Abstract

The accuracy and precision of time-resolved simultaneous temperature and O2-concentration measurements in binary N2–O2 mixtures by single-pulse dual-broadband pure rotational coherent anti-Stokes Raman scattering (CARS) have been investigated. We present a detailed comparison of the applicability of six evaluation procedures to measurements of air in a temperature range 300–2050 K. Special emphasis is put on the dependence of the results on experimental restrictions and distortions. This comparison includes the least-sum-of-squared-differences fit (LSF) in the frequency space obtained by use of three different kinds of weighting with respect to signal intensity and in Fourier space by use of the complex or the cosine Fourier transformation, both of which permit a great reduction in the number of data points necessary for multidimensional evaluation. Additionally, a cross-correlation technique is tested that, to the best of our knowledge, was not previously applied to pure rotational CARS. We also present the results of measurements directed to the determination of low O2-concentration levels that were performed for various binary mixtures (1.0–15.6% O2) and for natural air within a temperature range of 300–773 K. A comparison is given for the three evaluation techniques that have proved most promising for the high-temperature investigations, i.e., the constant and the inverse weighted LSF in frequency space and the Fourier analysis technique.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  30. J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).
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  42. T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
    [CrossRef]
  43. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  44. J. J. Moore, B. S. Garbow, K. E. Hillstrom, User Guide for MINPACK-1, Rep. ANL-80-74 (Argonne National Laboratory, Argonne, Ill., 1980).
  45. G. Engelen-Müllges, F. Reutter, Numerik-Algorithmen mit FORTRAN 77-Programmen, 7th ed. (Bibliographisches Institut Wissenschaftsverlag, Mannheim, Germany, 1993).
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    [CrossRef]

1997 (1)

1996 (2)

L. Martinsson, P.-E. Bengtsson, M. Alden, “Oxygen concentration and temperature measurements in N2–O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29–37 (1996).
[CrossRef]

T. Seeger, A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665–2671 (1996).
[CrossRef] [PubMed]

1995 (2)

1993 (2)

A. C. Eckbreth, T. J. Anderson, J. A. Shirley, “Laser Raman diagnostics for propulsion systems development,” Ber. Bunsenges. Phys. Chem. 97, 1597–1608 (1993).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

1992 (1)

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

1990 (3)

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

M. J. Cottereau, F. Grisch, J. J. Marie, “CARS measurements of temperature and species concentrations in an IC engine,” Appl. Phys. B 51, 63–66 (1990).
[CrossRef]

1989 (3)

1987 (2)

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

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, 99–110 (1987).
[CrossRef] [PubMed]

1985 (2)

1984 (3)

1982 (1)

1980 (1)

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

1979 (2)

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

M. A. Yuratich, “Effects of laser linewidth on coherent anti-Stokes Raman spectroscopy,” Mol. Phys. 38, 625–655 (1979).
[CrossRef]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Alden, M.

L. Martinsson, P.-E. Bengtsson, M. Alden, “Oxygen concentration and temperature measurements in N2–O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29–37 (1996).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

M. Alden, P.-E. Bengtsson, H. Edner, S. Kröll, D. Nilsson, “Rotational CARS: a comparison of different techniques with emphasis on accuracy in temperature determination,” Appl. Opt. 28, 3206–3219 (1989).
[CrossRef] [PubMed]

S. Kröll, M. Alden, P.-E. Bengtsson, C. Löfström, “An evaluation of precision and systematic errors in vibrational CARS thermometry,” Appl. Phys. B 49, 445–453 (1989).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, “Applications for rotational CARS for temperature measurements at high pressure and in particle-laden flames,” in Temperature: Its Measurements in Science and Industry, J. F. Schooley ed. (American Institute of Physics, New York, 1992), Vol. 6, pp. 679–684.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Anderson, T. J.

A. C. Eckbreth, T. J. Anderson, J. A. Shirley, “Laser Raman diagnostics for propulsion systems development,” Ber. Bunsenges. Phys. Chem. 97, 1597–1608 (1993).
[CrossRef]

Attal-Tretout, B.

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

Augustin, S. D.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Baker, D. R.

D. A. Greenhalgh, D. R. Williams, D. R. Baker, “The development and application of the CARS technique for in-cylinder IC engine Thermometry,” presented at the International Symposium on Automotive Technology and Automization (ISATA), Florence, Italy (1987).

Bengtsson, P.-E.

L. Martinsson, P.-E. Bengtsson, M. Alden, “Oxygen concentration and temperature measurements in N2–O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29–37 (1996).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

M. Alden, P.-E. Bengtsson, H. Edner, S. Kröll, D. Nilsson, “Rotational CARS: a comparison of different techniques with emphasis on accuracy in temperature determination,” Appl. Opt. 28, 3206–3219 (1989).
[CrossRef] [PubMed]

S. Kröll, M. Alden, P.-E. Bengtsson, C. Löfström, “An evaluation of precision and systematic errors in vibrational CARS thermometry,” Appl. Phys. B 49, 445–453 (1989).
[CrossRef]

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, “Applications for rotational CARS for temperature measurements at high pressure and in particle-laden flames,” in Temperature: Its Measurements in Science and Industry, J. F. Schooley ed. (American Institute of Physics, New York, 1992), Vol. 6, pp. 679–684.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Bombach, R.

R. Bombach, B. Hemmerlein, W. Kreutner, “CARS temperature measurements in a lean, turbulent, 120 kW natural gas flame,” in non-intrusive combustion diagnostics, K. K. Kuo, T. P. Parr, eds. (Begell, New York, 1994), pp. 145–151.

Bonamy, J.

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

Bood, J.

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

Bouchardy, P.

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

M. Pealat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Buchave, P.

C. H. Westergaard, P. Buchave, “PIV: comparison of three autocorrelation techniques,” in Fifth International Conference on Laser Anemometry: Advances and Applications, P. J. deGroot, ed., Proc. SPIE2052, 535–541 (1993).
[CrossRef]

Burgdorf, K.

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

Chang, R. K.

Cottereau, M. J.

M. J. Cottereau, F. Grisch, J. J. Marie, “CARS measurements of temperature and species concentrations in an IC engine,” Appl. Phys. B 51, 63–66 (1990).
[CrossRef]

Denbratt, I.

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

DePristo, A. E.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Dobbs, G. M.

Drake, J. D.

Eckbreth, A. C.

A. C. Eckbreth, T. J. Anderson, J. A. Shirley, “Laser Raman diagnostics for propulsion systems development,” Ber. Bunsenges. Phys. Chem. 97, 1597–1608 (1993).
[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, 1328–1339 (1984).
[CrossRef] [PubMed]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon & Breach, Amsterdam, 1996).

Edner, H.

Engelen-Müllges, G.

G. Engelen-Müllges, F. Reutter, Numerik-Algorithmen mit FORTRAN 77-Programmen, 7th ed. (Bibliographisches Institut Wissenschaftsverlag, Mannheim, Germany, 1993).

Farrow, R. L.

J. Zheng, J. B. Snow, D. V. Murphy, A. Leipertz, R. K. Chang, R. L. Farrow, “Experimental comparison of broadband rotational coherent anti-Stokes Raman scattering (CARS) and broadband vibrational CARS in a flame,” Opt. Lett. 9, 341–343 (1984).
[CrossRef] [PubMed]

L. A. Rahn, S. C. Johnston, R. L. Farrow, P. L. Mattern, “CARS thermometry in an internal combustion engine,” in Temperature: Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1982), Vol. 5, pp. 609–613.

Ferguson, C. R.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

Garbow, B. S.

J. J. Moore, B. S. Garbow, K. E. Hillstrom, User Guide for MINPACK-1, Rep. ANL-80-74 (Argonne National Laboratory, Argonne, Ill., 1980).

Görres, J.

Green, R. M.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

Greenhalgh, D. A.

D. A. Greenhalgh, D. R. Williams, D. R. Baker, “The development and application of the CARS technique for in-cylinder IC engine Thermometry,” presented at the International Symposium on Automotive Technology and Automization (ISATA), Florence, Italy (1987).

D. A. Greenhalgh, “Quantitative CARS spectroscopy,” in Advances in Non-Linear Spectroscopy, R. J. H. Clark, R. E. Hester, eds., Vol. 15 of Advances in Spectroscopy (Wiley, New York, 1988), pp. 193–251.

Grisch, F.

M. J. Cottereau, F. Grisch, J. J. Marie, “CARS measurements of temperature and species concentrations in an IC engine,” Appl. Phys. B 51, 63–66 (1990).
[CrossRef]

Haberäcker, P.

P. Haberäcker, Digitale Bildverarbeitung-Grundlagen und Anwendungen, 2nd ed. (Carl Hanser Verlag, Munich, 1987).

Hemmerlein, B.

R. Bombach, B. Hemmerlein, W. Kreutner, “CARS temperature measurements in a lean, turbulent, 120 kW natural gas flame,” in non-intrusive combustion diagnostics, K. K. Kuo, T. P. Parr, eds. (Begell, New York, 1994), pp. 145–151.

Hillstrom, K. E.

J. J. Moore, B. S. Garbow, K. E. Hillstrom, User Guide for MINPACK-1, Rep. ANL-80-74 (Argonne National Laboratory, Argonne, Ill., 1980).

Hirose, C.

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

Itoh, T.

T. Nakada, T. Itoh, Y. Takagi, “Application of CARS to development of high compression ratio spark ignition engine,” (Society of Automotive Engineers, Warrendale, Pa., 1993).

Johansson, B.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Johnston, S. C.

L. A. Rahn, S. C. Johnston, R. L. Farrow, P. L. Mattern, “CARS thermometry in an internal combustion engine,” in Temperature: Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1982), Vol. 5, pp. 609–613.

Jonuscheit, J.

Kajiyama, K.

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

Kampmann, S.

Katakoka, H.

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

Kreutner, W.

R. Bombach, B. Hemmerlein, W. Kreutner, “CARS temperature measurements in a lean, turbulent, 120 kW natural gas flame,” in non-intrusive combustion diagnostics, K. K. Kuo, T. P. Parr, eds. (Begell, New York, 1994), pp. 145–151.

Kröll, S.

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

M. Alden, P.-E. Bengtsson, H. Edner, S. Kröll, D. Nilsson, “Rotational CARS: a comparison of different techniques with emphasis on accuracy in temperature determination,” Appl. Opt. 28, 3206–3219 (1989).
[CrossRef] [PubMed]

S. Kröll, M. Alden, P.-E. Bengtsson, C. Löfström, “An evaluation of precision and systematic errors in vibrational CARS thermometry,” Appl. Phys. B 49, 445–453 (1989).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, “Applications for rotational CARS for temperature measurements at high pressure and in particle-laden flames,” in Temperature: Its Measurements in Science and Industry, J. F. Schooley ed. (American Institute of Physics, New York, 1992), Vol. 6, pp. 679–684.

Lasser, T.

T. Lasser, E. Magens, A. Leipertz, “Gas thermometry by Fourier analysis of rotational CARS,” Opt. Lett. 10, 535–537 (1985).
[CrossRef] [PubMed]

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

A. Leipertz, E. Magens, T. Lasser, “Flame temperature measurements using a novel rotational CARS analysis technique,” (American Institute of Aeronautics and Astronautics, New York, 1985).

Lassesson, B.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Lefebvre, M.

Leipertz, A.

A. Thumann, M. Schenk, J. Jonuscheit, T. Seeger, A. Leipertz, “Simultaneous temperature and relative nitrogen–oxygen concentration measurements in air using pure rotational coherent anti-Stokes Raman scattering for temperatures up to 2050 K,” Appl. Opt. 36, 3500–3505 (1997).
[CrossRef] [PubMed]

T. Seeger, A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665–2671 (1996).
[CrossRef] [PubMed]

S. Kampmann, T. Seeger, A. Leipertz, “Simultaneous coherent anti-Stokes Raman scattering and two-dimensional laser Rayleigh thermometry in a contained technical swirl combustor,” Appl. Opt. 34, 2780–2786 (1995).
[CrossRef] [PubMed]

T. Lasser, E. Magens, A. Leipertz, “Gas thermometry by Fourier analysis of rotational CARS,” Opt. Lett. 10, 535–537 (1985).
[CrossRef] [PubMed]

J. Zheng, J. B. Snow, D. V. Murphy, A. Leipertz, R. K. Chang, R. L. Farrow, “Experimental comparison of broadband rotational coherent anti-Stokes Raman scattering (CARS) and broadband vibrational CARS in a flame,” Opt. Lett. 9, 341–343 (1984).
[CrossRef] [PubMed]

A. Leipertz, E. Magens, T. Lasser, “Flame temperature measurements using a novel rotational CARS analysis technique,” (American Institute of Aeronautics and Astronautics, New York, 1985).

E. Magens, A. Leipertz, “Evaluation of accumulated pure rotational CARS spectra taken in mixing regions of flames,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 141–146.

A. Leipertz, “Temperaturbestimmung in Gasen mittels linearer und nichtlinearer Raman-Prozesse,” Habilitation thesis (Ruhr-Universität Bochum, Bochum, Germany, 1984).

Löfström, C.

S. Kröll, M. Alden, P.-E. Bengtsson, C. Löfström, “An evaluation of precision and systematic errors in vibrational CARS thermometry,” Appl. Phys. B 49, 445–453 (1989).
[CrossRef]

Lucht, R. P.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

Lückenrath, R.

Lundholm, G.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Maeda, S.

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

Magel, H.-J.

Magens, E.

T. Lasser, E. Magens, A. Leipertz, “Gas thermometry by Fourier analysis of rotational CARS,” Opt. Lett. 10, 535–537 (1985).
[CrossRef] [PubMed]

A. Leipertz, E. Magens, T. Lasser, “Flame temperature measurements using a novel rotational CARS analysis technique,” (American Institute of Aeronautics and Astronautics, New York, 1985).

E. Magens, “Nutzung von Rotations-CARS zur Temperatur- und Konzentrationsmessung in Flammen,” Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, Erlangen, Germany, 1993), Vol. 93.2.

E. Magens, A. Leipertz, “Evaluation of accumulated pure rotational CARS spectra taken in mixing regions of flames,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 141–146.

Magre, P.

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

Maier, H.

Marfori, K.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

Marie, J. J.

M. J. Cottereau, F. Grisch, J. J. Marie, “CARS measurements of temperature and species concentrations in an IC engine,” Appl. Phys. B 51, 63–66 (1990).
[CrossRef]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Martinsson, L.

L. Martinsson, P.-E. Bengtsson, M. Alden, “Oxygen concentration and temperature measurements in N2–O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29–37 (1996).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, “Applications for rotational CARS for temperature measurements at high pressure and in particle-laden flames,” in Temperature: Its Measurements in Science and Industry, J. F. Schooley ed. (American Institute of Physics, New York, 1992), Vol. 6, pp. 679–684.

Mattern, P. L.

L. A. Rahn, S. C. Johnston, R. L. Farrow, P. L. Mattern, “CARS thermometry in an internal combustion engine,” in Temperature: Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1982), Vol. 5, pp. 609–613.

Mauss, F.

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

Meier, W.

Moore, J. J.

J. J. Moore, B. S. Garbow, K. E. Hillstrom, User Guide for MINPACK-1, Rep. ANL-80-74 (Argonne National Laboratory, Argonne, Ill., 1980).

Murphy, D. V.

Nakada, T.

T. Nakada, T. Itoh, Y. Takagi, “Application of CARS to development of high compression ratio spark ignition engine,” (Society of Automotive Engineers, Warrendale, Pa., 1993).

Nilsson, D.

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

M. Alden, P.-E. Bengtsson, H. Edner, S. Kröll, D. Nilsson, “Rotational CARS: a comparison of different techniques with emphasis on accuracy in temperature determination,” Appl. Opt. 28, 3206–3219 (1989).
[CrossRef] [PubMed]

Palmer, R. E.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

Parameswaran, T.

Pealat, M.

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

M. Pealat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

Rabitz, H.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Rahn, L. A.

L. A. Rahn, S. C. Johnston, R. L. Farrow, P. L. Mattern, “CARS thermometry in an internal combustion engine,” in Temperature: Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1982), Vol. 5, pp. 609–613.

Ramaswany, R.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Reutter, F.

G. Engelen-Müllges, F. Reutter, Numerik-Algorithmen mit FORTRAN 77-Programmen, 7th ed. (Bibliographisches Institut Wissenschaftsverlag, Mannheim, Germany, 1993).

Robertson, G. N.

G. N. Robertson, Department of Physics, University of Cape Town, Rondebosch, South Africa (personal communications, 1997).

G. N. Robertson, A. Roblin, “Analysis of CARS spectra using Fourier transform techniques,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 39–42.

Roblin, A.

G. N. Robertson, A. Roblin, “Analysis of CARS spectra using Fourier transform techniques,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 39–42.

Sajiki, K.

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

Sawchuk, R. A.

Schenk, M.

Schnell, U.

Seeger, T.

Shirley, J. A.

A. C. Eckbreth, T. J. Anderson, J. A. Shirley, “Laser Raman diagnostics for propulsion systems development,” Ber. Bunsenges. Phys. Chem. 97, 1597–1608 (1993).
[CrossRef]

Smallwood, G. J.

Snelling, D. R.

Snow, J. B.

Spliethoff, H.

Squires, G. L.

G. L. Squires, Messergebnisse und ihre Auswertung (de Gruyter, Berlin, 1971).

Stricker, W.

Stufflebeam, J. H.

Takagi, Y.

T. Nakada, T. Itoh, Y. Takagi, “Application of CARS to development of high compression ratio spark ignition engine,” (Society of Automotive Engineers, Warrendale, Pa., 1993).

Taran, J. P.

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

Taran, J.-P.

Taylor, J. R.

J. R. Taylor, An Introduction to Error Analysis (University Science, Sausalito, Calif., 1982).

Teets, R. E.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

Tellex, P. A.

Thumann, A.

Westergaard, C. H.

C. H. Westergaard, P. Buchave, “PIV: comparison of three autocorrelation techniques,” in Fifth International Conference on Laser Anemometry: Advances and Applications, P. J. deGroot, ed., Proc. SPIE2052, 535–541 (1993).
[CrossRef]

Williams, D. R.

D. A. Greenhalgh, D. R. Williams, D. R. Baker, “The development and application of the CARS technique for in-cylinder IC engine Thermometry,” presented at the International Symposium on Automotive Technology and Automization (ISATA), Florence, Italy (1987).

Woyde, M.

Yuratich, M. A.

M. A. Yuratich, “Effects of laser linewidth on coherent anti-Stokes Raman spectroscopy,” Mol. Phys. 38, 625–655 (1979).
[CrossRef]

Zheng, J.

Appl. Opt. (10)

R. Lückenrath, M. Woyde, W. Meier, W. Stricker, U. Schnell, H.-J. Magel, J. Görres, H. Spliethoff, H. Maier, “Comparison of coherent anti-Stokes Raman-scattering thermometry with thermocouple measurements and model predictions in both natural-gas and coal-dust flames,” Appl. Opt. 34, 3303–3312 (1995).
[CrossRef]

S. Kampmann, T. Seeger, A. Leipertz, “Simultaneous coherent anti-Stokes Raman scattering and two-dimensional laser Rayleigh thermometry in a contained technical swirl combustor,” Appl. Opt. 34, 2780–2786 (1995).
[CrossRef] [PubMed]

D. R. Snelling, R. A. Sawchuk, G. J. Smallwood, “Multichannel light detectors and their use for CARS spectroscopy,” Appl. Opt. 23, 4083–4089 (1984).
[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, 99–110 (1987).
[CrossRef] [PubMed]

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, 1328–1339 (1984).
[CrossRef] [PubMed]

M. Pealat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

D. R. Snelling, G. J. Smallwood, T. Parameswaran, “Effect of detector nonlinearity and image persistence on CARS derived temperatures,” Appl. Opt. 28, 3233–3241 (1989).
[CrossRef] [PubMed]

T. Seeger, A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665–2671 (1996).
[CrossRef] [PubMed]

A. Thumann, M. Schenk, J. Jonuscheit, T. Seeger, A. Leipertz, “Simultaneous temperature and relative nitrogen–oxygen concentration measurements in air using pure rotational coherent anti-Stokes Raman scattering for temperatures up to 2050 K,” Appl. Opt. 36, 3500–3505 (1997).
[CrossRef] [PubMed]

M. Alden, P.-E. Bengtsson, H. Edner, S. Kröll, D. Nilsson, “Rotational CARS: a comparison of different techniques with emphasis on accuracy in temperature determination,” Appl. Opt. 28, 3206–3219 (1989).
[CrossRef] [PubMed]

Appl. Phys. B (5)

B. Attal-Tretout, P. Bouchardy, P. Magre, M. Pealat, J. P. Taran, “CARS in combustion: prospects and problems,” Appl. Phys. B 51, 17–24 (1990).
[CrossRef]

L. Martinsson, P.-E. Bengtsson, M. Alden, “Oxygen concentration and temperature measurements in N2–O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29–37 (1996).
[CrossRef]

S. Kröll, P.-E. Bengtsson, M. Alden, D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25–30 (1990).
[CrossRef]

S. Kröll, M. Alden, P.-E. Bengtsson, C. Löfström, “An evaluation of precision and systematic errors in vibrational CARS thermometry,” Appl. Phys. B 49, 445–453 (1989).
[CrossRef]

M. J. Cottereau, F. Grisch, J. J. Marie, “CARS measurements of temperature and species concentrations in an IC engine,” Appl. Phys. B 51, 63–66 (1990).
[CrossRef]

Ber. Bunsenges. Phys. Chem. (1)

A. C. Eckbreth, T. J. Anderson, J. A. Shirley, “Laser Raman diagnostics for propulsion systems development,” Ber. Bunsenges. Phys. Chem. 97, 1597–1608 (1993).
[CrossRef]

Combust. Sci. Technol. (2)

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I. CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[CrossRef]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

J. Chem. Phys. (2)

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99, 2466–2477 (1993).
[CrossRef]

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

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

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Mol. Phys. (1)

M. A. Yuratich, “Effects of laser linewidth on coherent anti-Stokes Raman spectroscopy,” Mol. Phys. 38, 625–655 (1979).
[CrossRef]

Opt. Commun. (1)

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

Opt. Lett. (3)

Other (25)

A. Leipertz, E. Magens, T. Lasser, “Flame temperature measurements using a novel rotational CARS analysis technique,” (American Institute of Aeronautics and Astronautics, New York, 1985).

L. A. Rahn, S. C. Johnston, R. L. Farrow, P. L. Mattern, “CARS thermometry in an internal combustion engine,” in Temperature: Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1982), Vol. 5, pp. 609–613.

D. A. Greenhalgh, D. R. Williams, D. R. Baker, “The development and application of the CARS technique for in-cylinder IC engine Thermometry,” presented at the International Symposium on Automotive Technology and Automization (ISATA), Florence, Italy (1987).

T. Nakada, T. Itoh, Y. Takagi, “Application of CARS to development of high compression ratio spark ignition engine,” (Society of Automotive Engineers, Warrendale, Pa., 1993).

K. Kajiyama, K. Sajiki, H. Katakoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” (Society of Automotive Engineers, Warrendale, Pa., 1982).

R. Bombach, B. Hemmerlein, W. Kreutner, “CARS temperature measurements in a lean, turbulent, 120 kW natural gas flame,” in non-intrusive combustion diagnostics, K. K. Kuo, T. P. Parr, eds. (Begell, New York, 1994), pp. 145–151.

T. Seeger, “Anwendungsvergleich von Vibrations- und Rotations-CARS in der technischen Verbrennung,” Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, Erlangen, Germany, 1994), Vol. 94.1.

E. Magens, “Nutzung von Rotations-CARS zur Temperatur- und Konzentrationsmessung in Flammen,” Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, Erlangen, Germany, 1993), Vol. 93.2.

P.-E. Bengtsson, L. Martinsson, M. Alden, B. Johansson, B. Lassesson, K. Marfori, G. Lundholm, “Dual broadband rotational CARS measurements in an IC engine,” in Proceedings of the Twenty-Fifth International Symposium on Combustion (Combustion Institute, Pittsburgh, Pa., 1992), pp. 1735–1742.

G. N. Robertson, A. Roblin, “Analysis of CARS spectra using Fourier transform techniques,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 39–42.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon & Breach, Amsterdam, 1996).

D. A. Greenhalgh, “Quantitative CARS spectroscopy,” in Advances in Non-Linear Spectroscopy, R. J. H. Clark, R. E. Hester, eds., Vol. 15 of Advances in Spectroscopy (Wiley, New York, 1988), pp. 193–251.

A. Leipertz, “Temperaturbestimmung in Gasen mittels linearer und nichtlinearer Raman-Prozesse,” Habilitation thesis (Ruhr-Universität Bochum, Bochum, Germany, 1984).

J. Bood, P.-E. Bengtsson, F. Mauss, K. Burgdorf, I. Denbratt, “Knock in spark-ignition engines: end-gas temperature measurements using rotational CARS and detailed kinetic calculations of autoignition process,” (Society of Automotive Engineers, Warrendale, Pa., 1997).

E. Magens, A. Leipertz, “Evaluation of accumulated pure rotational CARS spectra taken in mixing regions of flames,” in Coherent Raman Spectroscopy: Applications and New Developments, E. Castellucci, R. Righini, P. Foggi, eds. (World Scientific, Singapore, 1993), pp. 141–146.

L. Martinsson, P.-E. Bengtsson, M. Alden, S. Kröll, “Applications for rotational CARS for temperature measurements at high pressure and in particle-laden flames,” in Temperature: Its Measurements in Science and Industry, J. F. Schooley ed. (American Institute of Physics, New York, 1992), Vol. 6, pp. 679–684.

D. V. Murphy, “Broad-band rotational CARS thermometry in nitrogen gas,” Ph.D. dissertation (Yale University, New Haven, Conn., 1981).

J. J. Moore, B. S. Garbow, K. E. Hillstrom, User Guide for MINPACK-1, Rep. ANL-80-74 (Argonne National Laboratory, Argonne, Ill., 1980).

G. Engelen-Müllges, F. Reutter, Numerik-Algorithmen mit FORTRAN 77-Programmen, 7th ed. (Bibliographisches Institut Wissenschaftsverlag, Mannheim, Germany, 1993).

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

P. Haberäcker, Digitale Bildverarbeitung-Grundlagen und Anwendungen, 2nd ed. (Carl Hanser Verlag, Munich, 1987).

G. N. Robertson, Department of Physics, University of Cape Town, Rondebosch, South Africa (personal communications, 1997).

G. L. Squires, Messergebnisse und ihre Auswertung (de Gruyter, Berlin, 1971).

J. R. Taylor, An Introduction to Error Analysis (University Science, Sausalito, Calif., 1982).

C. H. Westergaard, P. Buchave, “PIV: comparison of three autocorrelation techniques,” in Fifth International Conference on Laser Anemometry: Advances and Applications, P. J. deGroot, ed., Proc. SPIE2052, 535–541 (1993).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Theoretical CARS spectra of N2, O2, and air for room temperature and atmospheric pressure in frequency space (left, top to bottom) and real parts of their Fourier transforms (right). The separation of the two molecule species in Fourier space can be seen clearly.

Fig. 2
Fig. 2

Illustration of the periodic boundary condition underlying the CFT (top) and the FFT (bottom) for a theoretical spectrum of pure N2 at 0.1 MPa and 1300 K. In each case the spectrum occupies the first 512 channels (solid curves). The other spectrum is the periodic extension (dashed curves) specified by the particular transformation.

Fig. 3
Fig. 3

Comparison of an experimental single-shot CARS spectrum of air for a reference temperature of 1000 K with the best-fitting theoretical library spectrum related to the specific evaluation procedure: (a) constant weighted LSF (T CARS = 997 K, C O2 = 21.17%), (b) complex FAT (T CARS = 983 K, C O2 = 21.13%), (c) cosine FAT (T CARS = 992 K, C O2 = 20.99%), and (d) cross-correlation technique (T CARS = 990 K, C O2 = 21.0%). The plots represent either the particular Fourier or frequency space. At the bottoms (a)–(c) the particular differences between theory and the experimental spectrum are depicted; for (d) the cross-correlation function is given with the characteristic maximum encircled.

Fig. 4
Fig. 4

Pdf’s of 500 single-pulse CARS spectra obtained by (a) the constant, (b) the inverse, and (c) the inverse squared weighted LSF’s, by (d) the complex and (e) the cosine FAT’s, and (f) by the cross-correlation technique. The reference temperature was 1000 K. The complex FAT and the cosine FAT employed 36 complex and 63 real coefficients, respectively.

Fig. 5
Fig. 5

Evaluated temperature mean value for the constant weighted LSF and its inaccuracy for constant, inverse, and inverse squared weighted LSF’s as well as for Fourier and cosine Fourier analysis techniques and for cross-correlation evaluation as a function of temperature.

Fig. 6
Fig. 6

Comparison of the means of the absolute values of the relative deviations from (a) the reference temperature and (b) the O2 concentration. It should be emphasized that these values are relative with respect to the reference data. C. W., constant weighted; I. W., inverse weighted; I. S. W., inverse squared weighted; compl. complex.

Fig. 7
Fig. 7

Evaluated O2 concentration mean value for the constant, the inverse, and the inverse squared weighted LSF’s as well as for the complex and the cosine FAT’s and for the cross-correlation evaluation as a function of temperature.

Fig. 8
Fig. 8

Standard deviation of O2-concentration mean value for the evaluation techniques tested as a function of temperature.

Fig. 9
Fig. 9

Dependence of both accuracy and precision of the evaluated temperature as well as concentration results on the relative shift of the spectral starting point of the theoretical and the experimental spectrum for 1000 K.

Fig. 10
Fig. 10

Illustration of the increasingly restricted spectral range investigated in Fig. 11.

Fig. 11
Fig. 11

Dependence of both accuracy and precision of the evaluated temperature as well as concentration results (top to bottom) on an increasingly restricted spectral range of evaluation for 1000 K. The complex FAT and the cosine FAT employed 36 complex and 63 real coefficients, respectively.

Fig. 12
Fig. 12

Pdf’s of 500 single-pulse CARS spectra achieved by (a) the constant and (b) the inverse weighted LSF and (c) by the complex FAT (cell temperature, 773 K; gravimetric concentration, 15.6%). The complex FAT employed 35 complex coefficients.

Fig. 13
Fig. 13

Mean values for the evaluated temperature versus gravimetric O2 concentration. Each point represents the average value of 500 single-shot results. Here and in Figs. 14 and 15: Const. W., constant weighted; Inv. W., inverse weighted.

Fig. 14
Fig. 14

Mean values for the evaluated O2 concentration versus gravimetric O2 concentration from constant and inverse weighted least-squares fits as well as from the FAT. Each point represents the average value of 500 single-shot results.

Fig. 15
Fig. 15

Standard deviation of the O2 concentration versus gravimetric O2 concentration for a temperature of 300 K.

Equations (6)

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k   g k | i e k - i t k T ,   c | 2 = min T ,   c ,
g k = 1 c 0 + c 1 i k e + c 2 i k e 2 .
H n k = 0 N - 1   h k exp 2 π ikn / N
F j k = 0 N - 1   h k   cos π kj / N
max Corr i e h ,   i t l j = max T ,   c ,
Corr i e h ,   i t l j = k = 0 N - 1   i e j + k   i t k .

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