Abstract

A tunable diode laser was used for absorption tomography in an axisymmetric atmospheric pressure flat-flame burner. A rapid tomographic inversion algorithm was used to facilitate the many reconstructions at a relatively sparse set of projections typical of laser absorption tomography. Profiles of temperature and CO2 mole fraction were measured simultaneously in methane–air flames. Absorption measurements were made near the R-branch bandhead at 4.17 μm to minimize interferences with other species, while providing good temperature and concentration sensitivity at flame conditions. The procedure showed the advantage of reconstructing detailed spectra at each radial node.

© 2005 Optical Society of America

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  1. R. K. Hanson, P. A. Kuntz, C. H. Kruger, “High resolution spectroscopy of combustion gases using a tunable ir diode laser,” Appl. Opt. 16, 2045–2048 (1977).
    [CrossRef] [PubMed]
  2. R. K. Hanson, “Absorption spectroscopy in sooting flames using a tunable diode laser,” Appl. Opt. 19, 482–484 (1980).
    [CrossRef] [PubMed]
  3. R. K. Hanson, P. L. Varghese, S. Schoenung, P. K. Falcone, “Absorption spectroscopy of combustion gases using a tunable IR diode laser,” in Laser Probes for Combustion Chemistry, D.R. Crosley, ed., ACS Symp. Ser.134, 413–426 (1980).
    [CrossRef]
  4. L. Galatry, “Simultaneous effect of doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218–1223 (1961).
    [CrossRef]
  5. P. L. Varghese, R. K. Hanson, “Collisional narrowing effects on spectral line shapes measured at high resolution,” Appl. Opt. 23, 2376–2385 (1984).
    [CrossRef] [PubMed]
  6. M. Deutsch, I. Beniaminy, “Inversion of Abel’s integral equation for experimental Data,” J. Appl. Phys. 54, 137–143 (1983).
    [CrossRef]
  7. S. Gueron, M. Deutsch, “A fast Abel inversion algorithm,” J. Appl. Phys. 75, 4313–4318 (1994).
    [CrossRef]
  8. C. J. Dasch, “One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered back-projection methods,” Appl. Opt. 31, 1146–1152 (1992).
    [CrossRef] [PubMed]
  9. M. Ravichandran, F. C. Gouldin, “Determination of temperature and concentration profiles using (a limited number of) absorption-measurements,” Combust. Sci. Technol. 45, 47–64 (1986).
    [CrossRef]
  10. X. Ouyang, P. L. Varghese, “Selection of spectral lines for combustion diagnostics,” Appl. Opt. 29, 4884–4890 (1990).
    [CrossRef] [PubMed]
  11. L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
    [CrossRef]
  12. L. Rosenmann, J. M. Hartmann, M. Y. Perrin, J. Taine, “Accurate calculated tabulations of IR and Raman CO2 line broadening by CO2, H2O, N2, O2 in the 300–2400 K temperature range,” Appl. Opt. 27, 3902–3907 (1988).
    [CrossRef] [PubMed]
  13. R. Villarreal, “Diode laser tomography in flames,” M.S. thesis (Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, Texas, 1994).
  14. X. Ouyang, P. L. Varghese, “Reliable and efficient program for fitting Galatry and Voigt profiles to spectral data on multiple lines,” Appl. Opt. 28, 1538–1545 (1989).
    [CrossRef] [PubMed]
  15. C. de Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).
    [CrossRef]
  16. W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.
  17. W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
    [CrossRef]
  18. J. A. Silver, D. J. Kane, P. S. Greenberg, “Quantitative species measurements in microgravity flames with near-IR diode lasers,” Appl. Opt. 34, 2787–2801 (1995).
    [CrossRef] [PubMed]
  19. F.-Y. Zhang, T. Fujiwara, K. Komurasaki, “Diode-laser tomography for arcjet plume reconstruction,” Appl. Opt. 40, 957–964 (2001).
    [CrossRef]
  20. J. A. Silver, Southwest Sciences, Inc., 1570 Pacheco St., Suite E-11, Santa Fe, N.M. 87505 (personal communication).

2002 (1)

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

2001 (1)

1995 (1)

1994 (1)

S. Gueron, M. Deutsch, “A fast Abel inversion algorithm,” J. Appl. Phys. 75, 4313–4318 (1994).
[CrossRef]

1992 (2)

C. J. Dasch, “One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered back-projection methods,” Appl. Opt. 31, 1146–1152 (1992).
[CrossRef] [PubMed]

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

1990 (1)

1989 (1)

1988 (1)

1986 (1)

M. Ravichandran, F. C. Gouldin, “Determination of temperature and concentration profiles using (a limited number of) absorption-measurements,” Combust. Sci. Technol. 45, 47–64 (1986).
[CrossRef]

1984 (1)

1983 (1)

M. Deutsch, I. Beniaminy, “Inversion of Abel’s integral equation for experimental Data,” J. Appl. Phys. 54, 137–143 (1983).
[CrossRef]

1980 (1)

1977 (1)

1961 (1)

L. Galatry, “Simultaneous effect of doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218–1223 (1961).
[CrossRef]

Allen, M. G.

W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.

Beniaminy, I.

M. Deutsch, I. Beniaminy, “Inversion of Abel’s integral equation for experimental Data,” J. Appl. Phys. 54, 137–143 (1983).
[CrossRef]

Chen, S.-J.

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

Dahm, W. J. A.

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

Dasch, C. J.

de Boor, C.

C. de Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).
[CrossRef]

Deutsch, M.

S. Gueron, M. Deutsch, “A fast Abel inversion algorithm,” J. Appl. Phys. 75, 4313–4318 (1994).
[CrossRef]

M. Deutsch, I. Beniaminy, “Inversion of Abel’s integral equation for experimental Data,” J. Appl. Phys. 54, 137–143 (1983).
[CrossRef]

Falcone, P. K.

R. K. Hanson, P. L. Varghese, S. Schoenung, P. K. Falcone, “Absorption spectroscopy of combustion gases using a tunable IR diode laser,” in Laser Probes for Combustion Chemistry, D.R. Crosley, ed., ACS Symp. Ser.134, 413–426 (1980).
[CrossRef]

Fujiwara, T.

Galatry, L.

L. Galatry, “Simultaneous effect of doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218–1223 (1961).
[CrossRef]

Gamache, R. R.

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

Gouldin, F. C.

M. Ravichandran, F. C. Gouldin, “Determination of temperature and concentration profiles using (a limited number of) absorption-measurements,” Combust. Sci. Technol. 45, 47–64 (1986).
[CrossRef]

Greenberg, P. S.

Gueron, S.

S. Gueron, M. Deutsch, “A fast Abel inversion algorithm,” J. Appl. Phys. 75, 4313–4318 (1994).
[CrossRef]

Hanson, R. K.

Hartmann, J. M.

Hawkins, R. L.

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

Kane, D. J.

Kessler, W. J.

W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.

Komurasaki, K.

Kruger, C. H.

Kuntz, P. A.

Lo, E. Y.

W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.

Miller, M. F.

W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.

Mullin, J. A.

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

Ouyang, X.

Perrin, M. Y.

Piltch, N. D.

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

Ravichandran, M.

M. Ravichandran, F. C. Gouldin, “Determination of temperature and concentration profiles using (a limited number of) absorption-measurements,” Combust. Sci. Technol. 45, 47–64 (1986).
[CrossRef]

Rosenmann, L.

Rothman, L. S.

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

Schoenung, S.

R. K. Hanson, P. L. Varghese, S. Schoenung, P. K. Falcone, “Absorption spectroscopy of combustion gases using a tunable IR diode laser,” in Laser Probes for Combustion Chemistry, D.R. Crosley, ed., ACS Symp. Ser.134, 413–426 (1980).
[CrossRef]

Silver, J. A.

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

J. A. Silver, D. J. Kane, P. S. Greenberg, “Quantitative species measurements in microgravity flames with near-IR diode lasers,” Appl. Opt. 34, 2787–2801 (1995).
[CrossRef] [PubMed]

J. A. Silver, Southwest Sciences, Inc., 1570 Pacheco St., Suite E-11, Santa Fe, N.M. 87505 (personal communication).

Taine, J.

Varghese, P. L.

Villarreal, R.

R. Villarreal, “Diode laser tomography in flames,” M.S. thesis (Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, Texas, 1994).

Wattson, R. B.

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

Zhang, F.-Y.

Appl. Opt. (9)

R. K. Hanson, P. A. Kuntz, C. H. Kruger, “High resolution spectroscopy of combustion gases using a tunable ir diode laser,” Appl. Opt. 16, 2045–2048 (1977).
[CrossRef] [PubMed]

R. K. Hanson, “Absorption spectroscopy in sooting flames using a tunable diode laser,” Appl. Opt. 19, 482–484 (1980).
[CrossRef] [PubMed]

P. L. Varghese, R. K. Hanson, “Collisional narrowing effects on spectral line shapes measured at high resolution,” Appl. Opt. 23, 2376–2385 (1984).
[CrossRef] [PubMed]

C. J. Dasch, “One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered back-projection methods,” Appl. Opt. 31, 1146–1152 (1992).
[CrossRef] [PubMed]

X. Ouyang, P. L. Varghese, “Selection of spectral lines for combustion diagnostics,” Appl. Opt. 29, 4884–4890 (1990).
[CrossRef] [PubMed]

L. Rosenmann, J. M. Hartmann, M. Y. Perrin, J. Taine, “Accurate calculated tabulations of IR and Raman CO2 line broadening by CO2, H2O, N2, O2 in the 300–2400 K temperature range,” Appl. Opt. 27, 3902–3907 (1988).
[CrossRef] [PubMed]

X. Ouyang, P. L. Varghese, “Reliable and efficient program for fitting Galatry and Voigt profiles to spectral data on multiple lines,” Appl. Opt. 28, 1538–1545 (1989).
[CrossRef] [PubMed]

J. A. Silver, D. J. Kane, P. S. Greenberg, “Quantitative species measurements in microgravity flames with near-IR diode lasers,” Appl. Opt. 34, 2787–2801 (1995).
[CrossRef] [PubMed]

F.-Y. Zhang, T. Fujiwara, K. Komurasaki, “Diode-laser tomography for arcjet plume reconstruction,” Appl. Opt. 40, 957–964 (2001).
[CrossRef]

Combust. Sci. Technol. (1)

M. Ravichandran, F. C. Gouldin, “Determination of temperature and concentration profiles using (a limited number of) absorption-measurements,” Combust. Sci. Technol. 45, 47–64 (1986).
[CrossRef]

J. Appl. Phys. (2)

M. Deutsch, I. Beniaminy, “Inversion of Abel’s integral equation for experimental Data,” J. Appl. Phys. 54, 137–143 (1983).
[CrossRef]

S. Gueron, M. Deutsch, “A fast Abel inversion algorithm,” J. Appl. Phys. 75, 4313–4318 (1994).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

L. S. Rothman, R. L. Hawkins, R. B. Wattson, R. R. Gamache, “Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands,” J. Quant. Spectrosc. Radiat. Transfer 48, 537–566 (1992).
[CrossRef]

Phys. Rev. (1)

L. Galatry, “Simultaneous effect of doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218–1223 (1961).
[CrossRef]

Proc. Combust. Instit. (1)

W. J. A. Dahm, S.-J. Chen, J. A. Silver, J. A. Mullin, N. D. Piltch, “Mixture fraction measurements via WMS/ITAC in a microgravity vortex ring diffusion flame,” Proc. Combust. Instit. 29, 2519–2526 (2002).
[CrossRef]

Other (5)

J. A. Silver, Southwest Sciences, Inc., 1570 Pacheco St., Suite E-11, Santa Fe, N.M. 87505 (personal communication).

C. de Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).
[CrossRef]

W. J. Kessler, M. G. Allen, E. Y. Lo, M. F. Miller, “Tomographic reconstruction of air temperature and density profiles using tunable diode laser absorption measurements on O2,” AIAA Paper 95–1953, presented at the 26th AIAA Plasmadynamics and Lasers Conference, San Diego, California, June 1995.

R. Villarreal, “Diode laser tomography in flames,” M.S. thesis (Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, Texas, 1994).

R. K. Hanson, P. L. Varghese, S. Schoenung, P. K. Falcone, “Absorption spectroscopy of combustion gases using a tunable IR diode laser,” in Laser Probes for Combustion Chemistry, D.R. Crosley, ed., ACS Symp. Ser.134, 413–426 (1980).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Geometry of projections for tomographic reconstruction.

Fig. 2
Fig. 2

Comparison of the reconstruction of the radial test functions from a set of 10 noise-free projections. Open symbols are the reconstructions obtained using the corrected deconvolution matrix of Ref. 8. Closed symbols are the reconstructions using the modified deconvolution matrix presented using Eqs. (7) and (8). The symbols overlap closely except near the edge r = 1.

Fig. 3
Fig. 3

Comparison of the reconstruction error (ɛ) in the test functions shown in Fig. 2. Open symbols are the reconstructions obtained using the corrected deconvolution matrix of Ref. 8. Closed symbols are the reconstructions using the modified deconvolution matrix presented using Eqs. (7) and (8). The lines connecting the reconstruction points are shown to help see the radial variation of the error.

Fig. 4
Fig. 4

Schematic diagram of experimental setup.

Fig. 5
Fig. 5

Experimental data records obtained in a heated absorption cell containing pure CO2; T = 543.2 K, pCO2 = 0.078 atm.

Fig. 6
Fig. 6

(a) Transmission record and computed fit for the data of Fig. 5. Results: pCO2 = 0.0736 atm, T = 542.9 K. (b) Residual error from least-squares fit to data.

Fig. 7
Fig. 7

Raw projections and spline-smoothed transmissivity data obtained in a laminar flat-flame burner with a stoichiometric methane–air mixture for representative projections y/R = 0 and 0.895. The symbols are the original data, and the curves are the reassembled spectra after spline smoothing in y at each frequency. Symbols are plotted for only 20% of the data points for clarity.

Fig. 8
Fig. 8

Reconstructed transmissivity τ(νj; ri) at two radial nodes obtained by Abel inversion of the unsmoothed data; representative projections shown in Fig. 7.

Fig. 9
Fig. 9

Reconstructed transmissivity τ(νj; ri) at two radial nodes obtained by Abel inversion of the spline-smoothed data; representative records shown in Fig. 7.

Fig. 10
Fig. 10

Difference between the smoothed and original data for the records shown in Fig. 7. Reconstructed transmissivity τ(νj;ri) at two radial nodes obtained by Abel inversion of the spline-smoothed data; representative records shown in Fig. 7.

Fig. 11
Fig. 11

Comparison of temperature profiles obtained by tomographic reconstruction and by a thermocouple probe. The error bars represent estimated errors for the two procedures.

Fig. 12
Fig. 12

CO2 concentration profile over the burner obtained by tomographic reconstruction of absorption spectra recorded in a stoichiometric methane–air flame. The equilibrium values near the center are computed for a stoichiometric methane–air mixture using the tomographically determined temperature at the corresponding radial location.

Equations (9)

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τ ν ( I I o ) ν = exp [ - 0 L d x f ( x , ν ) ] ,
f ( x , ν ) = n CO 2 ( x ) j S j ( T ( x ) ) ϕ j ( ν - ν oj ; T ( x ) , n s ( x ) ) .
P ( y ; ν ) = - ln ( I I o ) ν , y = 2 y R f ( r , ν ) r d r ( r 2 - y 2 ) 1 / 2 , ν 1 < ν < ν 2 , - R < y < R .
f ( r , ν ) = - 1 π r R d P ( r , ν ) / d r ( y 2 - r 2 ) 1 / 2 d y ; ν 1 < ν < ν 2 , 0 < r < R .
f ( r i ; ν ) = 1 Δ r D i j P ( y j ; ν ) ,
D i j = { 0 j < i - 1 I i , j + 1 ( 0 ) - I i , j + 1 ( 1 ) j = i - 1 I i , j + 1 ( 0 ) - I i , j + 1 ( 1 ) + 2 I i , j ( 1 ) j = i I i , j + 1 ( 0 ) - I i , j + 1 ( 1 ) + 2 I i , j ( 1 ) - I i , j - 1 ( 0 ) - I i , j - 1 ( 1 ) j i + 1 I i , j + 1 ( 0 ) - I i , j + 1 ( 1 ) + 2 I i , j ( 1 ) - 2 I i , j - 1 ( 1 ) i = 0 , j = 1 .
I i j ( 0 ) = { 0 j < i or j = i = 0 or j = M 1 2 π ln { [ 4 j + 1 ] 1 / 2 + 2 j + 1 2 j } M - 1 > j = i 0 1 2 π ln { [ ( 2 j + 1 ) 2 - 4 i 2 ] 1 / 2 + 2 j + 1 [ ( 2 j - 1 ) 2 - 4 i 2 ] 1 / 2 + 2 j - 1 } M - 1 > j > i 1 2 π ln { [ 2 j + 1 ] 1 / 2 + j + 1 j } M - 1 = j = i 1 2 π ln [ [ ( 2 j + 2 ) 2 - 4 i 2 ] 1 / 2 + 2 j + 2 [ ( 2 j - 1 ) 2 - 4 i 2 ] 1 / 2 + 2 j - 1 ] M - 1 = j > i .
I i j ( 1 ) = { 0 j < i or j = M 1 2 π [ 4 j + 1 ] 1 / 2 - 2 j I j j ( 0 ) M - 1 > j = i 1 2 π { [ ( 2 j + 1 ) 2 - 4 i 2 ] 1 / 2 - [ ( 2 j - 1 ) 2 - 4 i 2 ] 1 / 2 } - 2 j I i j ( 0 ) M - 1 > j > i 1 2 π [ 8 j + 4 ] 1 / 2 - 2 j I j j ( 0 ) M - 1 = j = i 1 2 π { [ ( 2 j + 2 ) 2 - 4 i 2 ] 1 / 2 - [ ( 2 j - 1 ) 2 - 4 i 2 ] 1 / 2 } - 2 j I i j ( 0 ) M - 1 = j > i .
f 1 ( r ) = ( 1 - r 2 ) 2 P 1 ( y ) = 16 15 ( 1 - y 2 ) 5 / 2 , f 2 ( r ) = ( 1 - r 2 ) P 2 ( y ) = 4 3 ( 1 - y 2 ) 3 / 2 , f 3 ( r ) = ( 1 - r 2 ) 1 / 2 P 3 ( y ) = π 2 ( 1 - y 2 ) .

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