Abstract

A method for accurately inferring temperatures and concentrations from simultaneous multiplex CARS spectra of N2, CO, and H2 is introduced. Only a single dye laser is employed in these measurements. Temperatures inferred from the nitrogen portion of spectra taken in a furnace of preanalyzed samples of these gases show agreement with temperatures measured by thermocouple to well within the estimated accuracies of the thermocouple (1%). Carbon monoxide and hydrogen concentrations may be inferred from the remainder of the spectrum with accuracies of 2 and 1/2%, respectively. Spectra taken downstream from a combustor burning diesel fuel and preheated air indicated that simultaneous measurements of temperature and CO concentration with mole fractions from below 0.01 may be made in turbulent reacting flows. The S(9) rotational line of hydrogen is employed to infer concentrations of H2. Minimum detectable mole fractions of hydrogen are presented as functions of temperature and CO mole fraction. The effects of temporal instabilities of the dye laser and interspecies coupling during analysis on the accuracy of the inferred values are discussed.

© 1988 Optical Society of America

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  1. R. J. Hall, A. C. Eckbreth, “Coherent Anti-Stokes Raman. Spectroscopy (CARS): Application to Combustion Diagnostics,” in Laser Applications, Vol. 5, J. F. Ready, R. K. Erf, Eds. (AcademicSan Diego, 1984).
  2. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS Temperature and Species Measurements in Augmented Jet Engine Exhausts,” Appl. Opt. 23, 1328 (1984).
    [Crossref] [PubMed]
  3. A. C. Eckbreth, T. J. Anderson, “Dual Broadband CARS for Simultaneous, Multiple Species Measurements,” Appl. Opt. 24, 2731 (1985).
    [Crossref] [PubMed]
  4. A. C. Eckbreth, T. J. Anderson, “Dual Broadband USED CARS,” Appl. Opt. 25, 1534 (1986).
    [Crossref] [PubMed]
  5. R. P. Lucht, “Three-Laser Coherent Anti-Stokes Raman Scattering Measurements of Two Species,” Opt. Lett. 12, 78 (1987).
    [Crossref] [PubMed]
  6. S. Kroll, M. Alden, T. Berglind, R. J. Hall, “Noise Characteristics of Single Shot Broadband Raman-Resonant CARS with Single- and Multimode Lasers,” Appl. Opt. 26, 1068 (1987).
    [Crossref] [PubMed]
  7. K. Aron, L. E. Harris, J. Fendell, “N2 and CO Vibrational CARS and H2 Rotational CARS Spectroscopy of CH4/N2O Flames,” Appl. Opt. 22, 3604 (1983).
    [Crossref] [PubMed]
  8. E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
    [Crossref] [PubMed]
  9. Exciton Chemical Co., Dayton, OH.
  10. J. A. Shirley, R. J. Hall, A. C. Eckbreth, “Folded BOXCARS for Rotational Raman Studies,” Opt. Lett. 5, 380 (1980).
    [Crossref] [PubMed]
  11. Y. Prior, “Three-Dimensional Phase Matching in Four-Wave Mixing,” Appl. Opt. 19, 1741 (1980).
    [Crossref]
  12. E. J. Beiting, J. P. Singh, “Simple Particle Injection System for Laboratory Burners,” Rev. Sci. Instrum. 57, 377 (1986).
    [Crossref]
  13. M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
    [Crossref]
  14. H. Kataoka, S. Maeda, C. Hirose, “Effects of Laser Line-width on the Coherent Anti-Stokes Raman Spectroscopy Spectral Profile,” Appl. Spectrosc. 36, 565 (1982).
    [Crossref]
  15. R. E. Teets, “Accurate Convolutions of Coherent Anti-Stokes Raman Spectra,” Opt. Lett. 9, 226 (1984).
    [Crossref] [PubMed]
  16. R. L. Farrow, L. A. Rahn, “Interpreting Coherent Anti-Stokes Raman Spectra Measured with Multimode Nd:YAG Pump Lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
    [Crossref]
  17. G. Placzek, “The Rayleigh and Raman Scattering,” in Handbuch der Radiologie, Vol. 6, Part 2, E. Marx, Ed. (Akademische Verlagsgesellschaft, Leipzig, 1934).
  18. N. J. Bridge, A. D. Buckingham, “The Polarization of Laser Light Scattered by Gases,” Proc. R. Soc. London Ser. A 295, 334 (1966).
    [Crossref]
  19. R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison Between CARS and Corrected Thermocouple Temperature Measurements in a Diffusion Flame,” Appl. Opt. 21, 3119 (1982).
    [Crossref] [PubMed]
  20. C. James, W. Klemperer, “Line Intensities in the Raman Effect of 1∑ Diatomic Molecules,” J. Chem. Phys. 31, 130 (1959).
    [Crossref]
  21. D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for’ the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
    [Crossref]
  22. F. Y. Yueh, E. J. Beiting, “Analytical Expressions for Coherent Anti-Stokes Raman Spectral (CARS) Profiles,” Comput. Phys. Commun. 42, 65 (1986).
    [Crossref]
  23. J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
    [Crossref]
  24. R. J. Hall, L. R. Boedeker, “CARS Thermometry in Fuel-Rich Combustion Zones,” Appl. Opt. 23, 1340 (1984).
    [Crossref] [PubMed]
  25. W. G. Rado, “The Nonlinear Third Order Dielectric Susceptibility Coefficients of Gases and Optical Third Harmonic Generation,” Appl. Phys. Lett. 11, 123 (1967).
    [Crossref]
  26. T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
    [Crossref]
  27. T. H. Jefferson, Sandia Laboratories; SAND 73-0305.
  28. D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
    [Crossref]
  29. R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species Concentration Measurements using CARS with Non-resonant Susceptibility Normalization,” Appl. Opt. 24, 2241 (1985).
    [Crossref] [PubMed]
  30. L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an Optical Stark Effect on Vibrational and Rotational Transitions,” Phys. Rev. Lett. 45, 620 (1980).
    [Crossref]
  31. R. L. Farrow, L. A. Rahn, “Optical Stark Splitting of Rotational Raman Transitions,” Phys. Rev. Lett. 48, 395 (1982).
    [Crossref]
  32. M. C. Drake, C. Asawaroengchai, G. M. Rosenblatt, “Temperature from Rotational and Vibrational Raman Scattering: Effects of Vibrational-Rotational Interactions and Other Corrections,” in Laser Probes for Combustion Chemistry, D. R. Crosley, Ed., ACS Symp. Ser.134 (American Chemical Society, Washington, DC, 1980).
  33. L. M. Cheung, D. M. Bishop, D. L. Drapcho, G. M. Rosenblatt, “Relative Raman Line Intensities for H2 and D2 Correction Factors for Molecular Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
    [Crossref]
  34. D. E. Jennings, L. A. Rahn, A. Owyoung, “Laboratory Measurement of the S(9) Pure Rotational Frequency in H21,” Astrophys. Lett. 291, L15 (1985).
    [Crossref]
  35. E. J. Beiting, “Coherent Interference in Multiplex CARS Measurements: Nonresonant Susceptibility Enhancement due to Laser Breakdown,” Appl. Opt. 24, 3010 (1985).
    [Crossref] [PubMed]
  36. M. Alden, P.-E. Bengtsson, H. Edner, “Rotational CARS Generation through a Multiple Four-Color Interaction,” Appl. Opt. 25, 4493 (1986).
    [Crossref] [PubMed]
  37. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Precision of Multiplex CARS Temperatures using Both Single-Mode and Multimode Pump Lasers,” Appl. Opt. 26, 99 (1987).
    [Crossref] [PubMed]

1987 (3)

1986 (7)

M. Alden, P.-E. Bengtsson, H. Edner, “Rotational CARS Generation through a Multiple Four-Color Interaction,” Appl. Opt. 25, 4493 (1986).
[Crossref] [PubMed]

A. C. Eckbreth, T. J. Anderson, “Dual Broadband USED CARS,” Appl. Opt. 25, 1534 (1986).
[Crossref] [PubMed]

E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
[Crossref] [PubMed]

D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for’ the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
[Crossref]

F. Y. Yueh, E. J. Beiting, “Analytical Expressions for Coherent Anti-Stokes Raman Spectral (CARS) Profiles,” Comput. Phys. Commun. 42, 65 (1986).
[Crossref]

J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
[Crossref]

E. J. Beiting, J. P. Singh, “Simple Particle Injection System for Laboratory Burners,” Rev. Sci. Instrum. 57, 377 (1986).
[Crossref]

1985 (5)

1984 (3)

1983 (2)

T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
[Crossref]

K. Aron, L. E. Harris, J. Fendell, “N2 and CO Vibrational CARS and H2 Rotational CARS Spectroscopy of CH4/N2O Flames,” Appl. Opt. 22, 3604 (1983).
[Crossref] [PubMed]

1982 (3)

1981 (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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

1980 (3)

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an Optical Stark Effect on Vibrational and Rotational Transitions,” Phys. Rev. Lett. 45, 620 (1980).
[Crossref]

J. A. Shirley, R. J. Hall, A. C. Eckbreth, “Folded BOXCARS for Rotational Raman Studies,” Opt. Lett. 5, 380 (1980).
[Crossref] [PubMed]

Y. Prior, “Three-Dimensional Phase Matching in Four-Wave Mixing,” Appl. Opt. 19, 1741 (1980).
[Crossref]

1979 (1)

M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
[Crossref]

1967 (1)

W. G. Rado, “The Nonlinear Third Order Dielectric Susceptibility Coefficients of Gases and Optical Third Harmonic Generation,” Appl. Phys. Lett. 11, 123 (1967).
[Crossref]

1966 (1)

N. J. Bridge, A. D. Buckingham, “The Polarization of Laser Light Scattered by Gases,” Proc. R. Soc. London Ser. A 295, 334 (1966).
[Crossref]

1963 (1)

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[Crossref]

1959 (1)

C. James, W. Klemperer, “Line Intensities in the Raman Effect of 1∑ Diatomic Molecules,” J. Chem. Phys. 31, 130 (1959).
[Crossref]

Alden, M.

Anderson, T. J.

Aron, K.

Asawaroengchai, C.

M. C. Drake, C. Asawaroengchai, G. M. Rosenblatt, “Temperature from Rotational and Vibrational Raman Scattering: Effects of Vibrational-Rotational Interactions and Other Corrections,” in Laser Probes for Combustion Chemistry, D. R. Crosley, Ed., ACS Symp. Ser.134 (American Chemical Society, Washington, DC, 1980).

Beiting, E. J.

E. J. Beiting, J. P. Singh, “Simple Particle Injection System for Laboratory Burners,” Rev. Sci. Instrum. 57, 377 (1986).
[Crossref]

F. Y. Yueh, E. J. Beiting, “Analytical Expressions for Coherent Anti-Stokes Raman Spectral (CARS) Profiles,” Comput. Phys. Commun. 42, 65 (1986).
[Crossref]

J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
[Crossref]

E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
[Crossref] [PubMed]

E. J. Beiting, “Coherent Interference in Multiplex CARS Measurements: Nonresonant Susceptibility Enhancement due to Laser Breakdown,” Appl. Opt. 24, 3010 (1985).
[Crossref] [PubMed]

Bengtsson, P.-E.

Berglind, T.

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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

Boedeker, L. R.

Bridge, N. J.

N. J. Bridge, A. D. Buckingham, “The Polarization of Laser Light Scattered by Gases,” Proc. R. Soc. London Ser. A 295, 334 (1966).
[Crossref]

Buckingham, A. D.

N. J. Bridge, A. D. Buckingham, “The Polarization of Laser Light Scattered by Gases,” Proc. R. Soc. London Ser. A 295, 334 (1966).
[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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

Clark, G. L.

Dobbs, G. M.

Drake, M. C.

M. C. Drake, C. Asawaroengchai, G. M. Rosenblatt, “Temperature from Rotational and Vibrational Raman Scattering: Effects of Vibrational-Rotational Interactions and Other Corrections,” in Laser Probes for Combustion Chemistry, D. R. Crosley, Ed., ACS Symp. Ser.134 (American Chemical Society, Washington, DC, 1980).

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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

Eckbreth, A. C.

Edner, H.

Farrow, R. L.

Fendell, J.

Greenhalgh, D. A.

D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for’ the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
[Crossref]

Hall, R. J.

S. Kroll, M. Alden, T. Berglind, R. J. Hall, “Noise Characteristics of Single Shot Broadband Raman-Resonant CARS with Single- and Multimode Lasers,” Appl. Opt. 26, 1068 (1987).
[Crossref] [PubMed]

D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for’ the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
[Crossref]

R. J. Hall, L. R. Boedeker, “CARS Thermometry in Fuel-Rich Combustion Zones,” Appl. Opt. 23, 1340 (1984).
[Crossref] [PubMed]

J. A. Shirley, R. J. Hall, A. C. Eckbreth, “Folded BOXCARS for Rotational Raman Studies,” Opt. Lett. 5, 380 (1980).
[Crossref] [PubMed]

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

Harris, L. E.

Hirose, C.

Hou, S. Y.

T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
[Crossref]

James, C.

C. James, W. Klemperer, “Line Intensities in the Raman Effect of 1∑ Diatomic Molecules,” J. Chem. Phys. 31, 130 (1959).
[Crossref]

Jefferson, T. H.

T. H. Jefferson, Sandia Laboratories; SAND 73-0305.

Jennings, D. E.

D. E. Jennings, L. A. Rahn, A. Owyoung, “Laboratory Measurement of the S(9) Pure Rotational Frequency in H21,” Astrophys. Lett. 291, L15 (1985).
[Crossref]

Kataoka, H.

Klemperer, W.

C. James, W. Klemperer, “Line Intensities in the Raman Effect of 1∑ Diatomic Molecules,” J. Chem. Phys. 31, 130 (1959).
[Crossref]

Koszykowski, M. L.

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an Optical Stark Effect on Vibrational and Rotational Transitions,” Phys. Rev. Lett. 45, 620 (1980).
[Crossref]

Kroll, S.

Lucht, R. P.

Lundeen, T.

T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
[Crossref]

Luthe, J. C.

J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
[Crossref]

Maeda, S.

Marquardt, D. W.

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[Crossref]

Mattern, P. L.

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison Between CARS and Corrected Thermocouple Temperature Measurements in a Diffusion Flame,” Appl. Opt. 21, 3119 (1982).
[Crossref] [PubMed]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an Optical Stark Effect on Vibrational and Rotational Transitions,” Phys. Rev. Lett. 45, 620 (1980).
[Crossref]

Nibler, J. W.

T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
[Crossref]

Owyoung, A.

D. E. Jennings, L. A. Rahn, A. Owyoung, “Laboratory Measurement of the S(9) Pure Rotational Frequency in H21,” Astrophys. Lett. 291, L15 (1985).
[Crossref]

Palmer, R. E.

Parameswaran, T.

Placzek, G.

G. Placzek, “The Rayleigh and Raman Scattering,” in Handbuch der Radiologie, Vol. 6, Part 2, E. Marx, Ed. (Akademische Verlagsgesellschaft, Leipzig, 1934).

Prior, Y.

Rado, W. G.

W. G. Rado, “The Nonlinear Third Order Dielectric Susceptibility Coefficients of Gases and Optical Third Harmonic Generation,” Appl. Phys. Lett. 11, 123 (1967).
[Crossref]

Rahn, L. A.

D. E. Jennings, L. A. Rahn, A. Owyoung, “Laboratory Measurement of the S(9) Pure Rotational Frequency in H21,” Astrophys. Lett. 291, L15 (1985).
[Crossref]

R. L. Farrow, L. A. Rahn, “Interpreting Coherent Anti-Stokes Raman Spectra Measured with Multimode Nd:YAG Pump Lasers,” J. Opt. Soc. Am. B 2, 903 (1985).
[Crossref]

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison Between CARS and Corrected Thermocouple Temperature Measurements in a Diffusion Flame,” Appl. Opt. 21, 3119 (1982).
[Crossref] [PubMed]

R. L. Farrow, L. A. Rahn, “Optical Stark Splitting of Rotational Raman Transitions,” Phys. Rev. Lett. 48, 395 (1982).
[Crossref]

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an Optical Stark Effect on Vibrational and Rotational Transitions,” Phys. Rev. Lett. 45, 620 (1980).
[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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

M. C. Drake, C. Asawaroengchai, G. M. Rosenblatt, “Temperature from Rotational and Vibrational Raman Scattering: Effects of Vibrational-Rotational Interactions and Other Corrections,” in Laser Probes for Combustion Chemistry, D. R. Crosley, Ed., ACS Symp. Ser.134 (American Chemical Society, Washington, DC, 1980).

Sawchuk, R. A.

Shirley, J. A.

Singh, J. P.

E. J. Beiting, J. P. Singh, “Simple Particle Injection System for Laboratory Burners,” Rev. Sci. Instrum. 57, 377 (1986).
[Crossref]

Smallwood, G. J.

Snelling, D. R.

Stufflebeam, J. H.

Teets, R. E.

Tellex, P. A.

Yueh, F. Y.

F. Y. Yueh, E. J. Beiting, “Analytical Expressions for Coherent Anti-Stokes Raman Spectral (CARS) Profiles,” Comput. Phys. Commun. 42, 65 (1986).
[Crossref]

J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
[Crossref]

Yuratich, M. A.

M. A. Yuratich, “Effects of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
[Crossref]

Appl. Opt. (13)

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS Temperature and Species Measurements in Augmented Jet Engine Exhausts,” Appl. Opt. 23, 1328 (1984).
[Crossref] [PubMed]

A. C. Eckbreth, T. J. Anderson, “Dual Broadband CARS for Simultaneous, Multiple Species Measurements,” Appl. Opt. 24, 2731 (1985).
[Crossref] [PubMed]

A. C. Eckbreth, T. J. Anderson, “Dual Broadband USED CARS,” Appl. Opt. 25, 1534 (1986).
[Crossref] [PubMed]

S. Kroll, M. Alden, T. Berglind, R. J. Hall, “Noise Characteristics of Single Shot Broadband Raman-Resonant CARS with Single- and Multimode Lasers,” Appl. Opt. 26, 1068 (1987).
[Crossref] [PubMed]

K. Aron, L. E. Harris, J. Fendell, “N2 and CO Vibrational CARS and H2 Rotational CARS Spectroscopy of CH4/N2O Flames,” Appl. Opt. 22, 3604 (1983).
[Crossref] [PubMed]

E. J. Beiting, “Multiplex CARS Temperature Measurements in a Coal-Fired MHD Environment,” Appl. Opt. 25, 1684 (1986).
[Crossref] [PubMed]

Y. Prior, “Three-Dimensional Phase Matching in Four-Wave Mixing,” Appl. Opt. 19, 1741 (1980).
[Crossref]

R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison Between CARS and Corrected Thermocouple Temperature Measurements in a Diffusion Flame,” Appl. Opt. 21, 3119 (1982).
[Crossref] [PubMed]

R. J. Hall, L. R. Boedeker, “CARS Thermometry in Fuel-Rich Combustion Zones,” Appl. Opt. 23, 1340 (1984).
[Crossref] [PubMed]

R. L. Farrow, R. P. Lucht, G. L. Clark, R. E. Palmer, “Species Concentration Measurements using CARS with Non-resonant Susceptibility Normalization,” Appl. Opt. 24, 2241 (1985).
[Crossref] [PubMed]

E. J. Beiting, “Coherent Interference in Multiplex CARS Measurements: Nonresonant Susceptibility Enhancement due to Laser Breakdown,” Appl. Opt. 24, 3010 (1985).
[Crossref] [PubMed]

M. Alden, P.-E. Bengtsson, H. Edner, “Rotational CARS Generation through a Multiple Four-Color Interaction,” Appl. Opt. 25, 4493 (1986).
[Crossref] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Precision of Multiplex CARS Temperatures using Both Single-Mode and Multimode Pump Lasers,” Appl. Opt. 26, 99 (1987).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

W. G. Rado, “The Nonlinear Third Order Dielectric Susceptibility Coefficients of Gases and Optical Third Harmonic Generation,” Appl. Phys. Lett. 11, 123 (1967).
[Crossref]

Appl. Spectrosc. (1)

Astrophys. Lett. (1)

D. E. Jennings, L. A. Rahn, A. Owyoung, “Laboratory Measurement of the S(9) Pure Rotational Frequency in H21,” Astrophys. Lett. 291, L15 (1985).
[Crossref]

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 Non-Rigidity,” Chem. Phys, Lett. 80, 445 (1981).
[Crossref]

Comput. Phys. Commun. (2)

F. Y. Yueh, E. J. Beiting, “Analytical Expressions for Coherent Anti-Stokes Raman Spectral (CARS) Profiles,” Comput. Phys. Commun. 42, 65 (1986).
[Crossref]

J. C. Luthe, E. J. Beiting, F. Y. Yueh, “Algorithms for Calculating Coherent Anti-Stokes Raman Spectra: Application to Several Small Molecules,” Comput. Phys. Commun. 42, 73 (1986). This code, available through the CPC library, does not include the O- and S-branch corrections for the vibration and rotation interaction of Eq. (4).
[Crossref]

J. Chem. Phys. (2)

T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities for Various Gases,” J. Chem. Phys. 79, 6301 (1983).
[Crossref]

C. James, W. Klemperer, “Line Intensities in the Raman Effect of 1∑ Diatomic Molecules,” J. Chem. Phys. 31, 130 (1959).
[Crossref]

J. Opt. Soc. Am. B (1)

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

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[Crossref]

Mol. Phys. (1)

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[Crossref]

Opt. Commun. (1)

D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for’ the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (2)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Other (5)

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

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Exciton Chemical Co., Dayton, OH.

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Figures (5)

Fig. 1
Fig. 1

Multiplex CARS spectrum taken in a CH4/CO/air flame (solid line). The bands on the left are due to CO. The sharp feature near the peak of the (0–1) CO band is the H2S(9) pure rotational resonance. The nitrogen bands, excited by the wing of the dye laser, are seen at the right. The dashed line is the model fit to the data using the procedure described in the text. The values for the temperature and concentrations were inferred from the CARS data. This spectrum is an average of seventy-one pulses (7 s of data).

Fig. 2
Fig. 2

Three fits to the same (typical) dye laser profile. Errors of the magnitude shown in the top (Gaussian) fit can lead to errors in the inferred temperature approaching 100 K.

Fig. 3
Fig. 3

Sensitivity of inferred CO concentrations caused by errors in temperature for several temperatures and a CO concentration of 10%.

Fig. 4
Fig. 4

Minimum detectable concentration of H2 as a function of temperature for several CO concentrations. The results were obtained from model calculations and experimentally verified for three temperatures and two CO concentrations.

Fig. 5
Fig. 5

Simultaneous CO and N 2 multiplex CARS spectrum taken in the turbulent flow of postcombustion gases of a flame of diesel fuel and preheated air. The combustor was operating at an equivalence ratio of 1.25. The spectrum is an average of forty-seven pulses (4.7 s).

Tables (4)

Tables Icon

Table I Study of Induced Error Caused by Poorly Modeled Dye Laser Spectral Profile

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Table II Multiplex CARS Measurements of N2 and CO Made In a Furnace

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Table III Multiplex CARS Measurements of N2, CO, and H2 In Furnace

Tables Icon

Table IV Test Stand Measurements

Equations (14)

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I 4 ( ω 4 ) = 16 π 4 ω 4 2 c 4 n 1 n 2 n 3 n 4 [ sin ( Δ k z / 2 ) Δ k z / 2 ] 2 z 2 × 1 / 2 χ ( ω 1 - ω 2 ) + 1 / 2 χ ( ω 3 - ω 2 ) 2 I 1 ( ω 1 ) I 2 ( ω 2 ) I 3 ( ω 3 ) × δ ( ω 1 + ω 3 - ω 2 - ω 4 ) d ω 1 d ω 2 d ω 3 ,
χ ( ω 1 - ω 2 ) = 3 χ 1111 ( 3 ) = 3 χ 1111 n r + N s i , f [ Ω i f - ( ω 1 - ω 2 ) - i γ i f ] - 1 Δ ρ i f α i f 2 ,
α i f 2 v f a v i δ 2 J i J f + 4 45 v f γ v i b 2 J f J i
Δ ρ i f f i - ( 2 J i + 1 2 J f + 1 ) f f
v + 1 A v = ( v + 1 ) 1 / 2 ( 2 ω 0 M ) 1 / 2 A q | 0 ,
K ( J i , J f ) = { 1 - 4 B e ω e β [ J f ( J f + 1 ) - J i ( J i + 1 ) ] } 2 ,
= ( χ n r ) 2 F ( ω 4 ) [ 1 - 2 π γ ˜ 1 Im S 1 ( ω 4 ) + π 2 γ ˜ 1 2 S 1 ( ω 4 ) 2 - π 2 γ ˜ 1 S 2 ( ω 4 ) ] ,
S 1 ( ω 4 ) = s C s j a s j w ( z s j ) ,
S 2 ( ω 4 ) = s t C s C t j k a s j a t k * × Im [ w ( z s j + w * ( z t k ) ( Ω t k - Ω s j ) + i ( γ s j + γ t k ) ] , C s = f s χ n r ; f s mole fraction of species s , a s j = N Δ ρ s j α s j 2 , N composite number density , z s j = ( ω 4 - ω 1 - Ω s j + i γ s j ) / γ ˜ 1 , w ( z s j ) complex error function , Ω s j = j th Raman resonant frequency of species s ,
F ( ω 4 ) = I 1 ( ω 1 ) I 3 ( ω 3 ) I 2 ( ω 1 + ω 3 - ω 4 ) d ω 1 d ω 3 .
F ( ω 4 ) = 1 γ ˜ 2 π exp [ - ( ω 4 - ω 4 0 ) 2 / γ ˜ 2 2 ] .
F 4 ( ω 4 ) = 1 2 π { γ ˜ 2 - 1 exp [ - ( ω 4 - ω 4 0 ) 2 / γ ˜ 2 2 ] + γ ˜ 2 - 1 exp [ - ( ω 4 - ω 4 0 ) 2 / γ ˜ 2 2 ] } .
3 χ 1111 ( 3 ) = 3 χ 1111 n r + N ( Ω J - ω 1 + ω 2 - i γ J ) - 1 × [ f J - ( 2 J + 1 2 J + 5 ) f J + 2 ] 4 45 γ 00 2 b J + 2 J K ( J ) ,
K ( J ) = [ 1 + 4 η ( B e / ω e ) 2 ( J 2 + 3 J + 3 ) ] 2

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