Abstract

The Bayesian deconvolution algorithm described in a preceding paper [Appl. Opt. 43, 5669–5681 (2004)] is applied to measurement of the two-dimensional stoichiometry field in a combustible methane-air mixture by Raman imaging through a spectrograph. Stoichiometry (fuel equivalence ratio) is derived from the number density fields of methane and nitrogen, with a signal-to-noise ratio of ∼10 in a 600-laser-shot average. Prospects for single-shot Raman imaging are discussed.

© 2004 Optical Society of America

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References

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  1. R. A. L. Tolboom, N. J. Dam, J. J. ter Meulen, J. M. Mooij, J. D. M. Maassen, “Quantitative imaging through a spectrograph. 1. Principles and theory,” Appl. Opt. 43, 5669–5681 (2004).
    [CrossRef] [PubMed]
  2. R. A. L. Tolboom, N. J. Dam, N. M. Sijtsema, J. J. ter Meulen, “Quantitative spectrally resolved imaging through a spectrograph,” Opt. Lett. 28, 2046–2048 (2003).
    [CrossRef] [PubMed]
  3. I. Glassman, Combustion, 3rd ed. (Academic Press, San Diego, Calif., 1996).
  4. J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
    [CrossRef]
  5. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Vol. 7 of Energy and Engineering Science Series, A. K. Gupta, D. G. Lilley, eds. (Abacus, Cambridge, Mass., 1988).
  6. K. Kohse-Höinghaus, J. B. Jeffries, eds., Applied Combustion Diagnostics (Academic, San Diego, Calif., 2002).
  7. R. B. Miles, “Flow-field diagnostics,” in Applied Combustion Diagnostics, K. Kohse-Höinghaus, J. B. Jeffries, eds. (Academic, San Diego, Calif., 2002), pp. 194–223.
  8. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, Vol. II of Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1945).
  9. H. W. Schrötter, H. W. Klöckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed., Vol. 11 of Topics in Current Physics (Springer-Verlag, Heidelberg, Germany, 1979), pp. 123–166.
    [CrossRef]
  10. A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
    [CrossRef]
  11. R. Tolboom, “Expanding laser diagnostics in non-seeded compressible flow research,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 2002), available from http://webdoc.ubn.kun.nl/mono/t/tolboom_r/expaladii.pdf .
  12. M. B. Long, P. S. Levin, D. C. Fourguette, “Simultaneous two-dimensional mapping of species concentration and temperature in turbulent flames,” Opt. Lett. 10, 267–269 (1985).
    [CrossRef] [PubMed]
  13. R. W. Schefer, M. Namazian, J. Kelly, “Simultaneous Raman scattering and laser-induced-fluorescence for multispecies imaging in turbulent flames,” Opt. Lett. 16, 858–860 (1991).
    [CrossRef] [PubMed]

2004 (1)

2003 (1)

1994 (1)

A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
[CrossRef]

1991 (1)

1985 (1)

Dam, N. J.

de Goey, L. P. H.

A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
[CrossRef]

Dibble, R. W.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Vol. 7 of Energy and Engineering Science Series, A. K. Gupta, D. G. Lilley, eds. (Abacus, Cambridge, Mass., 1988).

Fourguette, D. C.

Glassman, I.

I. Glassman, Combustion, 3rd ed. (Academic Press, San Diego, Calif., 1996).

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, Vol. II of Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1945).

Kelly, J.

Klöckner, H. W.

H. W. Schrötter, H. W. Klöckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed., Vol. 11 of Topics in Current Physics (Springer-Verlag, Heidelberg, Germany, 1979), pp. 123–166.
[CrossRef]

Levin, P. S.

Long, M. B.

Maas, U.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
[CrossRef]

Maassen, J. D. M.

Miles, R. B.

R. B. Miles, “Flow-field diagnostics,” in Applied Combustion Diagnostics, K. Kohse-Höinghaus, J. B. Jeffries, eds. (Academic, San Diego, Calif., 2002), pp. 194–223.

Mooij, J. M.

Namazian, M.

Schefer, R. W.

Schrötter, H. W.

H. W. Schrötter, H. W. Klöckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed., Vol. 11 of Topics in Current Physics (Springer-Verlag, Heidelberg, Germany, 1979), pp. 123–166.
[CrossRef]

Sijtsema, N. M.

ter Meulen, J. J.

Thung, D. S.

A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
[CrossRef]

Tolboom, R.

R. Tolboom, “Expanding laser diagnostics in non-seeded compressible flow research,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 2002), available from http://webdoc.ubn.kun.nl/mono/t/tolboom_r/expaladii.pdf .

Tolboom, R. A. L.

van Maaren, A.

A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
[CrossRef]

Warnatz, J.

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
[CrossRef]

Appl. Opt. (1)

Combust. Sci. Technol. (1)

A. van Maaren, D. S. Thung, L. P. H. de Goey, “Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures,” Combust. Sci. Technol. 96, 327–344 (1994).
[CrossRef]

Opt. Lett. (3)

Other (8)

I. Glassman, Combustion, 3rd ed. (Academic Press, San Diego, Calif., 1996).

J. Warnatz, U. Maas, R. W. Dibble, Combustion (Springer-Verlag, Berlin, 1996).
[CrossRef]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Vol. 7 of Energy and Engineering Science Series, A. K. Gupta, D. G. Lilley, eds. (Abacus, Cambridge, Mass., 1988).

K. Kohse-Höinghaus, J. B. Jeffries, eds., Applied Combustion Diagnostics (Academic, San Diego, Calif., 2002).

R. B. Miles, “Flow-field diagnostics,” in Applied Combustion Diagnostics, K. Kohse-Höinghaus, J. B. Jeffries, eds. (Academic, San Diego, Calif., 2002), pp. 194–223.

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, Vol. II of Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1945).

H. W. Schrötter, H. W. Klöckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed., Vol. 11 of Topics in Current Physics (Springer-Verlag, Heidelberg, Germany, 1979), pp. 123–166.
[CrossRef]

R. Tolboom, “Expanding laser diagnostics in non-seeded compressible flow research,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 2002), available from http://webdoc.ubn.kun.nl/mono/t/tolboom_r/expaladii.pdf .

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Figures (10)

Fig. 1
Fig. 1

Schematic experimental configuration. (a) A thin ribbon of light (light gray) illuminates a sample. The probe volume, enclosed by the black box rule, is imaged onto the entrance slit of an imaging spectrograph with fixed length L s and adjustable width d s . The line of sight is perpendicular to the plane of the figure. (b) Each wavelength component in the scattered light produces one subimage of the probe volume on the exit plane of the spectrograph, some of them on the CCD detector chip. (Here we indicate schematically the hypothetical case of five discrete wavelength components, two of which produce overlapping subimages.)

Fig. 2
Fig. 2

Raman spectra of ambient air and of pure methane [1 bar (105 Pa)]. Note the logarithmic ordinate; the curves have been offset for clarity. The spectra were recorded through a spectrograph with a 1200-groove/mm grating using 355-nm light (tripled Nd:YAG laser) for illumination. The N2 band and the strongest CH4 (ν 1, ν 3, 2ν 2) bands are isolated, but the O2 band overlaps a weak (ν 2) CH4 band. There is also a relatively small contribution of water vapor in the ambient air spectrum.

Fig. 3
Fig. 3

Simulated methane Raman spectrum near a 3000-cm-1 Raman shift under 355-nm illumination. See text for details of the calculation. The three spectra correspond to three different temperatures. Note the logarithmic ordinate.

Fig. 4
Fig. 4

Experimental setup; see text for details. (c) The rectangle shows an artist’s impression of the expected stoichiometry distribution over the field of view of the detection system. The coordinate system used in the discussion is shown.

Fig. 5
Fig. 5

Raw data Raman OMA graphs: (a) narrow slit measurement of ambient air; (b) broad slit measurement of a methane-dry-air flow at nominally stoichiometric conditions (for the field of view see Fig. 2); (c), (d) narrow slit measurements of a pure methane flow. All spectra are on different linear scales; image (b) is on a linear gray scale (white, low; black, high intensity).

Fig. 6
Fig. 6

(a) Raw data and (c) deconvolved Raman OMA graphs of a methane-dry-air flow at nominally stoichiometric conditions (for the field of view see Fig. 3). Both images contain a N2 (top) and a methane (bottom) contribution, which are truncated at the left and the right by the spectrograph entrance slit length. The vertical axis of (c) contains the label (wavelength *), as it is purely spatial only within the N2 and CH4 reconstructions (see text for computational details). Vertical cross sections through the images of (a) (raw data) and (c) (reconstruction) at the locations indicated by the arrows are plotted in (b). All images are on the same linear intensity scale.

Fig. 7
Fig. 7

Results of deconvolution of the raw data [Fig. 4(b)] according to Eq. (10) with R N2 [Fig. 4(a)] for [N2] and with R CH4 [Fig. 4(c)] for [CH4]. The latter was postmultiplied by 2β. Both images are (i) on a purely spatial scale in both dimensions; (ii) on the same gray scale; and (iii) in units of [N2]amb I L,ref(y)f s (d s = 0.10 mm)/ I L (y), that is, still dependent on the laser-sheet inhomogeneity. For clarity the error bars indicate the parts that were selected in Fig. 4(b) for species-specific deconvolution as well as the actual width of the entrance slit.

Fig. 8
Fig. 8

Average stoichiometry distributions, derived from images like those of Fig. 6. Experimental settings are indicated at the left; the spatially averaged stoichiometries derived from the images are listed at the right [region involved indicated in (a)]. All deconvolutions were performed for σ/τ = 6 counts-1.

Fig. 9
Fig. 9

Single-shot Raman image from a flow in nominally stoichiometric conditions. Linear, inverted gray scale from 0 ≤ I [counts] ≤ 150.

Fig. 10
Fig. 10

Stoichiometry distributions determined from different numbers of laser shots. Spatial averages and standard deviations are determined in the dashed rectangular region (4050 pixels) of the stoichiometry for 625 laser pulses. See text for discussion.

Tables (1)

Tables Icon

Table 1 Assignments,a Raman Shifts, and Peak Positions (λ248/355) of the Raman Bands Observed in a Methane-Air Mixture on 248- and 355-nm Illumination

Equations (17)

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Tx, y=Sλy, λ * Sxin, y,
Sx, y; λ=?Sλy; λSx, y.
Pλ, x  s,i NisxILxσisλ
Φx, y= CH4x, y/O2x, yCH4/O2|stoich= 2CH4x, yO2x, y,
Φx, y= 2CH4x, yO2x, y= 2βCH4x, yN2x, y.
Sλλ=i σiλgi exp-Ei/kBTZ,
Sx=NxILxΔt,
Txout, y=xin ηx, y×i σixgi exp-Ei/kBTZ ×Nxin, yILxin, yΔtdxin,
Rx, yfs=ηx, y×i σixgi exp-Ei/kBTZ ×NrefyIL,refyΔtref,
Txout, y=xin Rˆxout-Msxin-xin,0, y×RfsNxin, yNrefyILxin, yIL,refyΔtΔtrefdxin.
Nxin, y=cyτ/σ2-bR˜k=0yR˜k=02y+τ/σ2+FT-1R˜k,n0*yt˜ky|R˜k,n0y|2+τ/σ2gref,
gref= NrefyfsRyIL,refyILxin, yΔtrefΔt,
O2Φ+ N2Φ+CH4Φ=O2amb+N2amb= β+1βN2amb,
N2Φ= 2β+12+2β+ΦN2amb,
O2Φ= 2β+1β2+2β+ΦN2amb,
CH4Φ= β+1Φβ2+2β+ΦN2amb.
CH4ref= β+1βN2amb, N2ref=N2amb

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