Abstract

The use of a modeless laser as the Stokes source for multiplex coherent anti-Stokes Raman scattering in molecular hydrogen is reported. The elimination of noise associated with mode competition in conventional standing wave lasers is shown to result in reliable and accurate single-shot thermometry of H2 in a microwave-assisted diamond chemical vapor deposition plasma reactor. Single-shot temperatures are recorded with a precision of 7.3%. Possible improvements to this precision are discussed and applications of the technique for on-line process monitoring are briefly presented.

© 1997 Optical Society of America

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References

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  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Abacus Press, Tunbridge Wells, G.B., 1987).
  2. W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
    [CrossRef]
  3. C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
    [CrossRef]
  4. S. Kröll, M. Aldén, T. Berglind, R. J. Hall, “Noise characteristics of single shot broadband Raman-resonant CARS with single- and multimode lasers,” Appl. Opt. 26, 1068–1073 (1987).
    [CrossRef] [PubMed]
  5. D. R. Snelling, R. A. Sawchuk, T. Parameswaran, “Noise in single-shot coherent anti-Stokes Raman spectroscopy that employs a modeless dye laser,” Appl. Opt. 33, 8295–8301 (1994).
    [CrossRef] [PubMed]
  6. W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
    [CrossRef]
  7. M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
    [CrossRef]
  8. A. Slenczka, G. Marowsky, “H2 vibrational CARS thermometry,” Appl. Phys. B 47, 41–46 (1988).
    [CrossRef]
  9. K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
    [CrossRef]
  10. V. Bergmann, W. Stricker, “H2 CARS thermometry in a fuel-rich, premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar,” Appl. Phys. B 61, 49–57 (1995).
    [CrossRef]
  11. T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
    [CrossRef]
  12. P. Ewart, “A modeless, variable bandwidth, tunable laser,” Opt. Commun. 55, 124–126 (1985).
    [CrossRef]
  13. P. Snowdon, S. M. Skippon, P. Ewart, “Improved precision of single-shot temperature measurements by broadband CARS by use of a modeless laser,” Appl. Opt. 30, 1008–1010 (1991).
    [CrossRef] [PubMed]
  14. C. F. Kaminski, P. Ewart, “Absolute concentration measurements of C2 in a diamond CVD reactor by laser-induced fluorescence,” Appl. Phys. B 61, 581–592 (1995).
    [CrossRef]
  15. A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
    [CrossRef]
  16. G. Clark, R. E. Palmer, R. L. Farrow, “carsfit computer code,” developed at Los Alamos and Sandia National Laboratories.
  17. V. Bergmann, “H2-CARS Thermometrie bei hohem Druck,” Ph.D. dissertation (Deutsche Forschungsanstalt für Luft und Raumfahrt, Stuttgart, 1993).
  18. T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
    [CrossRef]
  19. C. F. Kaminski, P. Ewart, “Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma,” Appl. Phys. B 64 (1997).

1997 (1)

C. F. Kaminski, P. Ewart, “Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma,” Appl. Phys. B 64 (1997).

1996 (1)

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

1995 (2)

V. Bergmann, W. Stricker, “H2 CARS thermometry in a fuel-rich, premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar,” Appl. Phys. B 61, 49–57 (1995).
[CrossRef]

C. F. Kaminski, P. Ewart, “Absolute concentration measurements of C2 in a diamond CVD reactor by laser-induced fluorescence,” Appl. Phys. B 61, 581–592 (1995).
[CrossRef]

1994 (1)

1992 (2)

C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
[CrossRef]

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

1991 (2)

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

P. Snowdon, S. M. Skippon, P. Ewart, “Improved precision of single-shot temperature measurements by broadband CARS by use of a modeless laser,” Appl. Opt. 30, 1008–1010 (1991).
[CrossRef] [PubMed]

1990 (1)

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

1988 (2)

A. Slenczka, G. Marowsky, “H2 vibrational CARS thermometry,” Appl. Phys. B 47, 41–46 (1988).
[CrossRef]

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

1987 (1)

1985 (1)

P. Ewart, “A modeless, variable bandwidth, tunable laser,” Opt. Commun. 55, 124–126 (1985).
[CrossRef]

1978 (1)

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

1976 (1)

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
[CrossRef]

Aldén, M.

Bacal, M.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Banholzer, W. F.

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

Berglind, T.

Bergmann, V.

V. Bergmann, W. Stricker, “H2 CARS thermometry in a fuel-rich, premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar,” Appl. Phys. B 61, 49–57 (1995).
[CrossRef]

V. Bergmann, “H2-CARS Thermometrie bei hohem Druck,” Ph.D. dissertation (Deutsche Forschungsanstalt für Luft und Raumfahrt, Stuttgart, 1993).

Berlemont, P.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Bischel, W. K.

C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
[CrossRef]

Bornemann, T.

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

Breagne, J.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Chang, M.-C.

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

Chen, K.-H.

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

Clauss, W.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Döbele, H. F.

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

Dreier, T.

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

Dyer, M. J.

C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Abacus Press, Tunbridge Wells, G.B., 1987).

Ewart, P.

C. F. Kaminski, P. Ewart, “Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma,” Appl. Phys. B 64 (1997).

C. F. Kaminski, P. Ewart, “Absolute concentration measurements of C2 in a diamond CVD reactor by laser-induced fluorescence,” Appl. Phys. B 61, 581–592 (1995).
[CrossRef]

P. Snowdon, S. M. Skippon, P. Ewart, “Improved precision of single-shot temperature measurements by broadband CARS by use of a modeless laser,” Appl. Opt. 30, 1008–1010 (1991).
[CrossRef] [PubMed]

P. Ewart, “A modeless, variable bandwidth, tunable laser,” Opt. Commun. 55, 124–126 (1985).
[CrossRef]

Hall, R. J.

Hering, C. G.

C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
[CrossRef]

Hutcheon, R. J.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Il’yukhin, A. A.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Kaminski, C. F.

C. F. Kaminski, P. Ewart, “Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma,” Appl. Phys. B 64 (1997).

C. F. Kaminski, P. Ewart, “Absolute concentration measurements of C2 in a diamond CVD reactor by laser-induced fluorescence,” Appl. Phys. B 61, 581–592 (1995).
[CrossRef]

Kormas, V.

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

Kozlov, D. N.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Kröll, S.

Lange, B.

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

Lefebvre, M.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Marowsky, G.

A. Slenczka, G. Marowsky, “H2 vibrational CARS thermometry,” Appl. Phys. B 47, 41–46 (1988).
[CrossRef]

Parameswaran, T.

Péalat, M.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Penney, C. M.

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

Roh, W. B.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
[CrossRef]

Sawchuk, R. A.

Schreiber, P. W.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
[CrossRef]

Schulz-von der Gathen, V.

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

Skinner, D. A.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Skippon, S. M.

Slenczka, A.

A. Slenczka, G. Marowsky, “H2 vibrational CARS thermometry,” Appl. Phys. B 47, 41–46 (1988).
[CrossRef]

Smirnov, V. V.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Snelling, D. R.

Snowdon, P.

Stel’makh, O. M.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Stricker, W.

V. Bergmann, W. Stricker, “H2 CARS thermometry in a fuel-rich, premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar,” Appl. Phys. B 61, 49–57 (1995).
[CrossRef]

Taran, J. P.

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Taran, J. P. E.

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
[CrossRef]

Vereschagin, K. A.

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

Wolfrum, J.

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

Zahn, M.

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (7)

C. F. Kaminski, P. Ewart, “Absolute concentration measurements of C2 in a diamond CVD reactor by laser-induced fluorescence,” Appl. Phys. B 61, 581–592 (1995).
[CrossRef]

V. Bergmann, W. Stricker, “H2 CARS thermometry in a fuel-rich, premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar,” Appl. Phys. B 61, 49–57 (1995).
[CrossRef]

T. Bornemann, V. Kormas, V. Schulz-von der Gathen, H. F. Döbele, “Temperature and concentration measurements of molecular hydrogen in a filamentary discharge by coherent anti-Stokes Raman Spectroscopy,” Appl. Phys. B 51, 307–313 (1990).
[CrossRef]

T. Dreier, B. Lange, J. Wolfrum, M. Zahn, “Determination of temperature and concentration of molecular nitrogen, oxygen, and methane with coherent anti-Stokes Raman scattering,” Appl. Phys. B 45, 183–190 (1988).
[CrossRef]

C. F. Kaminski, P. Ewart, “Multiplex H2 CARS thermometry in a microwave assisted diamond CVD plasma,” Appl. Phys. B 64 (1997).

W. Clauss, A. A. Il’yukhin, D. N. Kozlov, V. V. Smirnov, O. M. Stel’makh, K. A. Vereschagin, “Two wavelength-CARS thermometry of hydrogen,” Appl. Phys. B 62, 279–285 (1996).
[CrossRef]

A. Slenczka, G. Marowsky, “H2 vibrational CARS thermometry,” Appl. Phys. B 47, 41–46 (1988).
[CrossRef]

Appl. Phys. Lett. (2)

W. B. Roh, P. W. Schreiber, J. P. E. Taran, “Single-pulse coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 29, 174–176 (1976).
[CrossRef]

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

J. Appl. Phys. (1)

K.-H. Chen, M.-C. Chang, C. M. Penney, W. F. Banholzer, “Temperature and concentration distribution of H2 and H atoms in hot filament chemical-vapour deposition of diamond,” J. Appl. Phys. 71, 1485–1493 (1991).
[CrossRef]

J. Phys. II France (1)

M. Lefebvre, M. Péalat, J. P. Taran, M. Bacal, P. Berlemont, D. A. Skinner, J. Breagne, R. J. Hutcheon, “Coherent anti-Stokes Raman scattering study of the dynamics of a multipolar plasma generator,” J. Phys. II France 2, 295–314 (1992).
[CrossRef]

Opt. Commun. (1)

P. Ewart, “A modeless, variable bandwidth, tunable laser,” Opt. Commun. 55, 124–126 (1985).
[CrossRef]

Phys. Rev. A (1)

C. G. Hering, M. J. Dyer, W. K. Bischel, “Temperature and density dependence of the linewidths and line shifts of the rotational Raman lines in N2 and H2,” Phys. Rev. A 34, 1944–1951 (1992).
[CrossRef]

Other (3)

G. Clark, R. E. Palmer, R. L. Farrow, “carsfit computer code,” developed at Los Alamos and Sandia National Laboratories.

V. Bergmann, “H2-CARS Thermometrie bei hohem Druck,” Ph.D. dissertation (Deutsche Forschungsanstalt für Luft und Raumfahrt, Stuttgart, 1993).

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Abacus Press, Tunbridge Wells, G.B., 1987).

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Figures (2)

Fig. 1
Fig. 1

Top: single-shot CARS spectrum of H2 (circles) and theoretical fit (solid curve). The best-fit theoretical spectrum corresponds to a temperature of 2340 K. Bottom: room-temperature spectrum included for comparison.

Fig. 2
Fig. 2

Temperature distribution corresponding to 250 single-shot CARS spectra. The histogram corresponds to a most probable temperature of 2337 K with a standard deviation of 171 K. A Gaussian fit to the distribution is also shown.

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