Abstract

The application of heterodyne lidar to observe molecular scattering is considered. Despite the reduced Rayleigh cross section, infrared systems are predicted to require mean power levels comparable with those of current and proposed direct detection lidars that operate with the thermally broadened spectra in the visible or ultraviolet. Rayleigh–Brillouin scattering in the kinetic and hydrodynamic (collisional) regimes encountered in the infrared is of particular interest because the observed spectrum approaches a triplet of relatively narrow lines that are more suitable for wind, temperature, and pressure measurements.

© 1998 Optical Society of America

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References

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  1. J. A. Lock, R. G. Seasholtz, W. T. John, “Rayleigh-Brillouin scattering to determine one-dimensional temperature and number density profiles of a gas flow field,” Appl. Opt. 31, 2839–2848 (1992).
    [CrossRef] [PubMed]
  2. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: Incoherent spectral accumulation and the Cramer-Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
    [CrossRef]
  3. S. Yip, “Rayleigh scattering in dilute gases,” J. Acous. Soc. Am. 49, 941–949 (1970).
    [CrossRef]
  4. R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
    [CrossRef]
  5. A. T. Young, G. W. Kattawar, “Rayleigh scattering line profiles,” Appl. Opt. 22, 3668–3670 (1983).
    [CrossRef] [PubMed]
  6. H. Shimizu, S. A. Lee, C. Y. She, “High spectral resolution lidar system with atomic blocking filters for measuring atmospheric parameters,” Appl. Opt. 22, 1373–1381 (1983).
    [CrossRef] [PubMed]
  7. J. N. Forkey, “Development and demonstration of filtered Rayleigh scattering: a laser-based flow diagnostic for planar measurement of velocity,” Ph.D. dissertation (Princeton University, Princeton N.J., 1996).
  8. G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).
  9. R. P. Sandoval, R. L. Armstrong, “Rayleigh-Brillouin scattering in molecular nitrogen,” Phys. Rev. A 13, 752–757 (1976).
    [CrossRef]
  10. Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
    [CrossRef]
  11. E. Holzhauer, “Forward scattering at 10.6 μm using light mixing to measure the ion temperature in a hydrogen arc plasma,” Phys. Lett. A 62, 495–497 (1997).
    [CrossRef]
  12. R. E. Slusher, C. M. Surko, “Study of density fluctuations in plasmas by small-angle CO2 laser scattering,” Phys. Fluids 23, 472–490 (1980).
    [CrossRef]
  13. R. G. Frehlich, “Cramer-Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
    [CrossRef]
  14. B. J. Rye, “The reference range for atmospheric backscatter lidar,” Opt. Quantum Electron. 11, 441–446 (1979).
    [CrossRef]
  15. R. T. H. Collins, P. B. Russell, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed., Vol. 14 of Topics in Applied Physics, (Springer-Verlag, Berlin, 1976).
    [CrossRef]
  16. 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]
  17. B. J. Rye, R. M. Hardesty, “Estimate optimization parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 36, 9425–9436 (1997); errata, 37, 4016 (1998).
  18. V. Hasson, F. Corbett, “Long-range coherent frequency agile laser radars for precision tracking, imaging, and chemical detection applications,” in Proceedings of the Ninth Conference on Coherent Laser Radar (Swedish Defence Research Establishment, Linkoping, Sweden, 1997), p. W1.
  19. D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
    [CrossRef]
  20. W. B. Davenport, W. T. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

1997 (3)

R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
[CrossRef]

E. Holzhauer, “Forward scattering at 10.6 μm using light mixing to measure the ion temperature in a hydrogen arc plasma,” Phys. Lett. A 62, 495–497 (1997).
[CrossRef]

B. J. Rye, R. M. Hardesty, “Estimate optimization parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 36, 9425–9436 (1997); errata, 37, 4016 (1998).

1993 (2)

R. G. Frehlich, “Cramer-Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

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

1992 (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]

1983 (2)

1980 (1)

R. E. Slusher, C. M. Surko, “Study of density fluctuations in plasmas by small-angle CO2 laser scattering,” Phys. Fluids 23, 472–490 (1980).
[CrossRef]

1979 (2)

B. J. Rye, “The reference range for atmospheric backscatter lidar,” Opt. Quantum Electron. 11, 441–446 (1979).
[CrossRef]

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

1976 (2)

R. P. Sandoval, R. L. Armstrong, “Rayleigh-Brillouin scattering in molecular nitrogen,” Phys. Rev. A 13, 752–757 (1976).
[CrossRef]

Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
[CrossRef]

1974 (1)

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

1970 (1)

S. Yip, “Rayleigh scattering in dilute gases,” J. Acous. Soc. Am. 49, 941–949 (1970).
[CrossRef]

Armstrong, R. L.

R. P. Sandoval, R. L. Armstrong, “Rayleigh-Brillouin scattering in molecular nitrogen,” Phys. Rev. A 13, 752–757 (1976).
[CrossRef]

Boley, C. D.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Buggele, A. E.

R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
[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]

Chu, B.

Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
[CrossRef]

Collins, R. T. H.

R. T. H. Collins, P. B. Russell, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed., Vol. 14 of Topics in Applied Physics, (Springer-Verlag, Berlin, 1976).
[CrossRef]

Corbett, F.

V. Hasson, F. Corbett, “Long-range coherent frequency agile laser radars for precision tracking, imaging, and chemical detection applications,” in Proceedings of the Ninth Conference on Coherent Laser Radar (Swedish Defence Research Establishment, Linkoping, Sweden, 1997), p. W1.

Davenport, W. B.

W. B. Davenport, W. T. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

Desai, R. C.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Forkey, J. N.

J. N. Forkey, “Development and demonstration of filtered Rayleigh scattering: a laser-based flow diagnostic for planar measurement of velocity,” Ph.D. dissertation (Princeton University, Princeton N.J., 1996).

Frehlich, R. G.

R. G. Frehlich, “Cramer-Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

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]

Hardesty, R. M.

B. J. Rye, R. M. Hardesty, “Estimate optimization parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 36, 9425–9436 (1997); errata, 37, 4016 (1998).

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

Hasson, V.

V. Hasson, F. Corbett, “Long-range coherent frequency agile laser radars for precision tracking, imaging, and chemical detection applications,” in Proceedings of the Ninth Conference on Coherent Laser Radar (Swedish Defence Research Establishment, Linkoping, Sweden, 1997), p. W1.

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]

Holzhauer, E.

E. Holzhauer, “Forward scattering at 10.6 μm using light mixing to measure the ion temperature in a hydrogen arc plasma,” Phys. Lett. A 62, 495–497 (1997).
[CrossRef]

John, W. T.

Kattawar, G. W.

Lao, Q. H.

Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
[CrossRef]

Lee, S. A.

Lock, J. A.

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]

Reeder, M. F.

R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
[CrossRef]

Root, W. T.

W. B. Davenport, W. T. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

Russell, P. B.

R. T. H. Collins, P. B. Russell, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed., Vol. 14 of Topics in Applied Physics, (Springer-Verlag, Berlin, 1976).
[CrossRef]

Rye, B. J.

B. J. Rye, R. M. Hardesty, “Estimate optimization parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 36, 9425–9436 (1997); errata, 37, 4016 (1998).

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

B. J. Rye, “The reference range for atmospheric backscatter lidar,” Opt. Quantum Electron. 11, 441–446 (1979).
[CrossRef]

Sandoval, R. P.

R. P. Sandoval, R. L. Armstrong, “Rayleigh-Brillouin scattering in molecular nitrogen,” Phys. Rev. A 13, 752–757 (1976).
[CrossRef]

Schoen, P. E.

Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
[CrossRef]

Seasholtz, R. G.

R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
[CrossRef]

J. A. Lock, R. G. Seasholtz, W. T. John, “Rayleigh-Brillouin scattering to determine one-dimensional temperature and number density profiles of a gas flow field,” Appl. Opt. 31, 2839–2848 (1992).
[CrossRef] [PubMed]

She, C. Y.

Shimizu, H.

Slusher, R. E.

R. E. Slusher, C. M. Surko, “Study of density fluctuations in plasmas by small-angle CO2 laser scattering,” Phys. Fluids 23, 472–490 (1980).
[CrossRef]

Surko, C. M.

R. E. Slusher, C. M. Surko, “Study of density fluctuations in plasmas by small-angle CO2 laser scattering,” Phys. Fluids 23, 472–490 (1980).
[CrossRef]

Tenti, G.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Yip, S.

S. Yip, “Rayleigh scattering in dilute gases,” J. Acous. Soc. Am. 49, 941–949 (1970).
[CrossRef]

Young, A. T.

Zrnic, D. S.

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

Appl. Opt. (4)

Can. J. Phys. (1)

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

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. Electron. (1)

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (2)

R. G. Frehlich, “Cramer-Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

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

J. Acous. Soc. Am. (1)

S. Yip, “Rayleigh scattering in dilute gases,” J. Acous. Soc. Am. 49, 941–949 (1970).
[CrossRef]

J. Chem. Phys. (1)

Q. H. Lao, P. E. Schoen, B. Chu, “Rayleigh-Brillouin scattering of gases with internal relaxation,” J. Chem. Phys. 64, 3547–3554 (1976).
[CrossRef]

Opt. Lasers (1)

R. G. Seasholtz, A. E. Buggele, M. F. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers 27, 543–570 (1997).
[CrossRef]

Opt. Quantum Electron. (1)

B. J. Rye, “The reference range for atmospheric backscatter lidar,” Opt. Quantum Electron. 11, 441–446 (1979).
[CrossRef]

Phys. Fluids (1)

R. E. Slusher, C. M. Surko, “Study of density fluctuations in plasmas by small-angle CO2 laser scattering,” Phys. Fluids 23, 472–490 (1980).
[CrossRef]

Phys. Lett. A (1)

E. Holzhauer, “Forward scattering at 10.6 μm using light mixing to measure the ion temperature in a hydrogen arc plasma,” Phys. Lett. A 62, 495–497 (1997).
[CrossRef]

Phys. Rev. A (1)

R. P. Sandoval, R. L. Armstrong, “Rayleigh-Brillouin scattering in molecular nitrogen,” Phys. Rev. A 13, 752–757 (1976).
[CrossRef]

Other (4)

J. N. Forkey, “Development and demonstration of filtered Rayleigh scattering: a laser-based flow diagnostic for planar measurement of velocity,” Ph.D. dissertation (Princeton University, Princeton N.J., 1996).

R. T. H. Collins, P. B. Russell, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed., Vol. 14 of Topics in Applied Physics, (Springer-Verlag, Berlin, 1976).
[CrossRef]

V. Hasson, F. Corbett, “Long-range coherent frequency agile laser radars for precision tracking, imaging, and chemical detection applications,” in Proceedings of the Ninth Conference on Coherent Laser Radar (Swedish Defence Research Establishment, Linkoping, Sweden, 1997), p. W1.

W. B. Davenport, W. T. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

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Figures (6)

Fig. 1
Fig. 1

Altitude at which the Rayleigh-scattering parameter y = 1 for backscatter lidar [Eq. (2)], or (equivalently) at which λ = 2Λmfp, where the collisional mean free path Λmfp is calculated using temperature and pressure values obtained from the U.S. Standard Atmosphere model. To the right of the curve, scattering is in the collisional or hydrodynamic regime whereas to the left of the curve it is relatively unaffected by collisions.

Fig. 2
Fig. 2

Spectra predicted using Tenti’s S6 theory for the backscatter signal at two altitudes with pressure and temperature obtained from the U.S. Standard Atmosphere model. The altitudes are 3 km (solid curve) and 10 km (dashed curve). The lidar wavelengths are (a) 0.355, (b) 2.1, and (c) 10.6 μm. The atmosphere is assumed to consist entirely of N2. At shorter wavelengths and higher altitudes, where y < 1 [Eq. (2)] and collisions have little influence, the spectral profile tends toward a thermally broadened Gaussian. At longer wavelengths and lower altitudes, collisions cause the spectrum to become, in the limit, a triplet of three Lorentzians, of which the outer (Brillouin) curves represent scattering from thermally generated sound waves.

Fig. 3
Fig. 3

Frequency separation of the peaks of the Brillouin sidebands (expressed as a velocity) calculated using Tenti’s S6 theory for a 10-μm backscatter lidar as a function of temperature. The points correspond to temperatures in the U.S. Standard Atmosphere at different altitudes (shown in kilometers). The pressures assumed correspond to the U.S. Standard Atmosphere values at the same altitudes (continuous line) and pressures 10% above an below these values (dashed lines). The lines show that sideband separation is essentially a function of temperature and is almost independent of pressure.

Fig. 4
Fig. 4

Number of lidar pulses n needed under stationary conditions to secure a standard deviation in the Doppler-shift estimate of 1 m/s by use of a ground-based heterodyne lidar. For the solid curve plots, the lidar parameters are those listed in Table 1. The wavelengths are 0.355 μm (x’s), 2 μm (filled squares), and 10.6 μm with an output energy of 1 J (open squares). The dashed curve corresponds to the same 10.6-μm system with an output energy increased to 30 J; similar improvement could be obtained by increasing the throughput of the other systems by 30 times. In each case the range gate is 1 km (for a 100-m gate the required pulse count increases by a factor of approximately 10).

Fig. 5
Fig. 5

Effective photocount needed to obtain the results of Fig. 4, showing that (i) the photocount needed to make a measurement is reduced by using lidar wavelengths in the collisional regime (y > 1) where the spectra are more highly structured; and (ii) for the infrared systems, the minima that indicate that the proposed lidar parameters encompass the optimal operating point for a heterodyne system (see Appendix A). The symbols represent the same lidar parameters as in Fig. 4.

Fig. 6
Fig. 6

Plot of estimate variance against signal energy or photocount, which is intended to illustrate the argument in Appendix A showing why the curves in Fig. 5 approximate tuning curves and to clarify the optimization criteria for heterodyne systems. The straight line labeled ideal represents the variance of an optimal optical Doppler estimator limited by signal shot noise [Eq. (1)]. The heavy continuous curve (1 pulse) is a schematic of the variance of a heterodyne estimator obtained by use of a single lidar pulse, and the dashed curve (n pulses) is the variance obtained by use of several pulses.

Tables (1)

Tables Icon

Table 1 Parameters of the Three Heterodyne Lidarsa

Equations (5)

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σ ν 2 = Λ F 2 2 N ,
y = Λ / Λ mfp ,
σ het 2 = F S 2 4 π 2 i = 0 M - 1 k = 0 M - 1 i - k 2 q ik γ ki .
x = Λ 2 k B T / m mol 1 / 2   F ,
δ = P S h ν F S = η L A TR β cE / 2 r 2 h ν F S ,

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