Abstract

The noise level in single-pulse resonant nitrogen CARS spectra is shown to decrease with increasing pump laser bandwidth. This is the reverse of the trend observed for nonresonant CARS spectra. The precision of single-pulse CARS temperature measurements is shown to be dramatically increased by performing a weighted fit of theoretical and experimental CARS spectra using the measured detector noise coefficients as weighting parameters. The inclusion of collisional narrowing and cross-coherence in the CARS theory calculations and their effect on best fit temperatures are discussed. These temperatures, measured in a flat-flame burner, are compared with those obtained by Na line-reversal.

© 1987 Optical Society of America

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References

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  1. S. A. J. Druet, J. P. E. Taran, “CARS Spectroscopy,” Prog. Quantum Electron. 7, 1 (1981).
    [CrossRef]
  2. 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. (Academic, New York, 1984), pp. 213–309.
  3. A. B. Harvey, Ed., Chemical Applications of Nonlinear Raman Spectroscopy (Academic, New York, 1981).
  4. J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer, Berlin, 1979), pp. 253–299.
    [CrossRef]
  5. 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]
  6. A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the Application of CARS to Turbulent Reacting Flows,” Exp. Fluids 3, 301 (1985).
    [CrossRef]
  7. D. R. Snelling, R. A. Sawchuk, R. E. Mueller, “Single-Pulse CARS Noise: A Comparison Between Single-Mode and Multimode Pump Lasers,” Appl. Opt. 24, 2771 (1985).
    [CrossRef] [PubMed]
  8. D. A. Greenhalgh, S. T. Whittley, “Mode Noise in Broadband CARS Spectroscopy,” Appl. Opt. 24, 907 (1985).
    [CrossRef] [PubMed]
  9. M. Pealat, P. Bourchardy, M. Lefebvre, J. P. Taran, “Precision of Multiplex CARS Temperature Measurements,” Appl. Opt. 24, 1012 (1985).
    [CrossRef] [PubMed]
  10. D. A. Greenhalgh, F. M. Porter, “CARS Applications in Chemical Reactors, Combustion and Heat Transfer,” in Proceedings, First International Laser Sciences Conference, Dallas (Nov.1985).
  11. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” at Sixty-seventh AGARD PEP Meeting on Advanced Instrumentation for Aeroengine Components, Philadelphia (May 1986).
  12. D. R. Snelling, R. A. Sawchuk, G. J. Smallwood, “Multichannel Light Detectors and Their Use for CARS Spectroscopy,” Appl. Opt. 23, 4083 (1984).
    [CrossRef] [PubMed]
  13. M. B. Morris, T. J. Mcllrath, “Portable High-Resolution Laser Monochromator-Interferometer with Multichannel Electronic Readout,” Appl. Opt. 18, 4145 (1979).
    [CrossRef] [PubMed]
  14. L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
    [CrossRef]
  15. J. P. Botha, D. B. Spalding, “The Laminar Flame Speed of Propane/Air Mixtures with Heat Extraction from the Flame,” Proc. R. Soc. London Ser. A 225, 71 (1954).
    [CrossRef]
  16. D. R. Snelling, M. Fischer, “Design and Calibration of a Flat-Flame Burner using Line-Reversal Techniques,” Technical Note 85-4, Defence Research Establishment Ottawa, Canada (1985).
  17. F. Printer, “Dependence of the Width of the Rotational Raman Lines of N2 and CO2 on the Quantum Number j,” Opt. Spectrosc. USSR 17, 428 (1964).
  18. A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
    [CrossRef]
  19. J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
    [CrossRef]
  20. R. J. Hall, “Coherent Anti-Stokes Modelling for Combustion Diagnostics,” Opt. Eng. 22, 322 (1983).
    [CrossRef]
  21. M. L. Koszykowski, R. L. Farrow, R. E. Palmer, “Calculation of Collisionally Narrowed Coherent Anti-Stokes Raman Spectroscopy Spectra,” Opt. Lett. 10, 478 (1985).
    [CrossRef] [PubMed]
  22. M. A. Yuratich, “Effect of Laser Linewidth on Coherent Anti-Stokes Raman Spectroscopy,” Mol. Phys. 38, 625 (1979).
    [CrossRef]
  23. R. J. Hall, “CARS Spectra of Combustion Gases,” Combust. Flame 35, 77 (1979).
    [CrossRef]
  24. 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]
  25. T. Lasser, “An Alternative Method for CARS Spectra Convolutions,” Opt. Commun. 35, 447 (1980).
    [CrossRef]
  26. E. E. Whiting, “An Empirical Approximation to the Voigt Function,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
    [CrossRef]
  27. H. Kim, “Computer Programming in Physical Chemistry Laboratory,” J. Chem. Educ. 2, 120 (1970).
    [CrossRef]
  28. C. M. Penney, R. L. St. Peters, M. Lapp, “Absolute Rotational Raman Cross Sections for N2, O2, and CO2,” J. Opt. Soc. Am. 64, 712 (1974).
    [CrossRef]
  29. L. A. Rahn, Sandia National Laboratories, unpublished results.
  30. R. J. Hall, “Pressure Broadened Linewidths for CARS Thermometry,” Appl. Spectrosc. 34, 780 (1980).
  31. G. J. Rosasco, W. S. Hurst, “Measurement of Resonant and Nonresonant Third Order Nonlinear Susceptibilities by Coherent Raman Spectroscopy,” Phys. Rev. A 32, 281 (1985).
    [CrossRef] [PubMed]
  32. T. Lundeen, S. Y. Hou, J. W. Nibler, “Nonresonant Third Order Susceptibilities of Various Gases,” J. Chem. Phys. 79, 6301 (1983).
    [CrossRef]
  33. R. L. Farrow, Sandia Laboratories, Livermore, CA; private communication.
  34. T. Parameswaran, D. R. Snelling, “A Computer Program to Generate Coherent Anti-Stokes Raman Spectra,” Technical Note 81-18, Defence Research Establishment Ottawa, Canada (1982).
  35. R. E. Teets, “Accurate Convolutions of Coherent Anti-Stokes Raman Spectra,” Opt. Lett. 9, 226 (1984).
    [CrossRef] [PubMed]
  36. 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]
  37. D. A. Greenhalgh, R. J. Hall, “A Closed Form Solution for the CARS Intensity Convolution,” Opt. Commun. 57, 125 (1986).
    [CrossRef]
  38. A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
    [CrossRef]
  39. S. A. Barton, J. M. Garneau, Defence Research Establishment Valcartier, Quebec City; private communication.
  40. L. A. Rahn, R. L. Farrow, R. P. Lucht, “Effects of Laser Field Statistics on Coherent Anti-Stokes Raman Spectroscopy Intensities,” Opt. Lett. 9, 223 (1984).
    [CrossRef] [PubMed]
  41. R. L. Farrow, L. A. Rahn, R. P. Lucht, “Effect of Non-Gaussian Pump Fuels Statistics on Unresolved CARS Spectra,” in Proceedings, Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 340–341.
  42. A. C. Eckbreth, T. J. Anderson, “Dual Broadband CARS for Simultaneous Multiple Species Measurements,” App. Opt. 24, 2731 (1985).
    [CrossRef]

1986 (1)

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

1985 (7)

1984 (4)

1983 (3)

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

R. J. Hall, “Coherent Anti-Stokes Modelling for Combustion Diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

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

1982 (2)

1981 (1)

S. A. J. Druet, J. P. E. Taran, “CARS Spectroscopy,” Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

1980 (2)

T. Lasser, “An Alternative Method for CARS Spectra Convolutions,” Opt. Commun. 35, 447 (1980).
[CrossRef]

R. J. Hall, “Pressure Broadened Linewidths for CARS Thermometry,” Appl. Spectrosc. 34, 780 (1980).

1979 (3)

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

R. J. Hall, “CARS Spectra of Combustion Gases,” Combust. Flame 35, 77 (1979).
[CrossRef]

M. B. Morris, T. J. Mcllrath, “Portable High-Resolution Laser Monochromator-Interferometer with Multichannel Electronic Readout,” Appl. Opt. 18, 4145 (1979).
[CrossRef] [PubMed]

1978 (1)

A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
[CrossRef]

1977 (1)

J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
[CrossRef]

1974 (1)

1970 (2)

A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
[CrossRef]

H. Kim, “Computer Programming in Physical Chemistry Laboratory,” J. Chem. Educ. 2, 120 (1970).
[CrossRef]

1968 (1)

E. E. Whiting, “An Empirical Approximation to the Voigt Function,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

1964 (1)

F. Printer, “Dependence of the Width of the Rotational Raman Lines of N2 and CO2 on the Quantum Number j,” Opt. Spectrosc. USSR 17, 428 (1964).

1954 (1)

J. P. Botha, D. B. Spalding, “The Laminar Flame Speed of Propane/Air Mixtures with Heat Extraction from the Flame,” Proc. R. Soc. London Ser. A 225, 71 (1954).
[CrossRef]

Anderson, T. J.

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

Armstrong, B. H.

A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
[CrossRef]

Barton, S. A.

S. A. Barton, J. M. Garneau, Defence Research Establishment Valcartier, Quebec City; private communication.

Bonamy, J.

J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
[CrossRef]

Bonamy, L.

J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
[CrossRef]

Botha, J. P.

J. P. Botha, D. B. Spalding, “The Laminar Flame Speed of Propane/Air Mixtures with Heat Extraction from the Flame,” Proc. R. Soc. London Ser. A 225, 71 (1954).
[CrossRef]

Bourchardy, P.

Dobbs, G. M.

Druet, S. A. J.

S. A. J. Druet, J. P. E. Taran, “CARS Spectroscopy,” Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Eckbreth, A. C.

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

A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the Application of CARS to Turbulent Reacting Flows,” Exp. Fluids 3, 301 (1985).
[CrossRef]

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]

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. (Academic, New York, 1984), pp. 213–309.

Farrow, R. L.

Fischer, M.

D. R. Snelling, M. Fischer, “Design and Calibration of a Flat-Flame Burner using Line-Reversal Techniques,” Technical Note 85-4, Defence Research Establishment Ottawa, Canada (1985).

Garneau, J. M.

S. A. Barton, J. M. Garneau, Defence Research Establishment Valcartier, Quebec City; private communication.

Goss, L. P.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Greenhalgh, D. A.

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

D. A. Greenhalgh, S. T. Whittley, “Mode Noise in Broadband CARS Spectroscopy,” Appl. Opt. 24, 907 (1985).
[CrossRef] [PubMed]

D. A. Greenhalgh, F. M. Porter, “CARS Applications in Chemical Reactors, Combustion and Heat Transfer,” in Proceedings, First International Laser Sciences Conference, Dallas (Nov.1985).

Hall, R. J.

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

R. J. Hall, “Coherent Anti-Stokes Modelling for Combustion Diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

R. J. Hall, “Pressure Broadened Linewidths for CARS Thermometry,” Appl. Spectrosc. 34, 780 (1980).

R. J. Hall, “CARS Spectra of Combustion Gases,” Combust. Flame 35, 77 (1979).
[CrossRef]

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. (Academic, New York, 1984), pp. 213–309.

Hirose, C.

Hou, S. Y.

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

Hui, A. K.

A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
[CrossRef]

Hurst, W. S.

G. J. Rosasco, W. S. Hurst, “Measurement of Resonant and Nonresonant Third Order Nonlinear Susceptibilities by Coherent Raman Spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Kataoka, H.

Kim, H.

H. Kim, “Computer Programming in Physical Chemistry Laboratory,” J. Chem. Educ. 2, 120 (1970).
[CrossRef]

Knighten, G. V.

J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer, Berlin, 1979), pp. 253–299.
[CrossRef]

Koszykowski, M. L.

Lapp, M.

Lasser, T.

T. Lasser, “An Alternative Method for CARS Spectra Convolutions,” Opt. Commun. 35, 447 (1980).
[CrossRef]

Lefebvre, M.

Lucht, R. P.

L. A. Rahn, R. L. Farrow, R. P. Lucht, “Effects of Laser Field Statistics on Coherent Anti-Stokes Raman Spectroscopy Intensities,” Opt. Lett. 9, 223 (1984).
[CrossRef] [PubMed]

R. L. Farrow, L. A. Rahn, R. P. Lucht, “Effect of Non-Gaussian Pump Fuels Statistics on Unresolved CARS Spectra,” in Proceedings, Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 340–341.

Lundeen, T.

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

MacDonald, B. G.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Maeda, S.

Mattern, P. L.

May, A. D.

A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
[CrossRef]

Mcllrath, T. J.

Morris, M. B.

Mueller, R. E.

Nibler, J. W.

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

J. W. Nibler, G. V. Knighten, “Coherent Anti-Stokes Raman Spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer, Berlin, 1979), pp. 253–299.
[CrossRef]

Palmer, R. E.

Parameswaran, T.

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” at Sixty-seventh AGARD PEP Meeting on Advanced Instrumentation for Aeroengine Components, Philadelphia (May 1986).

T. Parameswaran, D. R. Snelling, “A Computer Program to Generate Coherent Anti-Stokes Raman Spectra,” Technical Note 81-18, Defence Research Establishment Ottawa, Canada (1982).

Pealat, M.

Penney, C. M.

Peters, R. L. St.

Porter, F. M.

D. A. Greenhalgh, F. M. Porter, “CARS Applications in Chemical Reactors, Combustion and Heat Transfer,” in Proceedings, First International Laser Sciences Conference, Dallas (Nov.1985).

Printer, F.

F. Printer, “Dependence of the Width of the Rotational Raman Lines of N2 and CO2 on the Quantum Number j,” Opt. Spectrosc. USSR 17, 428 (1964).

Rahn, L. A.

L. A. Rahn, R. L. Farrow, R. P. Lucht, “Effects of Laser Field Statistics on Coherent Anti-Stokes Raman Spectroscopy Intensities,” Opt. Lett. 9, 223 (1984).
[CrossRef] [PubMed]

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, Sandia National Laboratories, unpublished results.

R. L. Farrow, L. A. Rahn, R. P. Lucht, “Effect of Non-Gaussian Pump Fuels Statistics on Unresolved CARS Spectra,” in Proceedings, Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 340–341.

Robert, D.

J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
[CrossRef]

Rosasco, G. J.

G. J. Rosasco, W. S. Hurst, “Measurement of Resonant and Nonresonant Third Order Nonlinear Susceptibilities by Coherent Raman Spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Sawchuk, R. A.

D. R. Snelling, R. A. Sawchuk, R. E. Mueller, “Single-Pulse CARS Noise: A Comparison Between Single-Mode and Multimode Pump Lasers,” Appl. Opt. 24, 2771 (1985).
[CrossRef] [PubMed]

D. R. Snelling, R. A. Sawchuk, G. J. Smallwood, “Multichannel Light Detectors and Their Use for CARS Spectroscopy,” Appl. Opt. 23, 4083 (1984).
[CrossRef] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” at Sixty-seventh AGARD PEP Meeting on Advanced Instrumentation for Aeroengine Components, Philadelphia (May 1986).

Smallwood, G. J.

D. R. Snelling, R. A. Sawchuk, G. J. Smallwood, “Multichannel Light Detectors and Their Use for CARS Spectroscopy,” Appl. Opt. 23, 4083 (1984).
[CrossRef] [PubMed]

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” at Sixty-seventh AGARD PEP Meeting on Advanced Instrumentation for Aeroengine Components, Philadelphia (May 1986).

Snelling, D. R.

D. R. Snelling, R. A. Sawchuk, R. E. Mueller, “Single-Pulse CARS Noise: A Comparison Between Single-Mode and Multimode Pump Lasers,” Appl. Opt. 24, 2771 (1985).
[CrossRef] [PubMed]

D. R. Snelling, R. A. Sawchuk, G. J. Smallwood, “Multichannel Light Detectors and Their Use for CARS Spectroscopy,” Appl. Opt. 23, 4083 (1984).
[CrossRef] [PubMed]

D. R. Snelling, M. Fischer, “Design and Calibration of a Flat-Flame Burner using Line-Reversal Techniques,” Technical Note 85-4, Defence Research Establishment Ottawa, Canada (1985).

T. Parameswaran, D. R. Snelling, “A Computer Program to Generate Coherent Anti-Stokes Raman Spectra,” Technical Note 81-18, Defence Research Establishment Ottawa, Canada (1982).

D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, T. Parameswaran, “Nonlinearity and Single Shot Noise Problems in CARS Spectroscopy,” at Sixty-seventh AGARD PEP Meeting on Advanced Instrumentation for Aeroengine Components, Philadelphia (May 1986).

Spalding, D. B.

J. P. Botha, D. B. Spalding, “The Laminar Flame Speed of Propane/Air Mixtures with Heat Extraction from the Flame,” Proc. R. Soc. London Ser. A 225, 71 (1954).
[CrossRef]

Stryland, J. C.

A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
[CrossRef]

Stufflebeam, J. H.

A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the Application of CARS to Turbulent Reacting Flows,” Exp. Fluids 3, 301 (1985).
[CrossRef]

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]

Switzer, G. L.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Taran, J. P.

Taran, J. P. E.

S. A. J. Druet, J. P. E. Taran, “CARS Spectroscopy,” Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Teets, R. E.

Tellex, P. A.

Trump, D. D.

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Varghese, G.

A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
[CrossRef]

Whiting, E. E.

E. E. Whiting, “An Empirical Approximation to the Voigt Function,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

Whittley, S. T.

Wray, A. A.

A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
[CrossRef]

Yuratich, M. A.

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

App. Opt. (1)

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

Appl. Opt. (7)

Appl. Spectrosc. (2)

Can. J. Phys. (1)

A. D. May, J. C. Stryland, G. Varghese, “Collisional Narrowing of the Vibrational Raman Band of Nitrogen and Carbon Monoxide,” Can. J. Phys. 48, 2331 (1970).
[CrossRef]

Combust. Flame (1)

R. J. Hall, “CARS Spectra of Combustion Gases,” Combust. Flame 35, 77 (1979).
[CrossRef]

Exp. Fluids (1)

A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the Application of CARS to Turbulent Reacting Flows,” Exp. Fluids 3, 301 (1985).
[CrossRef]

J. Chem. Educ. (1)

H. Kim, “Computer Programming in Physical Chemistry Laboratory,” J. Chem. Educ. 2, 120 (1970).
[CrossRef]

J. Chem. Phys. (2)

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

J. Bonamy, L. Bonamy, D. Robert, “Overlapping Effects and Motional Narowing in Molecular Band Shapes: Application to the Q-Branch of HD,” J. Chem. Phys. 67, 4441 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (2)

E. E. Whiting, “An Empirical Approximation to the Voigt Function,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[CrossRef]

A. K. Hui, B. H. Armstrong, A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509 (1978).
[CrossRef]

Mol. Phys. (1)

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

Opt. Commun. (2)

T. Lasser, “An Alternative Method for CARS Spectra Convolutions,” Opt. Commun. 35, 447 (1980).
[CrossRef]

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

Opt. Eng. (1)

R. J. Hall, “Coherent Anti-Stokes Modelling for Combustion Diagnostics,” Opt. Eng. 22, 322 (1983).
[CrossRef]

Opt. Lett. (3)

Opt. Spectrosc. USSR (1)

F. Printer, “Dependence of the Width of the Rotational Raman Lines of N2 and CO2 on the Quantum Number j,” Opt. Spectrosc. USSR 17, 428 (1964).

Phys. Rev. A (1)

G. J. Rosasco, W. S. Hurst, “Measurement of Resonant and Nonresonant Third Order Nonlinear Susceptibilities by Coherent Raman Spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

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[CrossRef]

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S. A. J. Druet, J. P. E. Taran, “CARS Spectroscopy,” Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Rev. Sci. Instrum. (1)

L. P. Goss, D. D. Trump, B. G. MacDonald, G. L. Switzer, “10 Hz Coherent Anti-Stokes Raman Spectroscopy Apparatus for Turbulent Combustion Studies,” Rev. Sci. Instrum. 54, 563 (1983).
[CrossRef]

Other (11)

D. R. Snelling, M. Fischer, “Design and Calibration of a Flat-Flame Burner using Line-Reversal Techniques,” Technical Note 85-4, Defence Research Establishment Ottawa, Canada (1985).

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A. B. Harvey, Ed., Chemical Applications of Nonlinear Raman Spectroscopy (Academic, New York, 1981).

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[CrossRef]

D. A. Greenhalgh, F. M. Porter, “CARS Applications in Chemical Reactors, Combustion and Heat Transfer,” in Proceedings, First International Laser Sciences Conference, Dallas (Nov.1985).

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L. A. Rahn, Sandia National Laboratories, unpublished results.

R. L. Farrow, Sandia Laboratories, Livermore, CA; private communication.

T. Parameswaran, D. R. Snelling, “A Computer Program to Generate Coherent Anti-Stokes Raman Spectra,” Technical Note 81-18, Defence Research Establishment Ottawa, Canada (1982).

S. A. Barton, J. M. Garneau, Defence Research Establishment Valcartier, Quebec City; private communication.

R. L. Farrow, L. A. Rahn, R. P. Lucht, “Effect of Non-Gaussian Pump Fuels Statistics on Unresolved CARS Spectra,” in Proceedings, Ninth International Conference on Raman Spectroscopy (Chemical Society of Japan, Tokyo, 1984), pp. 340–341.

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Figures (7)

Fig. 1
Fig. 1

Optical multichannel detector read sequence.

Fig. 2
Fig. 2

Average N2 spectrum with average nonresonant reference above and referenced spectrum below.

Fig. 3
Fig. 3

Flat-flame burner construction.

Fig. 4
Fig. 4

Detector shot noise as a function of incident light intensity.

Fig. 5
Fig. 5

Detector shot noise as a function of signal counts for a fixed intensifier setting.

Fig. 6
Fig. 6

Temperature histograms calculated for single-mode and multimode (0.1-cm−1) pump operation with weighted and unweighted least-mean-squares fits using isolated line computer program.

Fig. 7
Fig. 7

Experimental single-mode N2 CARS flame spectrum compared with a best fit theory spectrum calculated with collisional narrowing included.

Tables (5)

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Table I Noise statistics: Standard Deviation σ Expressed as Percent

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Table II Effect of Weighting Coefficients on Analysis of Single-Pulse Single-Mode Data with Collisional Narrowing Included in CARS Theory

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Table III Effect of weighting Coefficients on Analysis of Single-pulse multimode (0.10-cm−1) Pump Laser Data with Collisional Narrowing and Cross-Coherence included in CARS Theory

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Table IV Effect of Weighting Coefficients on Analysis of Single-Pulse Multimode (0.69-cm−1) Pump Laser Data with Collisional Narrowing and Cross-Coherence Included in CARS Theory

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Table V Summary of Multiplulse CARS Temperature Measurements 10 mm above Burner Center

Equations (19)

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I ( ω a s ) ~ I p 2 I s χ ( 3 ) 2 ,
G t s = i ( ω p - ω s - ω t ) δ t s + Γ t 2 δ t s + γ t s ( 1 - δ t s ) ,
χ R ( δ ) = j a j λ j - δ + i λ j .
χ R ( δ ) = 4 II N c 4 h ω s 4 j Δ ρ j j ( d σ / d Ω ) j 2 δ - i Γ j .
I ( ω a s ) ~ I p I s [ ω p ( 0 ) - δ ] I p ( ω a s - δ ) χ ( 3 ) ( δ ) 2 d δ ,
w V = w L 2 + ( w L 2 4 + w G 2 ) 1 / 2 .
I a s ( ω a s ) = χ N R 2 1 + 2 χ N R Re χ R ( ω a s - ω ) + ½ χ R ( ω a s - ω ) 2 + ½ χ R ( ω a s - ω ) χ R ( ω a s - ω ) ,
F = d ω I p ( ω ) d ω I p ( ω ) F ( ω , ω ) .
I a s ( c c ) ( ω a s ) = Π 2 Δ ω ˜ p 2 | j a j w j ( Z j ) | 2 ,
Z j = - { λ j - [ ω a s - ω p ( 0 ) ] } - i λ j Δ ω ˜ p .
σ 2 = σ 0 2 + k C .
S i j = I i j K i , i = 1 N diodes , J = 1 N pulses ,
X i j = ( S i j / S i ¯ ) = ( I i j / j I i j ) M .
Y i j = X i j / i = N L N U X i j .
σ N 2 = σ C 2 + σ D 2 .
σ T 2 = σ 0 2 + k C + m C 2 ,
i w i ( T i - E i ) 2 ,
j T i ( ln E i - ln T i ) 2 ,
σ I = [ k I k 2 ] 1 / 2 / k I k ,

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