Abstract

Temperatures can be measured from relative intensities of rotational Raman or rotational coherent anti-Stokes Raman scattering (CARS) from ground and vibrationally excited molecules, provided that relative Raman line strengths are known. Here rotational Raman line strengths are calculated and corrected for vibrational anharmonicity, for N2, O2, CO, and H2. These line-strength-correction factors for vibrational anharmonicity have a pronounced effect on temperature calculations; they lower temperatures previously calculated from O2 rotational CARS intensities at ~3000 K by more than 300 K.

© 1982 Optical Society of America

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References

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  1. R. E. Teets, J. H. Bechtel, “Coherent anti-Stokes Raman spectra of oxygen atoms in flames,” Opt. Lett. 6, 458 (1981).
    [CrossRef] [PubMed]
  2. R. J. Hall, “CARS spectra of combustion gases,” Combust. Flame 35, 47 (1979).
    [CrossRef]
  3. J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.
  4. R. Y. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137A, 1787 (1965).
    [CrossRef]
  5. C. Asawaroengchai, G. M. Rosenblatt, “Rotational Raman intensities and the measured change with internuclear distance of the polarizability anisotropy of H2, D2, N2, O2, and CO,” J. Chem. Phys. 72, 2664 (1980).
    [CrossRef]
  6. H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
    [CrossRef]
  7. L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
    [CrossRef]
  8. K. P. Huber, G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).
  9. A. B. Harvey, “Measurement of vibrational and rotational-translational temperatures independently from pure rotational Raman spectra,” in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, eds. (Plenum, New York, 1974), p. 147.
  10. M. C. Drake, G. M. Rosenblatt, “Rotational Raman scattering from premixed and diffusion flames,” Combust. Flame 33, 179 (1978).
    [CrossRef]
  11. M. C. Drake, L. Grabner, J. W. Hastie, “A comparison of spectroscopic flame temperature measurements: Na-D line reversal, rotational and vibrational Raman, and OH absorption,” in Characterization of High Temperature Vapors and Gases, J. W. Hastie, ed., NBS Special Pub. 561 (U.S. Government Printing Office, Washington, D.C., 1979), p. 1105.
  12. C. J. Dasch, J. H. Bechtel, “Spontaneous Raman scattering by ground-state oxygen atoms,” Opt. Lett. 6, 36 (1981).
    [CrossRef] [PubMed]
  13. M. C. Drake, J. W. Hastie, “Temperature profiles of inhibited flames using Raman spectroscopy,” Combust. Flame 40, 201 (1981).
    [CrossRef]
  14. M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

1981 (5)

R. E. Teets, J. H. Bechtel, “Coherent anti-Stokes Raman spectra of oxygen atoms in flames,” Opt. Lett. 6, 458 (1981).
[CrossRef] [PubMed]

H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
[CrossRef]

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

C. J. Dasch, J. H. Bechtel, “Spontaneous Raman scattering by ground-state oxygen atoms,” Opt. Lett. 6, 36 (1981).
[CrossRef] [PubMed]

M. C. Drake, J. W. Hastie, “Temperature profiles of inhibited flames using Raman spectroscopy,” Combust. Flame 40, 201 (1981).
[CrossRef]

1980 (1)

C. Asawaroengchai, G. M. Rosenblatt, “Rotational Raman intensities and the measured change with internuclear distance of the polarizability anisotropy of H2, D2, N2, O2, and CO,” J. Chem. Phys. 72, 2664 (1980).
[CrossRef]

1979 (1)

R. J. Hall, “CARS spectra of combustion gases,” Combust. Flame 35, 47 (1979).
[CrossRef]

1978 (1)

M. C. Drake, G. M. Rosenblatt, “Rotational Raman scattering from premixed and diffusion flames,” Combust. Flame 33, 179 (1978).
[CrossRef]

1965 (1)

R. Y. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137A, 1787 (1965).
[CrossRef]

Asawaroengchai, C.

C. Asawaroengchai, G. M. Rosenblatt, “Rotational Raman intensities and the measured change with internuclear distance of the polarizability anisotropy of H2, D2, N2, O2, and CO,” J. Chem. Phys. 72, 2664 (1980).
[CrossRef]

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

Bechtel, J. H.

Bishop, D. M.

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

Bloembergen, N.

R. Y. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137A, 1787 (1965).
[CrossRef]

Buckingham, A. D.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
[CrossRef]

Cheung, L. M.

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

Dasch, C. J.

Drake, M. C.

M. C. Drake, J. W. Hastie, “Temperature profiles of inhibited flames using Raman spectroscopy,” Combust. Flame 40, 201 (1981).
[CrossRef]

M. C. Drake, G. M. Rosenblatt, “Rotational Raman scattering from premixed and diffusion flames,” Combust. Flame 33, 179 (1978).
[CrossRef]

M. C. Drake, L. Grabner, J. W. Hastie, “A comparison of spectroscopic flame temperature measurements: Na-D line reversal, rotational and vibrational Raman, and OH absorption,” in Characterization of High Temperature Vapors and Gases, J. W. Hastie, ed., NBS Special Pub. 561 (U.S. Government Printing Office, Washington, D.C., 1979), p. 1105.

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

Drapcho, D. L.

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

Eckbreth, A. C.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.

Grabner, L.

M. C. Drake, L. Grabner, J. W. Hastie, “A comparison of spectroscopic flame temperature measurements: Na-D line reversal, rotational and vibrational Raman, and OH absorption,” in Characterization of High Temperature Vapors and Gases, J. W. Hastie, ed., NBS Special Pub. 561 (U.S. Government Printing Office, Washington, D.C., 1979), p. 1105.

Hall, R. J.

R. J. Hall, “CARS spectra of combustion gases,” Combust. Flame 35, 47 (1979).
[CrossRef]

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.

Hamaguchi, H.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
[CrossRef]

Harvey, A. B.

A. B. Harvey, “Measurement of vibrational and rotational-translational temperatures independently from pure rotational Raman spectra,” in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, eds. (Plenum, New York, 1974), p. 147.

Hastie, J. W.

M. C. Drake, J. W. Hastie, “Temperature profiles of inhibited flames using Raman spectroscopy,” Combust. Flame 40, 201 (1981).
[CrossRef]

M. C. Drake, L. Grabner, J. W. Hastie, “A comparison of spectroscopic flame temperature measurements: Na-D line reversal, rotational and vibrational Raman, and OH absorption,” in Characterization of High Temperature Vapors and Gases, J. W. Hastie, ed., NBS Special Pub. 561 (U.S. Government Printing Office, Washington, D.C., 1979), p. 1105.

Herzberg, G.

K. P. Huber, G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).

Huber, K. P.

K. P. Huber, G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).

Jones, W. J.

H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
[CrossRef]

Rosenblatt, G. M.

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

C. Asawaroengchai, G. M. Rosenblatt, “Rotational Raman intensities and the measured change with internuclear distance of the polarizability anisotropy of H2, D2, N2, O2, and CO,” J. Chem. Phys. 72, 2664 (1980).
[CrossRef]

M. C. Drake, G. M. Rosenblatt, “Rotational Raman scattering from premixed and diffusion flames,” Combust. Flame 33, 179 (1978).
[CrossRef]

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

Shen, R. Y.

R. Y. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137A, 1787 (1965).
[CrossRef]

Shirley, J. A.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.

Teets, R. E.

Verdieck, J. F.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.

Viers, K. D.

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

Chem. Phys. Lett. (1)

L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman line intensities for H2 and D2. Correction factors for molecular nonrigidity,” Chem. Phys. Lett. 80, 445 (1981).
[CrossRef]

Combust. Flame (3)

R. J. Hall, “CARS spectra of combustion gases,” Combust. Flame 35, 47 (1979).
[CrossRef]

M. C. Drake, G. M. Rosenblatt, “Rotational Raman scattering from premixed and diffusion flames,” Combust. Flame 33, 179 (1978).
[CrossRef]

M. C. Drake, J. W. Hastie, “Temperature profiles of inhibited flames using Raman spectroscopy,” Combust. Flame 40, 201 (1981).
[CrossRef]

J. Chem. Phys. (1)

C. Asawaroengchai, G. M. Rosenblatt, “Rotational Raman intensities and the measured change with internuclear distance of the polarizability anisotropy of H2, D2, N2, O2, and CO,” J. Chem. Phys. 72, 2664 (1980).
[CrossRef]

Mol. Phys. (1)

H. Hamaguchi, A. D. Buckingham, W. J. Jones, “Determination of derivatives of the polarizability anisotropy in diatomic molecules II. The hydrogen and nitrogen molecules,” Mol. Phys. 43, 1311 (1981).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

R. Y. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137A, 1787 (1965).
[CrossRef]

Other (5)

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “New directions in CARS diagnostics for combustion,” presented at the American Institute of Aeronautics and Astronautics Fifteenth Thermophysics Conference, Snowmass, Colorado, July 14–16, 1980.

K. P. Huber, G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).

A. B. Harvey, “Measurement of vibrational and rotational-translational temperatures independently from pure rotational Raman spectra,” in Laser Raman Gas Diagnostics, M. Lapp, C. M. Penney, eds. (Plenum, New York, 1974), p. 147.

M. C. Drake, C. Asawaroengchai, D. L. Drapcho, K. D. Viers, G. M. Rosenblatt, “The use of rotational Raman scattering for measurement of gas temperatures,” in Temperature: Its Measurement and Control in Science and Industry, Vol. 5 (American Institute of Phvsics, New York, 1982).

M. C. Drake, L. Grabner, J. W. Hastie, “A comparison of spectroscopic flame temperature measurements: Na-D line reversal, rotational and vibrational Raman, and OH absorption,” in Characterization of High Temperature Vapors and Gases, J. W. Hastie, ed., NBS Special Pub. 561 (U.S. Government Printing Office, Washington, D.C., 1979), p. 1105.

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Tables (1)

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Table 1 Rotational Raman Line-Strength Correction Factors for Vibrational Anharmonicity

Equations (6)

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I CARS I 1 2 I 2 [ ( 2 c 4 ћ ω 2 2 γ J ) Δ ν , J d σ d Ω ] 2 ,
d σ d Ω = ( ω 2 c ) 4 ћ 2 ω 0 α 2 ,
α υ 2 = C S ( J ) f ( J ) β υ 2 ,
r r e υ = r e [ ( 3 B e / ω e ) + ( α e / 2 B e ) ] ( υ + 1 2 )
β υ = β e + β e r r e υ + 1 2 β e r r e υ 2 + ,
I CARS ( υ , J υ , J + 2 ) I CARS ( 0 , J 0 , J + 2 ) = | N υ , J [ 1 exp ( Δ E 1 / k T ) ] β υ 2 γ 0 , J N 0 , J [ 1 exp ( Δ E 0 / k T ) ] β 0 2 γ υ , J | 2 .

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