Abstract

A multiple-pass cell is aligned to focus light at two regions at the center of the cell. The two “points” are separated by 2.0 mm. Each probe region is 200μm×300μm. The cell is used to amplify spontaneous Raman scattering from a CH4–air laminar flame. The signal gain is 20, and the improvement in signal-to-noise ratio varies according to the number of laser pulses used for signal acquisition. The temperature is inferred by curve fitting high-resolution spectra of the Stokes signal from N2. The model accounts for details, such as the angular dependence of Raman scattering, the presence of a rare isotope of N2 in air, anharmonic oscillator terms in the vibrational polarizability matrix elements, and the dependence of Herman–Wallis factors on the vibrational level. The apparatus function is modeled using a new line shape function that is the convolution of a trapezoid function and a Lorentzian. The uncertainty in the value of temperature arising from noise, the uncertainty in the model input parameters, and various approximations in the theory have been characterized. We estimate that the uncertainty in our measurement of flame temperature in the least noisy data is ±9K.

© 2013 Optical Society of America

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2012 (1)

F. Fuest, R. S. Barlow, J-Y. Chen, and A. Dreizler, “Raman/Rayleigh scattering and CO-LIF measurements in laminar and turbulent jet flames of dimethyl ether,” Combust. Flame 159, 2533–2562 (2012).
[CrossRef]

2011 (3)

M. Marrocco, “Herman-Wallis correction in vibrational CARS of oxygen,” J. Raman Spectrosc. 42, 1836–1842 (2011).
[CrossRef]

A. Bohlin, P.-E. Bengtsson, and M. Marrocco, “On the sensitivity of rotational CARS N2 thermometry to the Herman-Wallis factor,” J. Raman Spectrosc. 42, 1843–1847 (2011).
[CrossRef]

K. C. Utsav, J. A. Silver, D. C. Hovde, and P. L. Varghese, “Improved multiple-pass Raman spectrometer,” Appl. Opt. 50, 4805–4816 (2011).
[CrossRef]

2010 (1)

M. Marrocco, “CARS thermometry revisited in light of the intramolecular perturbation,” J. Raman Spectrosc. 41, 870–874 (2010).
[CrossRef]

2009 (2)

M. Marrocco, “Herman-Wallis factor to improve thermometric accuracy of vibrational coherent anti-Stokes Raman spectra of H2,” Proc. Combust. Inst. 32, 863–870 (2009).
[CrossRef]

M. Marroco, “Comparative analysis of Herman-Wallis factors for uses in coherent anti-Stokes Raman spectra of light molecules,” J. Raman Spectrosc. 40, 741–747 (2009).
[CrossRef]

2008 (4)

2007 (3)

B. N. Ganguly, “Hydrocarbon combustion enhancement by applied electric field and plasma kinetics,” Plasma Phys. Controlled Fusion 49, B239–B246 (2007).
[CrossRef]

D. L. Wisman, S. D. Marcum, and B. N. Ganguly, “Electrical control of the thermodiffusive instability in premixed propane–air flames,” Combust. Flame 151, 639–648 (2007).
[CrossRef]

M. Marrocco, “Reliability of Herman-Wallis factors for Raman spectroscopy of Q-branch molecular transitions,” Chem. Phys. Lett. 442, 224–227 (2007).
[CrossRef]

2006 (3)

M. Fink and J. Campbell, “An all-quartz cell for multipass cavity,” Rev. Sci. Instrum. 77, 036113 (2006).
[CrossRef]

M. Afzelius, P-E. Bengtsson, J. Bood, C. Brackmann, and A. Kurtz, “Development of multipoint vibrational coherent anti-Stokes Raman spectroscopy for flame applications,” Appl. Opt. 45, 1177–1186 (2006).
[CrossRef]

J. M. Fernánde, A. Punge, G. Tejeda, and S. Montero, “Quantitative diagnostics of a methane/air mini‐flame by Raman spectroscopy,” J. Raman Spectrosc. 37, 175–182 (2006).
[CrossRef]

2004 (1)

J. Kojima and Q.-V. Nguyen, “Measurement and simulation of spontaneous Raman scattering in high-pressure fuel-rich H2–air flames,” Meas. Sci. Technol. 15, 565–580 (2004).
[CrossRef]

2003 (2)

G. Maroulis, “Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2,” J. Chem. Phys. 118, 2673–2687 (2003).
[CrossRef]

M. A. Buldakov, V. N. Cherepanov, B. V. Korolev, and I. I. Matrosov, “Role of intramolecular interactions in Raman spectra of N2 and O2 molecules,” J. Mol. Spectrosc. 217, 1–8 (2003).
[CrossRef]

2002 (2)

M. Pecul and A. Rizzo, “Linear response coupled cluster calculation of Raman scattering cross sections,” J. Chem. Phys. 116, 1259–1268 (2002).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Laser pulse-stretching with multiple optical ring cavities,” Appl. Opt. 41, 6360–6370 (2002).
[CrossRef]

2001 (2)

R. H. Tipping and J.-P. Bouanich, “On the use of Herman-Wallis factors for diatomic molecules,” J. Quant. Spectrosc. Radiat. Transfer 71, 99–103 (2001).
[CrossRef]

J. Bendtsen, “High-resolution Fourier transform Raman spectra of the fundamental bands of N14N15 and N152,” J. Raman Spectrosc. 32, 989–995 (2001).
[CrossRef]

2000 (1)

A. T. Hartlieb, B. Atakan, and K. Kohse-Höinghaus, “Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames,” Appl. Phys. B 70, 435–445 (2000).
[CrossRef]

1996 (1)

1991 (1)

R. R. Laher and F. R. Gilmore, “Improved fits for the vibrational and rotational constants of many states of nitrogen and oxygen,” J. Phys. Chem. Ref. Data 20, 685–712 (1991).
[CrossRef]

1990 (1)

P. L. Polavarapu, “Ab initio vibrational Raman and Raman optical activity spectra,” J. Phys. Chem. 94, 8106–8112 (1990).
[CrossRef]

1986 (1)

1985 (1)

W. Knippers, K. van Helvoort, and S. Stolte, “Vibrational overtones of the homonuclear diatomics (N2, O2, D2) observed by the spontaneous Raman effect,” Chem. Phys. Lett. 121, 279–286 (1985).
[CrossRef]

1984 (1)

R. H. Tipping and J. F. Ogilvie, “Herman-Wallis factors for Raman transitions of Σ1-state diatomic molecules,” J. Raman Spectrosc. 15, 38–40 (1984).
[CrossRef]

1980 (2)

G. Alessandretti, “Some results on the measurement of temperature and density in a flame by Raman spectroscopy,” Opt. Acta 27, 1095–1103 (1980).
[CrossRef]

W. R. Trutna and R. L. Byer, “Multiple-pass Raman gain cell,” Appl. Opt. 19, 301–312 (1980).
[CrossRef]

1978 (1)

1976 (1)

M. C. Drake and G. M. Rosenblatt, “Flame temperatures from Raman scattering,” Chem. Phys. Lett. 44, 313–316 (1976).
[CrossRef]

1959 (1)

T. C. James and W. Klemperer, “Line intensities in the Raman effect of Σ1 diatomic molecules,” J. Chem. Phys. 31, 130–134 (1959).
[CrossRef]

Aeschliman, D. P.

Afzelius, M.

Alessandretti, G.

G. Alessandretti, “Some results on the measurement of temperature and density in a flame by Raman spectroscopy,” Opt. Acta 27, 1095–1103 (1980).
[CrossRef]

Angel, S. M.

Atakan, B.

A. T. Hartlieb, B. Atakan, and K. Kohse-Höinghaus, “Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames,” Appl. Phys. B 70, 435–445 (2000).
[CrossRef]

Barlow, R. S.

F. Fuest, R. S. Barlow, J-Y. Chen, and A. Dreizler, “Raman/Rayleigh scattering and CO-LIF measurements in laminar and turbulent jet flames of dimethyl ether,” Combust. Flame 159, 2533–2562 (2012).
[CrossRef]

Bendtsen, J.

J. Bendtsen, “High-resolution Fourier transform Raman spectra of the fundamental bands of N14N15 and N152,” J. Raman Spectrosc. 32, 989–995 (2001).
[CrossRef]

Bengtsson, P.-E.

A. Bohlin, P.-E. Bengtsson, and M. Marrocco, “On the sensitivity of rotational CARS N2 thermometry to the Herman-Wallis factor,” J. Raman Spectrosc. 42, 1843–1847 (2011).
[CrossRef]

Bengtsson, P-E.

Bohlin, A.

A. Bohlin, P.-E. Bengtsson, and M. Marrocco, “On the sensitivity of rotational CARS N2 thermometry to the Herman-Wallis factor,” J. Raman Spectrosc. 42, 1843–1847 (2011).
[CrossRef]

Bood, J.

Bouanich, J.-P.

R. H. Tipping and J.-P. Bouanich, “On the use of Herman-Wallis factors for diatomic molecules,” J. Quant. Spectrosc. Radiat. Transfer 71, 99–103 (2001).
[CrossRef]

Brackmann, C.

Buldakov, M. A.

M. A. Buldakov, V. N. Cherepanov, B. V. Korolev, and I. I. Matrosov, “Role of intramolecular interactions in Raman spectra of N2 and O2 molecules,” J. Mol. Spectrosc. 217, 1–8 (2003).
[CrossRef]

Byer, R. L.

Campbell, J.

M. Fink and J. Campbell, “An all-quartz cell for multipass cavity,” Rev. Sci. Instrum. 77, 036113 (2006).
[CrossRef]

Carter, J. C.

Chan, J. W.-J.

Chen, J-Y.

F. Fuest, R. S. Barlow, J-Y. Chen, and A. Dreizler, “Raman/Rayleigh scattering and CO-LIF measurements in laminar and turbulent jet flames of dimethyl ether,” Combust. Flame 159, 2533–2562 (2012).
[CrossRef]

Cherepanov, V. N.

M. A. Buldakov, V. N. Cherepanov, B. V. Korolev, and I. I. Matrosov, “Role of intramolecular interactions in Raman spectra of N2 and O2 molecules,” J. Mol. Spectrosc. 217, 1–8 (2003).
[CrossRef]

Drake, M. C.

M. C. Drake and G. M. Rosenblatt, “Flame temperatures from Raman scattering,” Chem. Phys. Lett. 44, 313–316 (1976).
[CrossRef]

Dreizler, A.

F. Fuest, R. S. Barlow, J-Y. Chen, and A. Dreizler, “Raman/Rayleigh scattering and CO-LIF measurements in laminar and turbulent jet flames of dimethyl ether,” Combust. Flame 159, 2533–2562 (2012).
[CrossRef]

Fateley, W. G.

Fernánde, J. M.

J. M. Fernánde, A. Punge, G. Tejeda, and S. Montero, “Quantitative diagnostics of a methane/air mini‐flame by Raman spectroscopy,” J. Raman Spectrosc. 37, 175–182 (2006).
[CrossRef]

Fink, M.

M. Fink and J. Campbell, “An all-quartz cell for multipass cavity,” Rev. Sci. Instrum. 77, 036113 (2006).
[CrossRef]

Flower, W. L.

Fuest, F.

F. Fuest, R. S. Barlow, J-Y. Chen, and A. Dreizler, “Raman/Rayleigh scattering and CO-LIF measurements in laminar and turbulent jet flames of dimethyl ether,” Combust. Flame 159, 2533–2562 (2012).
[CrossRef]

Ganguly, B. N.

D. L. Wisman, S. D. Marcum, and B. N. Ganguly, “Electrical control of the thermodiffusive instability in premixed propane–air flames,” Combust. Flame 151, 639–648 (2007).
[CrossRef]

B. N. Ganguly, “Hydrocarbon combustion enhancement by applied electric field and plasma kinetics,” Plasma Phys. Controlled Fusion 49, B239–B246 (2007).
[CrossRef]

Gilmore, F. R.

R. R. Laher and F. R. Gilmore, “Improved fits for the vibrational and rotational constants of many states of nitrogen and oxygen,” J. Phys. Chem. Ref. Data 20, 685–712 (1991).
[CrossRef]

Gomez, A.

Hammaker, R. M.

Hartlieb, A. T.

A. T. Hartlieb, B. Atakan, and K. Kohse-Höinghaus, “Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames,” Appl. Phys. B 70, 435–445 (2000).
[CrossRef]

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (D. van Nostrand Company, 1950).

Hill, R. A.

Hovde, D. C.

Huang, J.

James, T. C.

T. C. James and W. Klemperer, “Line intensities in the Raman effect of Σ1 diatomic molecules,” J. Chem. Phys. 31, 130–134 (1959).
[CrossRef]

Karpetis, A. N.

Kim, S. B.

Klemperer, W.

T. C. James and W. Klemperer, “Line intensities in the Raman effect of Σ1 diatomic molecules,” J. Chem. Phys. 31, 130–134 (1959).
[CrossRef]

Knippers, W.

W. Knippers, K. van Helvoort, and S. Stolte, “Vibrational overtones of the homonuclear diatomics (N2, O2, D2) observed by the spontaneous Raman effect,” Chem. Phys. Lett. 121, 279–286 (1985).
[CrossRef]

Kohse-Höinghaus, K.

A. T. Hartlieb, B. Atakan, and K. Kohse-Höinghaus, “Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames,” Appl. Phys. B 70, 435–445 (2000).
[CrossRef]

Kojima, J.

J. Kojima and Q.-V. Nguyen, “Single-shot rotational Raman thermometry for turbulent flames using a low-resolution bandwidth technique,” Meas. Sci. Technol. 19, 015406 (2008).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Measurement and simulation of spontaneous Raman scattering in high-pressure fuel-rich H2–air flames,” Meas. Sci. Technol. 15, 565–580 (2004).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Laser pulse-stretching with multiple optical ring cavities,” Appl. Opt. 41, 6360–6370 (2002).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Spontaneous Raman scattering diagnostics: applications in practical combustion systems,” in Handbook of Combustion, M. Lackner, F. Winter, and A. K. Agarwal, eds. (Wiley-VCH, 2010), pp. 125–154.

Korolev, B. V.

M. A. Buldakov, V. N. Cherepanov, B. V. Korolev, and I. I. Matrosov, “Role of intramolecular interactions in Raman spectra of N2 and O2 molecules,” J. Mol. Spectrosc. 217, 1–8 (2003).
[CrossRef]

Kurtz, A.

Laher, R. R.

R. R. Laher and F. R. Gilmore, “Improved fits for the vibrational and rotational constants of many states of nitrogen and oxygen,” J. Phys. Chem. Ref. Data 20, 685–712 (1991).
[CrossRef]

Levinsky, H. B.

A. V. Sepman, V. V. Toro, A. V. Mokhov, and H. B. Levinsky, “Determination of temperature and concentrations of main components in flames by fitting measured Raman spectra,” Appl. Phys. B (to be published, 2013).
[CrossRef]

Li, X.

Lin, H.

Long, D. A.

D. A. Long, The Raman Effect (Wiley, 2002).

D. A. Long, Raman Spectroscopy (McGraw-Hill, 1977).

Marcum, S. D.

D. L. Wisman, S. D. Marcum, and B. N. Ganguly, “Electrical control of the thermodiffusive instability in premixed propane–air flames,” Combust. Flame 151, 639–648 (2007).
[CrossRef]

Maroulis, G.

G. Maroulis, “Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2,” J. Chem. Phys. 118, 2673–2687 (2003).
[CrossRef]

Marrocco, M.

A. Bohlin, P.-E. Bengtsson, and M. Marrocco, “On the sensitivity of rotational CARS N2 thermometry to the Herman-Wallis factor,” J. Raman Spectrosc. 42, 1843–1847 (2011).
[CrossRef]

M. Marrocco, “Herman-Wallis correction in vibrational CARS of oxygen,” J. Raman Spectrosc. 42, 1836–1842 (2011).
[CrossRef]

M. Marrocco, “CARS thermometry revisited in light of the intramolecular perturbation,” J. Raman Spectrosc. 41, 870–874 (2010).
[CrossRef]

M. Marrocco, “Herman-Wallis factor to improve thermometric accuracy of vibrational coherent anti-Stokes Raman spectra of H2,” Proc. Combust. Inst. 32, 863–870 (2009).
[CrossRef]

M. Marrocco, “Reliability of Herman-Wallis factors for Raman spectroscopy of Q-branch molecular transitions,” Chem. Phys. Lett. 442, 224–227 (2007).
[CrossRef]

Marroco, M.

M. Marroco, “Comparative analysis of Herman-Wallis factors for uses in coherent anti-Stokes Raman spectra of light molecules,” J. Raman Spectrosc. 40, 741–747 (2009).
[CrossRef]

Matrosov, I. I.

M. A. Buldakov, V. N. Cherepanov, B. V. Korolev, and I. I. Matrosov, “Role of intramolecular interactions in Raman spectra of N2 and O2 molecules,” J. Mol. Spectrosc. 217, 1–8 (2003).
[CrossRef]

Mokhov, A. V.

A. V. Sepman, V. V. Toro, A. V. Mokhov, and H. B. Levinsky, “Determination of temperature and concentrations of main components in flames by fitting measured Raman spectra,” Appl. Phys. B (to be published, 2013).
[CrossRef]

Montero, S.

J. M. Fernánde, A. Punge, G. Tejeda, and S. Montero, “Quantitative diagnostics of a methane/air mini‐flame by Raman spectroscopy,” J. Raman Spectrosc. 37, 175–182 (2006).
[CrossRef]

Mulac, A. J.

Nguyen, Q.-V.

J. Kojima and Q.-V. Nguyen, “Single-shot rotational Raman thermometry for turbulent flames using a low-resolution bandwidth technique,” Meas. Sci. Technol. 19, 015406 (2008).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Measurement and simulation of spontaneous Raman scattering in high-pressure fuel-rich H2–air flames,” Meas. Sci. Technol. 15, 565–580 (2004).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Laser pulse-stretching with multiple optical ring cavities,” Appl. Opt. 41, 6360–6370 (2002).
[CrossRef]

J. Kojima and Q.-V. Nguyen, “Spontaneous Raman scattering diagnostics: applications in practical combustion systems,” in Handbook of Combustion, M. Lackner, F. Winter, and A. K. Agarwal, eds. (Wiley-VCH, 2010), pp. 125–154.

Ogilvie, J. F.

R. H. Tipping and J. F. Ogilvie, “Herman-Wallis factors for Raman transitions of Σ1-state diatomic molecules,” J. Raman Spectrosc. 15, 38–40 (1984).
[CrossRef]

Pearman, W. F.

Pecul, M.

M. Pecul and A. Rizzo, “Linear response coupled cluster calculation of Raman scattering cross sections,” J. Chem. Phys. 116, 1259–1268 (2002).
[CrossRef]

Polavarapu, P. L.

P. L. Polavarapu, “Ab initio vibrational Raman and Raman optical activity spectra,” J. Phys. Chem. 94, 8106–8112 (1990).
[CrossRef]

Punge, A.

J. M. Fernánde, A. Punge, G. Tejeda, and S. Montero, “Quantitative diagnostics of a methane/air mini‐flame by Raman spectroscopy,” J. Raman Spectrosc. 37, 175–182 (2006).
[CrossRef]

Rizzo, A.

M. Pecul and A. Rizzo, “Linear response coupled cluster calculation of Raman scattering cross sections,” J. Chem. Phys. 116, 1259–1268 (2002).
[CrossRef]

Rosenblatt, G. M.

M. C. Drake and G. M. Rosenblatt, “Flame temperatures from Raman scattering,” Chem. Phys. Lett. 44, 313–316 (1976).
[CrossRef]

Sepman, A. V.

A. V. Sepman, V. V. Toro, A. V. Mokhov, and H. B. Levinsky, “Determination of temperature and concentrations of main components in flames by fitting measured Raman spectra,” Appl. Phys. B (to be published, 2013).
[CrossRef]

Silver, J. A.

Stolte, S.

W. Knippers, K. van Helvoort, and S. Stolte, “Vibrational overtones of the homonuclear diatomics (N2, O2, D2) observed by the spontaneous Raman effect,” Chem. Phys. Lett. 121, 279–286 (1985).
[CrossRef]

Tejeda, G.

J. M. Fernánde, A. Punge, G. Tejeda, and S. Montero, “Quantitative diagnostics of a methane/air mini‐flame by Raman spectroscopy,” J. Raman Spectrosc. 37, 175–182 (2006).
[CrossRef]

Tipping, R. H.

R. H. Tipping and J.-P. Bouanich, “On the use of Herman-Wallis factors for diatomic molecules,” J. Quant. Spectrosc. Radiat. Transfer 71, 99–103 (2001).
[CrossRef]

R. H. Tipping and J. F. Ogilvie, “Herman-Wallis factors for Raman transitions of Σ1-state diatomic molecules,” J. Raman Spectrosc. 15, 38–40 (1984).
[CrossRef]

Toro, V. V.

A. V. Sepman, V. V. Toro, A. V. Mokhov, and H. B. Levinsky, “Determination of temperature and concentrations of main components in flames by fitting measured Raman spectra,” Appl. Phys. B (to be published, 2013).
[CrossRef]

Trutna, W. R.

Utsav, K. C.

van Helvoort, K.

W. Knippers, K. van Helvoort, and S. Stolte, “Vibrational overtones of the homonuclear diatomics (N2, O2, D2) observed by the spontaneous Raman effect,” Chem. Phys. Lett. 121, 279–286 (1985).
[CrossRef]

Varghese, P. L.

Waldherr, G. A.

Wisman, D. L.

D. L. Wisman, S. D. Marcum, and B. N. Ganguly, “Electrical control of the thermodiffusive instability in premixed propane–air flames,” Combust. Flame 151, 639–648 (2007).
[CrossRef]

Xia, Y.

Zhan, L.

Appl. Opt. (7)

Appl. Phys. B (1)

A. T. Hartlieb, B. Atakan, and K. Kohse-Höinghaus, “Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames,” Appl. Phys. B 70, 435–445 (2000).
[CrossRef]

Appl. Spectrosc. (1)

Chem. Phys. Lett. (3)

M. Marrocco, “Reliability of Herman-Wallis factors for Raman spectroscopy of Q-branch molecular transitions,” Chem. Phys. Lett. 442, 224–227 (2007).
[CrossRef]

W. Knippers, K. van Helvoort, and S. Stolte, “Vibrational overtones of the homonuclear diatomics (N2, O2, D2) observed by the spontaneous Raman effect,” Chem. Phys. Lett. 121, 279–286 (1985).
[CrossRef]

M. C. Drake and G. M. Rosenblatt, “Flame temperatures from Raman scattering,” Chem. Phys. Lett. 44, 313–316 (1976).
[CrossRef]

Combust. Flame (2)

D. L. Wisman, S. D. Marcum, and B. N. Ganguly, “Electrical control of the thermodiffusive instability in premixed propane–air flames,” Combust. Flame 151, 639–648 (2007).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (18)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Pattern on the rear mirror.

Fig. 3.
Fig. 3.

Probe region above the burner.

Fig. 4.
Fig. 4.

Raman signal from flame on the image sensor. Top, ring mode; bottom, two-point mode.

Fig. 5.
Fig. 5.

Horizontally binned versions of the raw data in Fig. 4.

Fig. 6.
Fig. 6.

Curve fit on atomic line emissions from Ne to determine the pixel positions of the line centers.

Fig. 7.
Fig. 7.

Determination of the wavelength calibration function.

Fig. 8.
Fig. 8.

Residuals in the curve fit on pixel versus wavelength. Uncertainty error bars on the cubic points reflect 0.01 pixel uncertainty in line center location and corresponding uncertainty in wavelength based on local slope.

Fig. 9.
Fig. 9.

Black body and lamp counts as a function of wavelength. The power supply of the lamp was set at 5 V and 9 A. Both the lamp and the black body spectra are recorded under identical camera settings.

Fig. 10.
Fig. 10.

Comparison of some of the models considered for the line shape function.

Fig. 11.
Fig. 11.

Curve fit to O and S branches from room air and the residuals. Angular dependence, Herman–Wallis factors, scattering from N14N15, anharmonic oscillator assumption, and polarization sensitivity factor are excluded from the model.

Fig. 12.
Fig. 12.

Residuals of curve fit to O and S branches from room air. Scattering from N14N14, anharmonic oscillator assumption, and polarization sensitivity factor are excluded from the model.

Fig. 13.
Fig. 13.

Residuals of curve fit to O and S branches from room air. Anharmonic oscillator assumption and polarization sensitivity factor are excluded from the model. Note the expanded scale of the error plot relative to the errors in Figs. 11 and 12.

Fig. 14.
Fig. 14.

Curve fit to O and S branches from room air. Note the expanded scale of the error plot relative to the errors in Figs. 11 and 12.

Fig. 15.
Fig. 15.

Residuals in the curve fit to flame data by using different levels of theory. Theory level of Fig. 11 (top—I), Fig. 13 (mid—II), and Fig. 14 (bottom—III).

Fig. 16.
Fig. 16.

Simultaneous curve fit to (a) O branch and (b) S branch in flame using the most (III) and the least (I) sophisticated theory by floating the line shape parameters at known temperature. Theory level in simulation II of (c) Q branch corresponds to that of Fig. 13.

Fig. 17.
Fig. 17.

Simultaneous curve fit to (a) O branch, (b) Q branch, and (c) S branch from flame for temperature determination.

Fig. 18.
Fig. 18.

Errors in the value of inferred temperature in the spectra acquired over 100 and 1000 pulses.

Tables (7)

Tables Icon

Table 1. Level of Theory Used in the Simulation

Tables Icon

Table 2. Values of Polarizability Parameters (in Å3) of N214 Used in the Simulations

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Table 3. Temperature from Curve Fit for Different Values of SNR

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Table 4. Signal to Noise in the Fundamental Band and the First and Second Hot Bands

Tables Icon

Table 5. Temperature Sensitivity to Slight Changes in the Model (T=1800K)

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Table 6. Possible Values of the Line Shape Parameters in the Flame

Tables Icon

Table 7. Gain in Signal and SNR Relative to Single Pass

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

Plancks functionBlackbody counts×Raman counts=Calibrated Raman intensity.
I(λ)=GT[ν0νk(v,J)]4×gs(J)(2J+1)exp(hcEv(v)kT)exp(hcEJ(v,J)kT)Q(T)Φx(v,J)L(λ;λk(v,J),b,ΔλL,t).
gs(J)(2J+1)exp(hcEv(ν)kT)exp(hcEJ(ν,J)kT)Q(T),
Ev(v)=ωe(v+12)ωexe(v+12)2+ωeye(v+12)3+ωeze(v+12)4,
EJ(v,J)=[Beαe(v+12)+γe(v+12)2]J(J+1)DJ2(J+1)2.
ΦJJ±2=745M(v,γ)F(v,J,γ)bJ±2,J4ϕcosθ+145M(v,γ)F(v,J,γ)bJ±2,J112(9cosθcos3θ)(sin2ϕ2ϕ),
ΦJJ=[M(v,α)F(v,J,α)+745M(v,γ)F(v,J,γ)bJ,J]4ϕcosθ+[M(v,α)F(v,J,α)+745M(v,γ)F(v,J,γ)bJ,J112(9cosθcos3θ)(sin2ϕ2ϕ)].
bJJ2=3J(J1)2(2J+1)(2J1),bJJ=J(J+1)(2J1)(2J+3),bJJ+2=3(J+1)(J+2)2(2J+1)(2J+3).
M(v,p)=Beωe(v+1)Rp2{pe+(v+1)(2Beωe)[(1116a1234a2)pe54a1pe+14pe]}2.
F(v,J,γ)=[1+RγM(v,γ)1/2{m(v+12)12(2Beωe)32{2γe+(v+1)(2Beωe)[(92a2418a12152a16)γe+(134a1+34)γe12γe]}+(m2+3)(v+12)12(2Beωe)52[316(a1+1)γe+14γe]}]2,
F(v,J,p)=[1+RpM(v,p)1/2{m(v+12)12(2Beωe)52[34(1+a1)pe+pe]}]2,
T(x,b,t)={0,<x<b.x+b(b+t)(bt),b<x<t.1b+t,t<x<t.xb(b+t)(bt),t<x<b.0,b<x<.
x=λλk.
L(x,ΔλL)=1πΔλLΔλL2+x2.
I(λ;λk(v,J),b,ΔλL,t)=12π(b2t2){(xb)tan1(xbΔλL)+(x+b)tan1(x+bΔλL)(xt)tan1(xtΔλL)(x+t)tan1(x+tΔλL)+ΔλL2Ln[ΔλL2+(xt)2][ΔλL2+(x+t)2][ΔλL2+(xb)2][ΔλL2+(x+b)2]}.
|Rv=1anh|2|Rv=0anh|2=((1.871+0.105v)v=1(1.871+0.105v)v=0)2=1.0113,
|Rv=1h|2|Rv=0h|2=ν0ν1=2329.9142301.238=1.0125.

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