Abstract

Experimental and theoretical investigations of N2 coherent anti-Stokes Raman scattering (CARS) thermometry in laboratory ethylene–air diffusion flames have revealed significant nonresonant susceptibility effects in fuel-rich regions of the flames. The effects appear to be due to the size of the nonresonant susceptibility for typical hydrocarbon fuels and can give rise to significant temperature errors if not accounted for. An efficient theoretical algorithm for reducing spectra affected by nonresonant interference is presented and shown to give excellent agreement with experiment. It is shown that uncertainty about mixture composition or the values of nonresonant susceptibilities of individual constituents need not have a significant effect on CARS temperature measurement.

© 1984 Optical Society of America

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  1. S. Druet, J. P. E. Taran, “Coherent Anti-Stokes Raman Spectroscopy,” in Chemical and Biological Applications of Lasers, C. B. Moore, Ed. (Academic, New York, 1979).
  2. J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Topics in Current Physics, Vol. 2, A. Weber, Ed. (Springer, Heidelberg, 1979).
    [CrossRef]
  3. J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).
  4. R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS): Application to Combustion Diagnostics,” in Laser Applications, Vol. 5, R. K. Erf, Ed. (Academic, San Diego, 1984).
  5. A. C. Eckbreth, R. J. Hall, Combust. Sci. Technol. 25, 175 (1981).
    [CrossRef]
  6. W. G. Rado, Appl. Phys. Lett. 11, 123 (1967).
    [CrossRef]
  7. F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
    [CrossRef]
  8. G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).
  9. R. L. Farrow, paper presented at Lasers ’82 International Conference (Dec. 1982).
  10. G. S. Rosasco, National Bureau of Standards; private communication (July1983).
  11. J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
    [CrossRef]
  12. A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).
  13. L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
    [CrossRef]
  14. M. A. Yuratich, Mol. Phys. 38, 625 (1979).
    [CrossRef]
  15. R. J. Hall, Appl. Spectrosc. 34, 700 (1980).
    [CrossRef]
  16. P. L. Varghese, R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 26, 339 (1981).
    [CrossRef]
  17. R. J. Hall, Combust. Flame 35, 47 (1979).
    [CrossRef]
  18. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).
  19. D. A. Greenhalgh, F. M. Porter, (reference is not available); to be published.
  20. D. W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431 (1963); K. Levenberg, Q. Appl. Math. 2, 164 (1944).
    [CrossRef]
  21. I. Glassman, P. Yaccarino, Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Philadelphia, 1981), p. 1175.
  22. J. A. Shirley, R. J. Hall, A. C. Eckbreth, Opt. Lett. 5, 380 (1980).
    [CrossRef] [PubMed]
  23. A. C. Eckbreth, R. J. Hall, Combust. Flame 36, 87 (1979).
    [CrossRef]
  24. R. E. Mitchell, A. F. Sarofin, L. A. Clomburg, Combust. Flame 37, 227 (1980).
    [CrossRef]

1981 (2)

A. C. Eckbreth, R. J. Hall, Combust. Sci. Technol. 25, 175 (1981).
[CrossRef]

P. L. Varghese, R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 26, 339 (1981).
[CrossRef]

1980 (3)

1979 (5)

A. C. Eckbreth, R. J. Hall, Combust. Flame 36, 87 (1979).
[CrossRef]

R. J. Hall, Combust. Flame 35, 47 (1979).
[CrossRef]

J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
[CrossRef]

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

1977 (1)

A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).

1973 (1)

F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
[CrossRef]

1971 (1)

G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).

1967 (1)

W. G. Rado, Appl. Phys. Lett. 11, 123 (1967).
[CrossRef]

1963 (1)

D. W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431 (1963); K. Levenberg, Q. Appl. Math. 2, 164 (1944).
[CrossRef]

Bunkin, A. F.

A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).

Clomburg, L. A.

R. E. Mitchell, A. F. Sarofin, L. A. Clomburg, Combust. Flame 37, 227 (1980).
[CrossRef]

DeMartini, F.

F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
[CrossRef]

Dobbs, G. M.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).

Druet, S.

S. Druet, J. P. E. Taran, “Coherent Anti-Stokes Raman Spectroscopy,” in Chemical and Biological Applications of Lasers, C. B. Moore, Ed. (Academic, New York, 1979).

Eckbreth, A. C.

A. C. Eckbreth, R. J. Hall, Combust. Sci. Technol. 25, 175 (1981).
[CrossRef]

J. A. Shirley, R. J. Hall, A. C. Eckbreth, Opt. Lett. 5, 380 (1980).
[CrossRef] [PubMed]

A. C. Eckbreth, R. J. Hall, Combust. Flame 36, 87 (1979).
[CrossRef]

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).

R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS): Application to Combustion Diagnostics,” in Laser Applications, Vol. 5, R. K. Erf, Ed. (Academic, San Diego, 1984).

Farrow, R. L.

L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
[CrossRef]

R. L. Farrow, paper presented at Lasers ’82 International Conference (Dec. 1982).

Glassman, I.

I. Glassman, P. Yaccarino, Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Philadelphia, 1981), p. 1175.

Greenhalgh, D. A.

D. A. Greenhalgh, F. M. Porter, (reference is not available); to be published.

Hall, R. J.

A. C. Eckbreth, R. J. Hall, Combust. Sci. Technol. 25, 175 (1981).
[CrossRef]

R. J. Hall, Appl. Spectrosc. 34, 700 (1980).
[CrossRef]

J. A. Shirley, R. J. Hall, A. C. Eckbreth, Opt. Lett. 5, 380 (1980).
[CrossRef] [PubMed]

A. C. Eckbreth, R. J. Hall, Combust. Flame 36, 87 (1979).
[CrossRef]

R. J. Hall, Combust. Flame 35, 47 (1979).
[CrossRef]

R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS): Application to Combustion Diagnostics,” in Laser Applications, Vol. 5, R. K. Erf, Ed. (Academic, San Diego, 1984).

Hanson, R. K.

P. L. Varghese, R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 26, 339 (1981).
[CrossRef]

Harvey, A. B.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).

Havchecorne, G.

G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).

Ivanov, S. G.

A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).

Kerhervé, F.

G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).

Knighten, G. V.

J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Topics in Current Physics, Vol. 2, A. Weber, Ed. (Springer, Heidelberg, 1979).
[CrossRef]

Koroteev, N. I.

A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).

Marquardt, D. W.

D. W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431 (1963); K. Levenberg, Q. Appl. Math. 2, 164 (1944).
[CrossRef]

Mattern, P. L.

L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
[CrossRef]

Mayer, G.

G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).

McDonald, J. R.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).

Mitchell, R. E.

R. E. Mitchell, A. F. Sarofin, L. A. Clomburg, Combust. Flame 37, 227 (1980).
[CrossRef]

Nibler, J. W.

J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Topics in Current Physics, Vol. 2, A. Weber, Ed. (Springer, Heidelberg, 1979).
[CrossRef]

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).

Oudar, J. L.

J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Porter, F. M.

D. A. Greenhalgh, F. M. Porter, (reference is not available); to be published.

Rado, W. G.

W. G. Rado, Appl. Phys. Lett. 11, 123 (1967).
[CrossRef]

Rahn, L. A.

L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
[CrossRef]

Rosasco, G. S.

G. S. Rosasco, National Bureau of Standards; private communication (July1983).

Santomato, E.

F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
[CrossRef]

Sarofin, A. F.

R. E. Mitchell, A. F. Sarofin, L. A. Clomburg, Combust. Flame 37, 227 (1980).
[CrossRef]

Shaub, W. M.

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).

Shen, Y. R.

J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Shirley, J. A.

Simoni, F.

F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
[CrossRef]

Smith, R. W.

J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Stufflebeam, J. H.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).

Taran, J. P. E.

S. Druet, J. P. E. Taran, “Coherent Anti-Stokes Raman Spectroscopy,” in Chemical and Biological Applications of Lasers, C. B. Moore, Ed. (Academic, New York, 1979).

Tellex, P. A.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).

Varghese, P. L.

P. L. Varghese, R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 26, 339 (1981).
[CrossRef]

Yaccarino, P.

I. Glassman, P. Yaccarino, Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Philadelphia, 1981), p. 1175.

Yuratich, M. A.

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

Appl. Phys. Lett. (2)

W. G. Rado, Appl. Phys. Lett. 11, 123 (1967).
[CrossRef]

J. L. Oudar, R. W. Smith, Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Appl. Spectrosc. (1)

Combust. Flame (3)

R. J. Hall, Combust. Flame 35, 47 (1979).
[CrossRef]

A. C. Eckbreth, R. J. Hall, Combust. Flame 36, 87 (1979).
[CrossRef]

R. E. Mitchell, A. F. Sarofin, L. A. Clomburg, Combust. Flame 37, 227 (1980).
[CrossRef]

Combust. Sci. Technol. (1)

A. C. Eckbreth, R. J. Hall, Combust. Sci. Technol. 25, 175 (1981).
[CrossRef]

J. Phys. Paris (1)

G. Havchecorne, F. Kerhervé, G. Mayer, J. Phys. Paris 32, 47 (1971).

J. Quant. Spectrosc. Radiat. Transfer (1)

P. L. Varghese, R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 26, 339 (1981).
[CrossRef]

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431 (1963); K. Levenberg, Q. Appl. Math. 2, 164 (1944).
[CrossRef]

Mol. Phys. (1)

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

Opt. Commun. (2)

L. A. Rahn, P. L. Mattern, R. L. Farrow, Opt. Commun. 39, 249 (1979).
[CrossRef]

F. DeMartini, F. Simoni, E. Santomato, Opt. Commun. 9, 176 (1973).
[CrossRef]

Opt. Lett. (1)

Sov. Tech. Phys. Lett. (1)

A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, Sov. Tech. Phys. Lett. 3, 182 (1977).

Other (9)

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, AIAA Paper No. 83-1294 (1983).

D. A. Greenhalgh, F. M. Porter, (reference is not available); to be published.

R. L. Farrow, paper presented at Lasers ’82 International Conference (Dec. 1982).

G. S. Rosasco, National Bureau of Standards; private communication (July1983).

S. Druet, J. P. E. Taran, “Coherent Anti-Stokes Raman Spectroscopy,” in Chemical and Biological Applications of Lasers, C. B. Moore, Ed. (Academic, New York, 1979).

J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Topics in Current Physics, Vol. 2, A. Weber, Ed. (Springer, Heidelberg, 1979).
[CrossRef]

J. W. Nibler, W. M. Shaub, J. R. McDonald, A. B. Harvey, “Coherent Anti-Stokes Raman Spectroscopy,” in Vibrational Spectra and Structure, Vol. 6, J. R. Durig, Ed. (Elsevier, Amsterdam, 1977).

R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman Spectroscopy (CARS): Application to Combustion Diagnostics,” in Laser Applications, Vol. 5, R. K. Erf, Ed. (Academic, San Diego, 1984).

I. Glassman, P. Yaccarino, Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Philadelphia, 1981), p. 1175.

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Figures (6)

Fig. 1
Fig. 1

Ethylene–air diffusion flame. Burner tube radius = 5 mm; air flow diameter = 105 mm; flow rates = 917 cm3/sec (air), 3.37 cm3/sec (ethylene).

Fig. 2
Fig. 2

Radial temperature profiles at (a) h = 15.2 mm, (b) 7.6 mm, and (c) 3.8 mm. Δ denotes prediction of one-parameter (T) fit; ○ prediction of two-parameter (T and C) fit. Dashed vertical lines indicate approximate boundary of luminous zone.

Fig. 3
Fig. 3

Fits of N2 signature at h = 7.6 mm, r = 1.91 mm; (a) one-parameter fit, (b) two-parameter fit, … experiment, — theory.

Fig. 4
Fig. 4

Fits of N2 signature at h = 7.6 mm, r = 4.76 mm; (a) one-parameter fit, (b) two-parameter fit, … experiment, — theory.

Fig. 5
Fig. 5

Fits of N2 signature at h = 15.2 mm, r = 1.27 mm; (a) one-parameter fit, (b) two-parameter fit, … experiment, — theory.

Fig. 6
Fig. 6

Fit of N2 signature with large background interference at h = 3.8 mm, r = 0. Best fit C = 0.04.

Equations (10)

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P = χ ( 1 ) E + χ ( 3 ) E 3 + ,
χ ( 3 ) = j ( χ j + i χ j ) + χ N R ,
χ j + i χ j = 2 N p c 4 ω 2 4 ( σ z z ) j Δ ρ j ( 0 ) 2 [ ω j - ( ω 1 - ω 2 ) ] - i Γ j .
I 3 ( ω 3 ) ~ ( j χ j ) 2 + ( j χ j ) 2 + 2 χ N R ( j χ j ) + χ N R 2 ,
I 3 ( ω 3 ) ~ 1 + 2 ( x χ ¯ N R ) j χ ¯ j + ( x χ ¯ N R ) 2 [ ( j χ ¯ j ) 2 + ( j χ ¯ j ) 2 ] ,
F = ( I ^ 1 2 I ^ 2 ) - 1 d Δ I 1 ( ω 3 - Δ ) F ( Δ ) d ω 1 I 1 ( ω 1 ) I 2 ( ω 1 - Δ ) ,
I 3 ( ω 3 ) ~ 1 + 2 ( x χ ¯ N R ) j χ ¯ j + ( x χ ¯ N R ) 2 ( j χ ¯ j ) 2 + ( j χ ¯ j ) 2 .
I ( ω 3 ) ~ e ( ω 3 ) + 2 C f ( ω 3 , T ) + C 2 g ( ω 3 , T ) ,
I 3 ( ω 3 ) ~ e ( ω 3 ) + 2 C f ( ω 3 , T ) .
I 3 ( ω 3 ) ~ C 2 g ( ω 3 , T ) ,

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