, C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
[CrossRef]

C. Souprayen, A. Garnier, A. Hertzog, A. Hauchecorne, J. Porteneuve, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. I. Instrumental setup, validation, and first climatological results,” Appl. Opt. 38, 2410–2421 (1999).
[CrossRef]

C. Souprayen, A. Garnier, A. Hertzog, “Rayleigh–Mie Doppler wind lidar for atmospheric measurements. II. Mie scattering effect, theory, and calibration,” Appl. Opt. 38, 2422–2431 (1999).
[CrossRef]

Appl. Phys. B (1)

A. Garnier, M.-L. Chanin, “Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere,” Appl. Phys. B 55, 35–40 (1992).
[CrossRef]

Geophys. Res. Lett. (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (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 Sens. 31, 16–27 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Rad. (1)

R. Chabbal, “Finesse limite d’un Fabry–Perot formé de lames imparfaites,” J. Phys. Rad. 19, 295–299 (1958).
[CrossRef]

Opt. Eng. (1)

M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng. 37, 2675–2686 (1998).
[CrossRef]

Opt. Lett. (1)

Opt. Rev. (1)

Z. Liu, T. Kobayashi, “Differential discrimination technique for incoherent Doppler lidar to measure atmospheric wind and backscatter ratio,” Opt. Rev. 3, 47–52 (1996).
[CrossRef]

Other (2)

J. M. Vaughan, “Wind lidar: fundamental review of heterodyne and direct detection methods,” (Defense Evaluation and Research Agency, Farnborough, Hamphire, UK, 1999).

European Space Agency/Earth Sciences Division, P. Ingman, “The four candidate Earth explorer core missions—atmospheric dynamics,” , B. Battrick, ed. (ESA Publication Division, European Space Research and Technology Center, Noordwijk, The Netherlands, July1999).

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Figures (8)

Fig. 1
Fig. 1

Optical arrangement of the DMZ interferometer: BS, beam splitter; M, mirror; D1, D2, detectors.

Fig. 2
Fig. 2

Transmission of the DMZ channels, dashed curve, and the Rayleigh signal spectral distribution, solid curve, as a function of σ/γ.

Fig. 3
Fig. 3

Signal delivered by each channel of the DMZ, QMZ, and DFP analyzers for the Rayleigh distribution as a function of the normalized wind velocity.

Fig. 4
Fig. 4

Discriminator signal of the DMZ, QMZ, and DFP analyzers for the Rayleigh distribution as a function of the normalized wind velocity.

Fig. 5
Fig. 5

Optical arrangement of the QMZ interferometer.

Fig. 6
Fig. 6

Transmission of the QMZ channels, dashed curves, and Rayleigh signal spectral distribution, solid curves, as a function of σ/γ.

Fig. 7
Fig. 7

ISA-normalized standard deviation of the wind-velocity measurement error as a function of the normalized wind velocity.

Fig. 8
Fig. 8

Transmission of the DFP channels, dashed curve, and the Rayleigh signal spectral distribution, solid curve, as a function of σ/γ.

Equations (61)

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σ=σ01+2uc,
INσ=1γπexp-σ-σ2γ2,
γ=2σ0c2kTm1/2,
u=ukT0m-1/2.
T1σ=sin2π σδ,  T2σ=cos2π σδ,
S1σ=sIσT1σ, S2σ=sIσT2σ,
Q=S1-S2S1+S2.
δOPT=4πσ0ckT0m1/2.
S1=121+sin ue,  S2=121-sin ue,
Q=sin ue,
εuDMZ=1SNRe1+1+eetan2 u1/2,
Rβr=βRr+βMrβRr
ur=arcsinRβrQrexp-Tr2T0+Rβr-1.
δuuδRβRβ1-exp-T2T0+δT2T0exp-T2T0Rβ-1+exp-T2T0.
T1=P sin2πσδ,T2=P cos2πσδ,T3=1-Psin2πσδ+π4,T4=1-Pcos2πσδ+π4.
Q=S1-S2S1+S2S3-S4S3+S4-1.
S1=121+sin ue,S2=121-sin ue,S3=121+cos ue,S4=121-cos ue.
Q=tan u
εuQMZ=1SNR2e1+12esin2 2u1/2.
εσISA=γ2ηN¯-1/2.
εuISA=ηN¯-1/2,
SNR=ηN¯1/2.
T1σ=Aσ-σS,  T2σ=Aσ+σS,
Aσ1+σ/δP2-1,
S1=12 INAσ-σS, S2=12 INAσ+σS.
τR0.25.
εuDFPu=01.2SNRDFP,
SNRDFP=ητRN¯1/2,
εuDFPu=0=2.4ηN¯-1/2=2.4εuISA.
εuDFP1.4εuDMZ.
N¯PDFP2N¯PDMZ.
SNR=ητRN¯1+τBτRN¯BN¯1/2,
S1=1γπexp-σ2γ2sin2πσδ,S2=1γπexp-σ2γ2cos2πσδ.
S1=121-exp-π2γ2δ2cos2πσδ,S2=121+exp-π2γ2δ2cos2πσδ.
Q=S1-S2S1+S2=-exp-π2γ2δ2cos2πσδ.
Qu=-exp-πγδ2cos2πσ0δ1+2uc.
Q¯S¯1-S¯2S¯1+S¯2,
varQQ¯2varS1-S2S¯1-S¯22+varS1+S2S¯1+S¯22,
εQ=varQ1/2=1+Q¯21/2SNR,
SNR=S¯1+S¯2varS1+varS21/2.
εu=εQdQdu-1=1+Q¯21/2SNRdQdu-1.
σ0=2k+1δ/4.
δOPT=2πγ=4.44γ.
S1=121-exp-T/2T0sin u,S2=121+exp-T/2T0sin u,
Q=exp-T/2T0sin u,
S1=P21-exp-π2γ2δ2cos2πσδ,S2=P21+exp-π2γ2δ2cos2πσδ,S3=1-P21+exp-π2γ2δ2sin2πσδ,S4=1-P21-exp-π2γ2δ2sin2πσδ.
Q1=S1-S2S1+S2=-exp-π2γ2δ2cos2πσδ,Q2=S3-S4S3+S4=exp-π2γ2δ2sin2πσδ
Q=Q1Q2=-cot2πσδ.
varQQ¯2varQ1Q¯12+varQ2Q¯22Q¯21+Q¯12Q¯12SNR12+1+Q¯22Q¯22SNR22,
SNR=i=14 S¯ii=14varSi1/2.
εQ=varQ1/2=2Q¯SNR2+Q¯1-2+Q¯2-21/2,
εu=εQdQdu-1=2Q¯2+Q¯1-2+Q¯2-21/2SNRdQdu-1.
σ0=2k+1δ4, δOPT=2πγ=4.44γ.
S1=121+exp-T/2T0sin u,S2=121-exp-T/2T0sin u,S3=121+exp-T/2T0cos u),S4=12 [1-exp-T/2T0cos u,
τRMZI=τBMZI=1
τRDFP0.25, τRDFP=1-R1+R,
εuDFPεuDMZu=0=1.2eτRDFP1+N¯BN¯1+τBDFPτRDFPN¯BN¯1/2.
εuDFPεuDMZu=0=1.2eτRDFPτBDFP1/2.
τBDPF<0.12,
R>0.8.
N¯B/N¯>2.

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