Abstract

Planar laser-induced fluorescence is often used to obtain two-dimensional density distributions of specific molecules in reactive or nonreactive flows. In opaque environments, such as sooty flames or dusty air flows, the laser intensity decrease over the field of view must be taken into account. We describe two methods to determine the local extinction factor, and, from that, the local laser intensity. Both methods are based on elastic light scattering, one of which employs two elastic light scattering images, recorded simultaneously from the same probe volume, but illuminated from opposite directions. Although exact in principle, this method requires considerable experimental expenditure, and for this reason a more approximate method by use of only a single elastic scattering image is described as well. The results of both methods, applied to combustion diagnostics in an optically accessible Diesel engine, are compared.

© 2000 Optical Society of America

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References

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  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus Press, Cambridge, Mass., 1988).
  2. K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
    [CrossRef]
  3. E. W. Rothe, P. Andresen, “Application of tunable excimer lasers to combustion diagnostics: a review,” Appl. Opt. 36, 3971–4033 (1997).
    [CrossRef] [PubMed]
  4. D. Stepowski, “Auto calibration of OH laser induced fluorescence signals by local absorption measurement in a flame,” in Proceedings of the Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1839–1846.
  5. M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
    [CrossRef]
  6. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  7. G. G. M. Stoffels, “Nitric oxide in a Diesel engine: laser-based detection and interpretation,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 1999).
  8. G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).
  9. S. Stoks, “Interpretation of 2D NO LIF images from a Diesel engine,” Internal Report (University of Nijmegen, Nijmegen, The Netherlands, 1999).
  10. Data for Suprasil 1, supplied by the manufacturer, Heraeus Amersil, Inc., 3473 Satellite Boulevard, Duluth, Ga. 30096-5821.
  11. J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
    [CrossRef]
  12. J. B. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, Singapore, 1988).

1997 (2)

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

E. W. Rothe, P. Andresen, “Application of tunable excimer lasers to combustion diagnostics: a review,” Appl. Opt. 36, 3971–4033 (1997).
[CrossRef] [PubMed]

1994 (1)

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[CrossRef]

1965 (1)

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Aldén, M.

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Andresen, P.

Birkhoff, R. D.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Carter, J. G.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Dam, N.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Duff, J. L. C.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus Press, Cambridge, Mass., 1988).

Georgiev, N.

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Hamm, R. N.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Heywood, J. B.

J. B. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, Singapore, 1988).

Huebner, R. H.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kohse-Höinghaus, K.

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[CrossRef]

Kröll, S.

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Martinsson, L.

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Meerts, W. L.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Rickeard, D. J.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Rothe, E. W.

Spaanjaars, C. M. I.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Stepowski, D.

D. Stepowski, “Auto calibration of OH laser induced fluorescence signals by local absorption measurement in a flame,” in Proceedings of the Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1839–1846.

Stoffels, G. G. M.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

G. G. M. Stoffels, “Nitric oxide in a Diesel engine: laser-based detection and interpretation,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 1999).

Stoks, S.

S. Stoks, “Interpretation of 2D NO LIF images from a Diesel engine,” Internal Report (University of Nijmegen, Nijmegen, The Netherlands, 1999).

ter Meulen, J. J.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

van den Boom, E. J.

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

Versluis, M.

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Versluis, N. Georgiev, L. Martinsson, M. Aldén, S. Kröll, “2-D absolute concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration,” Appl. Phys. B 65, 411–417 (1997).
[CrossRef]

Phys. Rev. A (1)

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical properties of graphite in region 1100 to 1300 Å,” Phys. Rev. A 137, A639–A641 (1965).
[CrossRef]

Prog. Energy Combust. Sci. (1)

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactive intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994).
[CrossRef]

Other (8)

D. Stepowski, “Auto calibration of OH laser induced fluorescence signals by local absorption measurement in a flame,” in Proceedings of the Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1839–1846.

J. B. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, Singapore, 1988).

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus Press, Cambridge, Mass., 1988).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

G. G. M. Stoffels, “Nitric oxide in a Diesel engine: laser-based detection and interpretation,” Ph.D. dissertation (University of Nijmegen, Nijmegen, The Netherlands, 1999).

G. G. M. Stoffels, E. J. van den Boom, C. M. I. Spaanjaars, N. Dam, W. L. Meerts, J. J. ter Meulen, J. L. C. Duff, D. J. Rickeard, “In-cylinder measurements of NO formation in a Diesel engine,” SAE paper #1999-01-1487 (Society of Automotive Engineers, Warrendale, Pa., 1999).

S. Stoks, “Interpretation of 2D NO LIF images from a Diesel engine,” Internal Report (University of Nijmegen, Nijmegen, The Netherlands, 1999).

Data for Suprasil 1, supplied by the manufacturer, Heraeus Amersil, Inc., 3473 Satellite Boulevard, Duluth, Ga. 30096-5821.

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Figures (8)

Fig. 1
Fig. 1

(a) Geometry of a field of view (f.o.v.) illuminated by two oppositely directed laser beams. (b) Schematic top view of the laser light sheet that traverses the engine in the forward direction, from side window W1 to side window W2 (compare with Fig. 3). The x axis is along the laser beam propagation direction and the scattered light from the central part (25 mmϕ) is observed in the direction perpendicular to the laser sheet (z direction) through top window W3 between the boundaries x = 0 and x = L(y). The piston surface with diameter D = 81 mm is also indicated.

Fig. 2
Fig. 2

Effect of noise on the reconstruction of scatterer distribution by use of the single-image method: (a) artificial input distribution [nσ]sca, (b) corresponding elastic scattering signal, (c) reconstructed [from trace (b)] input distribution, (d) reconstructed input distribution with 10% multiplicative noise added to (b), (e) reconstructed input distribution with 10% additive noise added to (b).

Fig. 3
Fig. 3

(a) Schematic view of the experimental setup. One laser light sheet traverses the engine from side window W1 to side window W2 (forward direction), whereas the other traverses the engine from W2 to W1 (backward direction). The plane of both light sheets is parallel to the piston upper surface. Elastically scattered radiation is detected through top window W3 in a direction perpendicular to the laser sheets by two intensified CCD cameras. B, beam splitter; M, mirror. (b) Timing sequence.

Fig. 4
Fig. 4

Column 1: elastic scattering images, illuminated in the forward direction, averaged over five engine cycles, obtained at 37°, 43°, 62°, 68°, 74°, and 93° aTDC. Column 2: same, but illuminated in the backward direction. Column 3: the attenuation coefficient, [nσ]ext(x, y), derived from the elastic scattering images by use of the double-image method (Subsection 2.B). The 100% corresponds to an attenuation coefficient of 0.08 mm-1. Columns 4 and 5: local laser intensity decrease in the forward, D for(x, y), and the backward, D back(x, y), directions, obtained from the local attenuation factor. The 100% corresponds to D = 1. Columns 6 and 7: effective scatterer distributions determined from the forward, Q for(x, y), and the backward, Q back(x, y), elastic scattering images, and corresponding laser intensity decrease image. Laser beam directions are indicated in the figure. The dark spots that are present in all the scattering images are the result of dirt on the top window. All the images are represented in a linear gray scale, and all except those of D for/back and nσ are individually scaled to improve contrast. The faint horizontal structure in some of the images is an artifact of the software that was used for image processing. The arrows are explained in the text.

Fig. 5
Fig. 5

Three pairs of single-shot elastic scattering images, S for(x, y) and S back(x, y) (columns 1 and 2), obtained at 62° aTDC, the corresponding attenuation coefficient distribution, [nσ]ext(x, y) (column 3), the laser intensity decrease, D for(x, y) and D back(x, y) (columns 4 and 5), and effective scatterer distributions, Q for(x, y) and Q back(x, y) (columns 6 and 7). Laser beam directions are indicated in the figure. All the images are represented in a linear gray scale, and all except those of D for/back and nσ are individually scaled to improve contrast.

Fig. 6
Fig. 6

One pair of single-shot elastic scattering images S for(x, y) and S back(x, y) obtained at 62° aTDC, laser intensity decrease D for(x, y) and D back(x, y), and effective scatterer distributions Q for(x, y) and Q back(x, y) obtained with the double-image method (row 1). Laser intensity decrease images and corresponding scatterer distributions obtained from the elastic scattering images with the single-image method with the transmission obtained from the average attenuation coefficient with the double-image method (row 2), a five times higher transmission (row 3), and a five times lower transmission (row 4). Laser beam directions are indicated in the figure. All the images are represented in a linear gray scale, and all except those of D for/back are individually scaled to improve contrast.

Fig. 7
Fig. 7

Pairs of forward S for(x, y) (column 1) and backward S back(x, y) (column 2) elastic scattering images averaged over five cycles obtained at 37°, 43°, 62°, 68°, 74°, and 93° aTDC. The local laser intensity decrease in the forward D for(x, y) (column 3) and the backward D back(x, y) (column 4) directions obtained by use of the single-image method (Subsection 2.B) with the transmission obtained with the double-image method. The effective scatterer distributions determined from the forward Q for(x, y) (column 5) and the backward Q back(x, y) (column 6) elastic scattering image and corresponding laser intensity decrease image. Laser beam directions are indicated in the figure. All the images are represented in a linear gray scale, and all except those of D for/back are individually scaled to improve contrast.

Fig. 8
Fig. 8

Transmission of 193-nm laser radiation through the firing engine (excluding the losses in the side windows) derived from the average attenuation coefficient obtained with the double-image method for the averaged scattering images (■). The error bars on the 62° aTDC data point are based on observed cycle-to-cycle variations. The solid curve is based on direct transmission measurements, scaled to fit the double-image data. The resulting scale factor leads to the conclusion that the combined window transmission is only 0.5%.

Equations (29)

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Sx, y=CAx, ynx, yσx, yILx, y,
Iforx, y=Ifor0, yexp-0xnσextx, ydx,
nσextx, y=nσscax, y+nσabsx, y,
Ibackx, y=IbackL, y×exp-Lxnσextx, y-dx,
Rx, y=defSbackx, ySforx, y=CCIbackL, yIfor0, yexp-Lxnσextx, y-dx+0xnσextx, ydx=CCIbackL, yIfor0, yexp2 0xnσextx, ydx-0Lnσextx, ydx.
ln Rx, y=lnCCIbackL, yIfor0, y+2 0xnσextx, ydx-0Lnσextx, ydx.
ddxln Rx, y=2nσextx, y,
nσextx, y=12ddxlnSbackx, ySforx, y.
nσscax, y=ξnσabsx, y.
Iforx, y=Ifor0, yexp-0x1+ξnσabsx, ydx.
Sforx, y=CIfor0, yξnσabsx, y×exp-0x1+ξnσabsx, ydx=-Cξ1+ξ Ifor0, yddx×exp-0x1+ξnσabsx, ydx.
0x Sforx, ydx=Cξ1+ξ Ifor0, y×1-exp-0x1+ξ×nσabsx, ydx,
Ifor0, y=IW1TW1 exp-W10nσextx, ydx,
Ifor0, y=IW1TW1 exp-nσ¯extD-Ly2,
IW2=IW1TW1TW2 exp-nσ¯extD,
nσ¯ext=-1DlnIW2IW1TW1TW2,
0Ly Sforx, ydx=Cξ1+ξ Ifor0, y×1-exp-1+ξnσ¯absLy,
Ifor0, y=1+ξCξ1-IW2IW1TW1TW2Ly/D-1×0Ly Sforx, ydx.
Iforx, yIfor0, y=exp-0x1+ξnσ¯absx, ydx=1-1+ξCξ Ifor-10, y0x Sforx, ydx=1-1-IW2IW1TW1TW2Ly/D×0x Sforx, ydx0Ly Sforx, ydx.
exp-0xnσextx, ydx=Iforx, yIfor0, y=def Dforx, y.
exp-Lyxnσextx, yd-x=Ibackx, yIbackLy, y=def Dbackx, y.
Sforx, yDforx, y=CAx, yIfor0, ynσscax, y=def Qforx, y,
Sbackx, yDbackx, y=CAx, yIbackLx, ynσscax, y=def Qbackx, y,
Qforx, yQbackx, y=CIfor0, yCIbackLy, y=Cy.
nσscax, y=ξnσabsx, y.
Ψext=4x Imm2-1m2+21+x215m2-1m2+2×m4+27m2+382m2+3+83 x4Rem2-1m2+12,
Ψsca=83 x4m2-1m2+12,
Ψabs=Ψext-Ψsca.
ξ=ΨscaΨabs=x31.44+0.13x2-1.99x3.

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