Abstract

Atmospheric lidar techniques for the measurement of wind, temperature, and optical properties of aerosols as well as nonintrusive measurement techniques for temperature, density, and bulk velocity in gas flows rely on the exact knowledge of the spectral line shape of the scattered laser light on molecules. A mathematically complex, numerical model (Tenti S6 model) is currently the best model for describing these spectra. In this paper an easy processable, alternative analytical model for describing spontaneous Rayleigh–Brillouin spectra in air at atmospheric conditions is introduced. The deviations between the analytical and Tenti S6 models are shown to be smaller than 0.85%.

© 2011 Optical Society of America

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Errata

B. Witschas, "Analytical model for Rayleigh–Brillouin line shapes in air: errata," Appl. Opt. 50, 5758-5758 (2011)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-50-29-5758

References

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  1. O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
    [CrossRef]
  2. B. Y. Liu, M. Esselborn, M. Wirth, A. Fix, D. B. Bi, and G. Ehret, “Influence of molecular scattering models on aerosol optical properties measured by high spectral resolution lidar,” Appl. Opt. 48, 5143–5153 (2009).
    [CrossRef] [PubMed]
  3. Z.-S. Liu, D.-C. Bi, X.-Q. Song, J.-B. Xia, R.-Z. Li, Z.-J. Wang, and C.-Y. She, “Iodine-filter-based high spectral resolution lidar for atmospheric temperature measurements,” Opt. Lett. 34, 2712–2714 (2009).
    [CrossRef] [PubMed]
  4. G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
    [CrossRef]
  5. R. Seasholtz, A. Buggele, and M. Reeder, “Flow measurements based on Rayleigh scattering and Fabry-Perot interferometer,” Opt. Lasers Eng. 27, 543–570 (1997).
    [CrossRef]
  6. A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
    [CrossRef]
  7. G. Tenti, C. Boley, and R. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).
  8. J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, 1980), pp. 246–254.
  9. B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
    [CrossRef] [PubMed]
  10. M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
    [CrossRef]
  11. C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
    [CrossRef]
  12. J. Gustavsson, “Molecular velocity distribution in air,” http://plaza.ufl.edu/jgu/public_html/UF/AirMolVelDistr.pdf.
  13. Q. Zheng, “On the Rayleigh-Brillouin scattering in air,” Ph.D. dissertation (University of New Hampshire, 2004).
  14. H. Shimizu, K. Noguchi, and C. Y. She, “Atmospheric temperature measurement by a high spectral resolution lidar,” Appl. Opt. 25, 1460–1466 (1986).
    [CrossRef] [PubMed]
  15. T.D.Rossing, ed., Springer Handbook of Acoustics(Springer, 2007), p. 31.

2010

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

2009

2008

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

2001

G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
[CrossRef]

1997

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

1986

1974

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

1972

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Bi, D. B.

Bi, D.-C.

Boley, C.

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

Boley, C. D.

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Boon, J. P.

J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, 1980), pp. 246–254.

Buggele, A.

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

Carter, C.

G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
[CrossRef]

Dabas, A.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Dam, N. J.

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

de Wijn, A. S.

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

Denneulin, M.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Desai, R.

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

Desai, R. C.

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Dolfi-Bouteyre, A.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Ehret, G.

Elliott, G.

G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
[CrossRef]

Esselborn, M.

Fix, A.

Flamant, P.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Garnier, A.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Glumac, N.

G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
[CrossRef]

Gustavsson, J.

J. Gustavsson, “Molecular velocity distribution in air,” http://plaza.ufl.edu/jgu/public_html/UF/AirMolVelDistr.pdf.

Lemmerz, C.

O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
[CrossRef]

Li, R.-Z.

Liu, B. Y.

Liu, Z.-S.

Loth, C.

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Meijer, A.

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

Nagel, E.

O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
[CrossRef]

Noguchi, K.

Paffrath, U.

O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
[CrossRef]

Reeder, M.

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

Reitebuch, O.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
[CrossRef]

Seasholtz, R.

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

She, C. Y.

She, C.-Y.

Shimizu, H.

Song, X.-Q.

Tenti, G.

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

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Ubachs, W.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

van de Water, W.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

van Duijn, E. J.

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

van Duijn, E.-J.

Vieitez, M. O.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

Wang, Z.-J.

Wirth, M.

Witschas, B.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef] [PubMed]

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

Xia, J.-B.

Yip, S.

J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, 1980), pp. 246–254.

Zheng, Q.

Q. Zheng, “On the Rayleigh-Brillouin scattering in air,” Ph.D. dissertation (University of New Hampshire, 2004).

Appl. Opt.

Can. J. Phys.

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158 (1972).
[CrossRef]

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

J. Atmos. Ocean. Technol.

O. Reitebuch, C. Lemmerz, E. Nagel, and U. Paffrath, “The airborne demonstrator for the direct-detection Doppler wind lidar ALADIN on ADM-aeolus. Part I: Instrument design and comparison to satellite instrument,” J. Atmos. Ocean. Technol. 26, 2501–2515 (2009).
[CrossRef]

Meas. Sci. Technol.

G. Elliott, N. Glumac, and C. Carter, “Molecular filtered Rayleigh scattering applied to combustion,” Meas. Sci. Technol. 12, 452–466 (2001).
[CrossRef]

Opt. Lasers Eng.

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

Opt. Lett.

Phys. Rev. A

M. O. Vieitez, E. J. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 0438361–14 (2010).
[CrossRef]

Tellus A

A. Dabas, M. Denneulin, P. Flamant, C. Loth, A. Garnier, and A. Dolfi-Bouteyre, “Correcting winds measured with a Rayleigh Doppler lidar from pressure and temperature effects,” Tellus A 60, 206–215 (2008).
[CrossRef]

Other

J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, 1980), pp. 246–254.

J. Gustavsson, “Molecular velocity distribution in air,” http://plaza.ufl.edu/jgu/public_html/UF/AirMolVelDistr.pdf.

Q. Zheng, “On the Rayleigh-Brillouin scattering in air,” Ph.D. dissertation (University of New Hampshire, 2004).

T.D.Rossing, ed., Springer Handbook of Acoustics(Springer, 2007), p. 31.

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Figures (3)

Fig. 1
Fig. 1

Spectrum of SRB scattered light in air for y = 0.652 according to the Tenti S6 model (black dots). The gray line represents the superposition of a central Gaussian line with standard deviation σ R = 0.68 and integrated intensity A = 0.82 (dashed black line) and two shifted Gaussian lines at ± x B = 0.73 with standard deviation σ B = 0.28 , and integrated intensity ( 1 A ) / 2 = 0.09 (dotted black line). The Tenti modeled line shape as well as the superposition of the Gaussians is normalized to yield unity integrated intensity.

Fig. 2
Fig. 2

Integrated intensity A of the central peak (top, black diamonds), the standard deviation σ R of the central peak (bottom, black squares), the standard deviation σ B of the side peaks (bottom, black triangles) and the frequency shift x B of the side peaks (bottom, black circles), determined by applying Eq. (2) to a set of Tenti S6 modeled line shapes ( y = 0 1.027 ) in a least square fit procedure. The gray lines depict well fitting functions which are given by Eqs. (3, 4, 5, 6), respectively.

Fig. 3
Fig. 3

(Top) Tenti modeled line shapes for y = 0.108 (black square), y = 0.507 (black circles), y = 1.027 (black triangles), and the best fit of Eq. (2) in black, dark gray, and light gray, respectively. (Bottom) Residual between Tenti model and analytical model with respect to peak intensity.

Equations (6)

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

x = ω 2 k v 0 , y = n k B T 2 k v 0 η = p 2 k v 0 η ,
S ( x , y ) = 1 2 π σ R A exp [ 1 2 ( x σ R ) 2 ] + 1 A 2 2 π σ B exp [ 1 2 ( x + x B σ B ) 2 ] + 1 A 2 2 π σ B exp [ 1 2 ( x x B σ B ) 2 ] .
A ( y ) = 0.18526 · exp [ 1.31255 y ] + 0.07103 · exp [ 18.26117 y ] + 0.74421 ,
σ R ( y ) = 0.70813 + 0.16366 y 2 + 0.19132 y 3 0.07217 y 4 ,
σ B ( y ) = 0.07845 · exp [ 4.88663 y ] + 0.80400 · exp [ 0.15003 y ] 0.45142 ,
x B ( y ) = 0.80893 0.30208 · 0.10898 y

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