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 the measurement of wind velocity from the signal that is backscattered by the molecules. In the proposed fringe-imaging Mach-Zehnder (FIMZ) interferometer, a pattern of equally spaced linear fringes is formed and detected by two conventional detector linear arrays. Assuming a pure molecular signal with Gaussian spectral profile, an analytic expression for the standard deviation of the measurement error is obtained and compared with the Cramer-Rao lower bound given by an ideal spectral analyzer (ISA) in the case of shot-noise-limited signal. The FIMZ measurement error is shown to be 2.3 times that of the ISA and is comparable with the error given by previously developed multichannel spectral analyzers that are based on Fabry-Perot interferometers that, in contrast, have the disadvantages of producing unequally spaced circular fringes and requiring dedicated detectors. The optimal path difference for a FIMZ operating at 355 nm is approximately 3 cm. The interferometer is shown to match important lidar beam étendues without significant performance reduction.

© 2002 Optical Society of America

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References

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  1. European Space Agency (Earth Sciences Division), “The four candidate Earth explorer core missions–atmospheric dynamics,” Report SP-1233 (4) (ESA Publication Division, Noordwijk, The Netherlands, 1999).
  2. 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]
  3. 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]
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    [CrossRef] [PubMed]
  5. C. Flesia, C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
    [CrossRef]
  6. 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]
  7. 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]
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    [CrossRef] [PubMed]
  9. M. J. McGill, W. R. Skinner, T. D. Irgang, “Analysis techniques for the recovery of winds and backscatter coefficients from a multiple-channel incoherent Doppler lidar,” Appl. Opt. 36, 1253–1268 (1997).
    [CrossRef] [PubMed]
  10. B. J. Rye, “Comparative precision of distributed-backscatter Doppler lidars,” Appl. Opt. 34, 8341–8344 (1995).
    [CrossRef] [PubMed]
  11. M. J. McGill, J. D. Spinhirne, “Comparison of two direct-detection Doppler lidar techniques,” Opt. Eng. 37, 2675–2686 (1998).
    [CrossRef]
  12. J. A. McKay, “Modeling of direct detection Doppler wind lidar. I. the edge technique,” Appl. Opt. 37, 6480–6486 (1998).
    [CrossRef]
  13. J. A. McKay, “Modeling of direct detection Doppler wind lidar. II. the fringe-imaging technique,” Appl. Opt. 37, 6487–6493 (1998).
    [CrossRef]
  14. J. M. Vaughan, “Wind lidar: fundamental review of heterodyne and direct detection methods,” Report DERA/EL/ID/CR992111/1.0 on European Space Agency Contract 12510/97/NL/RE (Defense Evaluation and Research Agency, Farnborough, Hampshire, U.K., 1999).
  15. D. Bruneau, “Mach-Zehnder interferometer as a spectral analyzer for molecular Doppler wind lidar,” Appl. Opt. 40, 391–399 (2001).
    [CrossRef]
  16. 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 Sen. 31, 16–27 (1993).
    [CrossRef]
  17. R. Chabbal, “Finesse limite d’un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958), in French.
    [CrossRef]
  18. M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975), pp. 291–300.

2001 (1)

1999 (1)

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)

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 Sen. 31, 16–27 (1993).
[CrossRef]

1992 (2)

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]

1958 (1)

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

Abreu, V. J.

Barnes, J. E.

Bloom, S. H.

Born, M.

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975), pp. 291–300.

Bruneau, D.

Chabbal, R.

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

Flesia, C.

Garnier, A.

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 Sen. 31, 16–27 (1993).
[CrossRef]

Hauchecorne, A.

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]

Hays, P. B.

Irgang, T. 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.

McKay, J. A.

Menders, J.

Porteneuve, J.

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]

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 Sen. 31, 16–27 (1993).
[CrossRef]

Searcy, P. A.

Skinner, W. R.

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,” Report DERA/EL/ID/CR992111/1.0 on European Space Agency Contract 12510/97/NL/RE (Defense Evaluation and Research Agency, Farnborough, Hampshire, U.K., 1999).

Weng, C. Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975), pp. 291–300.

Appl. Opt. (9)

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 Sen. (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 Sen. 31, 16–27 (1993).
[CrossRef]

J. Phys. Radium (1)

R. Chabbal, “Finesse limite d’un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958), in French.
[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 (3)

J. M. Vaughan, “Wind lidar: fundamental review of heterodyne and direct detection methods,” Report DERA/EL/ID/CR992111/1.0 on European Space Agency Contract 12510/97/NL/RE (Defense Evaluation and Research Agency, Farnborough, Hampshire, U.K., 1999).

European Space Agency (Earth Sciences Division), “The four candidate Earth explorer core missions–atmospheric dynamics,” Report SP-1233 (4) (ESA Publication Division, Noordwijk, The Netherlands, 1999).

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975), pp. 291–300.

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Figures (5)

Fig. 1
Fig. 1

Optical arrangement of the FMZ. S, source; L, collimation lens; BS1 and BS2, beam splitters; M, mirror; W, W′, and W″, optical wavefronts; D1 and D2, detectors.

Fig. 2
Fig. 2

Interference fringe pattern on (a) D 1 and (b) D 2.

Fig. 3
Fig. 3

Variation of [SNR.(∊ u′ )FMZ], with ℓ0γ.

Fig. 4
Fig. 4

Variation of the fringe modulation M with ℓ0γ.

Fig. 5
Fig. 5

Parameters for the fringe visibility study (Appendix B).

Equations (43)

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INσ=1γπ exp- σ-σ2γ2,
γ=2σ0c2kTm1/2,
δσ=σ-σ0=σ02uc σ0,
u=ukTm-1/2.
=0+θx,
T1σ=sin2πσ;  T2σ=cos2πσ.
Si=121+-1iM cos 2πσ,
M=exp-π22γ2
Siφ=121+-1iM cosφ+δφ
ϕ=2πσ00+θx,
δφ=2π0δσ=2π0σ02uc.
k-1dxj>kd
Si,j=1dj-1djd Sixdx.
Si,j=121+-1iMM cosφj+δφ,
φj=2πσ00+2j+12 θd,
M=sinπσ0θdπσ0θd
ni,j=ηN2P1+-1iMM cosφj+δφ+ηNB2P,
nj=n1,j-n2,j=- ηNPMM cosφj+δφ,
I1=j=1P nj cos φj,  I2=j=1P nj sin φj.
σ0θD=K,
δφ=-arctanI2I1.
δφ=2MM SNR-1
SNR=ηN1+NB/N1/2.
u=2Mc4πσ0expπ0γ0SNR-1.
p>10,  M1.
0=2πγ-1.
u=2ekTm1/2SNR-1.
uFMZ=2e1/2SNR-1.
uISA=ηN-1/2.
SNR=ηN1/2.
uFMZ=2e1/2uISA.
dδφ=I1dI2-I2dI1I12+I22.
dδφ=-2NMMdI1 sin δφ+dI2 cos δφ.
varδφ=2N¯MM2varI1sin2 δφ+varI2×cos2 δφ+covI1, I2sin 2δφ
varni,j=n¯i,j,
varI1=varI2=ηN¯+N¯B2,  covI1, I2=0.
varδφ=2M2M2N¯+N¯BηN¯2.
Δφ=2πσ0s2-s1,
Δφ=2πσ0βρ cos γ+ρ221R2-1R1,
Δφ=2πσ0αδT cos γ+α22 δL,
MS cosφ+Ψ=γ=02πα=0αScosφ+Δφαdαdγ,
MT=1-12πσ0δTαS2,
ML=1-112πσ0δLαS22.

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