Abstract

An inverse radiation analysis using soot emission measured by a high-speed stereoscopic imaging system is described for simultaneous estimation of the 3-D soot temperature and volume fraction distributions in unsteady sooty flames. A new iterative reconstruction method taking self attenuation into account is developed based on the least squares minimum-residual algorithm. Numerical assessment and experimental measurement results of an ethylene/air diffusive flame show that the proposed method is efficient and capable of reconstructing the soot temperature and volume fraction distributions in unsteady flames. The accuracy is improved when self attenuation is considered.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
    [CrossRef]
  15. D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. M. M. Hossain, G. Lu, and Y. Yan, “Three-dimensional reconstruction of combustion flames through optical fibre sensing and CCD imaging,” in Proceedings of IEEE I2MTC (IEEE, 2011), pp. 79–83.
  19. Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
    [CrossRef]
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    [CrossRef]
  21. M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003) pp. 373–376.
  22. H. Chang and T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices offlame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
    [CrossRef]
  23. D. C. L. Fong and M. A. Saunders, “LSMR: An iterative algorithm for sparse least-squares problems,” SIAM J. Sci. Comput. 33 (2011).
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    [CrossRef]
  25. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
    [CrossRef]
  26. S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
    [CrossRef]

2011 (2)

J. Floyd, P. Geipel, and A. M. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158, 376–391(2011).
[CrossRef]

D. C. L. Fong and M. A. Saunders, “LSMR: An iterative algorithm for sparse least-squares problems,” SIAM J. Sci. Comput. 33 (2011).

2010 (3)

Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
[CrossRef]

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

N. Anikin, R. Suntz, and H. Bochhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100, 675–694 (2010).
[CrossRef]

2009 (2)

C. Lou and H. C. Zhou, “Simultaneous determination of distributions of temperature and soot volume fraction in sooting flames using decoupled reconstruction method,” Numer. Heat Transfer A 56, 153–169 (2009).

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

2008 (1)

2007 (2)

G. Gilabert, G. Lu, and Y. Yan, “Tomographic reconstruction of the luminosity distribution of a combustion flame,” IEEE Trans. Instrum. Meas. 56, 1300–1306 (2007).
[CrossRef]

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

2006 (1)

2005 (1)

Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J., Ser. B 48, 34–41 (2005).
[CrossRef]

2002 (1)

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

2001 (3)

L. H. Liu and J. Jiang, “Inverse radiation problem for reconstruction of temperature profile in axisymmetric free flames,” J. Quant. Spectrosc. Radiat. Transfer 70, 207–215 (2001).
[CrossRef]

F. Cignoli, S. De Luliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370–5378 (2001).
[CrossRef]

D. P. Correia, P. Ferrão, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163, 1–24 (2001).
[CrossRef]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
[CrossRef]

1998 (1)

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

1997 (1)

P. J. Coelho, and M. G. Carvalho, “A conservative formulation of the discrete transfer method,” J. Heat Transfer 119, 118–128 (1997).
[CrossRef]

1990 (3)

H. Chang and T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices offlame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
[CrossRef]

P. C. Hansen, “The discrete picard condition for discrete ill-posed problems,” BIT 30, 658–672 (1990).
[CrossRef]

R. J. Hall and P. A. Bonczyk, “Sooting flame thermometry using emission absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
[CrossRef]

1988 (1)

1985 (1)

Akesson, E. O.

André, F.

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

Anikin, N.

N. Anikin, R. Suntz, and H. Bochhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100, 675–694 (2010).
[CrossRef]

Ayranci, I.

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

Barbini, M.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

Benecchi, S.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

Bochhorn, H.

N. Anikin, R. Suntz, and H. Bochhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100, 675–694 (2010).
[CrossRef]

Bonczyk, P. A.

Caldeira-Pires, A.

D. P. Correia, P. Ferrão, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163, 1–24 (2001).
[CrossRef]

Carvalho, M. G.

P. J. Coelho, and M. G. Carvalho, “A conservative formulation of the discrete transfer method,” J. Heat Transfer 119, 118–128 (1997).
[CrossRef]

Cen, K. F.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Chang, H.

H. Chang and T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices offlame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
[CrossRef]

Charalampopoulos, T. T.

H. Chang and T. T. Charalampopoulos, “Determination of the wavelength dependence of refractive indices offlame soot,” Proc. R. Soc. London, Ser. A 430, 577–591 (1990).
[CrossRef]

Chi, Y.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Cignoli, F.

F. Cignoli, S. De Luliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370–5378 (2001).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

Coelho, P. J.

P. J. Coelho, and M. G. Carvalho, “A conservative formulation of the discrete transfer method,” J. Heat Transfer 119, 118–128 (1997).
[CrossRef]

Correia, D. P.

D. P. Correia, P. Ferrão, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163, 1–24 (2001).
[CrossRef]

Daun, K. J.

De Iuliis, S.

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

De Luliis, S.

Escudié, D.

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

Faris, G. W.

Ferrão, P.

D. P. Correia, P. Ferrão, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163, 1–24 (2001).
[CrossRef]

Floyd, J.

J. Floyd, P. Geipel, and A. M. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158, 376–391(2011).
[CrossRef]

Fong, D. C. L.

D. C. L. Fong and M. A. Saunders, “LSMR: An iterative algorithm for sparse least-squares problems,” SIAM J. Sci. Comput. 33 (2011).

Fraser, R. A.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Gao, Y. Q.

Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
[CrossRef]

Geipel, P.

J. Floyd, P. Geipel, and A. M. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158, 376–391(2011).
[CrossRef]

Gilabert, G.

G. Gilabert, G. Lu, and Y. Yan, “Tomographic reconstruction of the luminosity distribution of a combustion flame,” IEEE Trans. Instrum. Meas. 56, 1300–1306 (2007).
[CrossRef]

Guider, O. L.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Hall, R. J.

Hansen, P. C.

P. C. Hansen, “The discrete picard condition for discrete ill-posed problems,” BIT 30, 658–672 (1990).
[CrossRef]

Hertz, H. M.

Hossain, M. M.

M. M. Hossain, G. Lu, and Y. Yan, “Three-dimensional reconstruction of combustion flames through optical fibre sensing and CCD imaging,” in Proceedings of IEEE I2MTC (IEEE, 2011), pp. 79–83.

Huang, Q. X.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Ishino, Y.

Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J., Ser. B 48, 34–41 (2005).
[CrossRef]

Jiang, J.

L. H. Liu and J. Jiang, “Inverse radiation problem for reconstruction of temperature profile in axisymmetric free flames,” J. Quant. Spectrosc. Radiat. Transfer 70, 207–215 (2001).
[CrossRef]

Jiang, W. B.

Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
[CrossRef]

Kempf, A. M.

J. Floyd, P. Geipel, and A. M. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158, 376–391(2011).
[CrossRef]

Liu, D.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Liu, F.

Liu, L. H.

L. H. Liu and J. Jiang, “Inverse radiation problem for reconstruction of temperature profile in axisymmetric free flames,” J. Quant. Spectrosc. Radiat. Transfer 70, 207–215 (2001).
[CrossRef]

Lou, C.

C. Lou and H. C. Zhou, “Simultaneous determination of distributions of temperature and soot volume fraction in sooting flames using decoupled reconstruction method,” Numer. Heat Transfer A 56, 153–169 (2009).

Lu, G.

G. Gilabert, G. Lu, and Y. Yan, “Tomographic reconstruction of the luminosity distribution of a combustion flame,” IEEE Trans. Instrum. Meas. 56, 1300–1306 (2007).
[CrossRef]

M. M. Hossain, G. Lu, and Y. Yan, “Three-dimensional reconstruction of combustion flames through optical fibre sensing and CCD imaging,” in Proceedings of IEEE I2MTC (IEEE, 2011), pp. 79–83.

Ma, Z. Y.

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Manta, V.

Modest, M. F.

M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003) pp. 373–376.

Nakajima, M.

Ohiwa, N.

Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J., Ser. B 48, 34–41 (2005).
[CrossRef]

Saunders, M. A.

D. C. L. Fong and M. A. Saunders, “LSMR: An iterative algorithm for sparse least-squares problems,” SIAM J. Sci. Comput. 33 (2011).

Selçuk, N.

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

Smallwood, G. J.

K. J. Daun, K. A. Thomson, F. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45, 4638–4646 (2006).
[CrossRef]

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Snelling, D. R.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Suntz, R.

N. Anikin, R. Suntz, and H. Bochhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100, 675–694 (2010).
[CrossRef]

Thomson, K. A.

K. J. Daun, K. A. Thomson, F. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45, 4638–4646 (2006).
[CrossRef]

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Uchiyama, H.

Vaillon, R.

I. Ayrancı, R. Vaillon, N. Selçuk, F. André, and D. Escudié, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Radiat. Transfer 104, 266–276 (2007).
[CrossRef]

Wan, X.

Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
[CrossRef]

Wang, F.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Weekman, E. J.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Yan, J. H.

D. Liu, Q. X. Huang, F. Wang, Y. Chi, K. F. Cen, and J. H. Yan, “Simultaneous measurement of three-dimensional soot temperature and volume fraction fields in axisymmetric or asymmetric small unconfined flames with CCD cameras,” J. Heat Transfer 132, 1202–1207 (2010).
[CrossRef]

Q. X. Huang, F. Wang, D. Liu, Z. Y. Ma, J. H. Yan, Y. Chi, and K. F. Cen, “Reconstruction of soot temperature and volume fraction profiles of an asymmetric flame using stereoscopic tomography,” Combust. Flame 156, 565–573 (2009).
[CrossRef]

Yan, Y.

G. Gilabert, G. Lu, and Y. Yan, “Tomographic reconstruction of the luminosity distribution of a combustion flame,” IEEE Trans. Instrum. Meas. 56, 1300–1306 (2007).
[CrossRef]

M. M. Hossain, G. Lu, and Y. Yan, “Three-dimensional reconstruction of combustion flames through optical fibre sensing and CCD imaging,” in Proceedings of IEEE I2MTC (IEEE, 2011), pp. 79–83.

Yu, Q. X.

Y. Q. Gao, Q. X. Yu, W. B. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42, 61–69 (2010).
[CrossRef]

Yuta, S.

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
[CrossRef]

Zhou, H. C.

C. Lou and H. C. Zhou, “Simultaneous determination of distributions of temperature and soot volume fraction in sooting flames using decoupled reconstruction method,” Numer. Heat Transfer A 56, 153–169 (2009).

Zizak, G.

F. Cignoli, S. De Luliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370–5378 (2001).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, F. Cignoli, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multi-wavelength analysis of soot radiation,” Combust. Flame 115, 253–261 (1998).
[CrossRef]

AIAA J. (1)

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weekman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40, 1789–1795 (2002).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

N. Anikin, R. Suntz, and H. Bochhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100, 675–694 (2010).
[CrossRef]

BIT (1)

P. C. Hansen, “The discrete picard condition for discrete ill-posed problems,” BIT 30, 658–672 (1990).
[CrossRef]

Combust. Flame (3)

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Figures (12)

Fig. 1.
Fig. 1.

Stereoscopic imaging system using a single high-speed camera.

Fig. 2.
Fig. 2.

Assumed soot temperature and volume fraction values.

Fig. 3.
Fig. 3.

The Picard condition of the least squares problem described by Eq. (12).

Fig. 4.
Fig. 4.

Effect of stereoscopic angle on average reconstruction error.

Fig. 5.
Fig. 5.

Effect of flame distance on average reconstruction error.

Fig. 6.
Fig. 6.

Condition number of contribution coefficient matrix under different settings.

Fig. 7.
Fig. 7.

Effect of self attenuation on average reconstruction errors.

Fig. 8.
Fig. 8.

Effect of self attenuation on the distribution of relative reconstruction errors.

Fig. 9.
Fig. 9.

Blackbody furnace calibration results.

Fig. 10.
Fig. 10.

Stereoscopic image and reconstructed temperature and soot volume fraction.

Fig. 11.
Fig. 11.

Average temperatures obtained with and without self attenuation.

Fig. 12.
Fig. 12.

Optical thickness obtained with and without self attenuation.

Equations (16)

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Iλ,s^,k+1=Iλ,s^,kexp(κλ,kΔls^,k)+Ib,λ,k[1exp(κλ,kΔls^,k)],
κλ,k=6πfv,kE(m)/λ,
n¯=1.811+0.1263ln(λ)+0.027ln2(λ)+0.0417ln3(λ)
k¯=0.582+0.1213ln(λ)+0.2309ln2(λ)0.01In3(λ)
Iλ,s^,k+1=Iλ,s^,kexp(κλ,kΔls^,k)+Ib,λ,k[1(1κλ,kΔls^,k+(κλ,kΔls^,k)22+)]Iλ,s^,kexp(κλ,kΔls^,k)+Ib,λ,k(κλ,kΔls^,k)(1κλ,kΔls^,k/2).
Pλ,s^=Iλ,s^,0exp(m=0K1κλ,mΔls^,m)+k=0K1Ib,λ,k(κλ,kΔls^,k)(1κλ,kΔls^,k/2)exp(m=k+1K1κλ,mΔls^,m),
[Pλ(1)·Pλ(j)·Pλ(N)]=[aλ,1,1···aλ,1,M··aλ,j1,i···aλ,j,i1aλ,j,iaλ,j,i+1···aλ,j+1,i··aλ,N,1···aλ,N,M]·[Sb,λ,1·Sb,λ,i·Sb,λ,M],
P=A·S,
aλ,j,i=(Δlj,i)(1κλ,iΔlj,i/2)·exp(m=0K1κλ,j,i,mΔlj,i,m),
Sb,λ,i=κλ,iIb,λ,i.
[Pλ(1)·Pλ(j)·Pλ(N)]=[a1,1···a1,M··aj1,i···aj,i1aj,iaj,i+1···aj+1,i··aN,1···aN,M]·[Sb,λ,1·Sb,λ,i·Sb,λ,M],
f(S)=min{A·SP2}.
Ti=C2(1λ21λ1)/[ln(Eλ1(m)/λ1)Sb,λ1,i(Eλ2(m)/λ2)Sb,λ2,i+5ln(λ1λ2)],
fv,i=112C1[1Eλ1(m)Sb,λ1,iλ16exp(C2λ1Ti)+1Eλ2(m)Sb,λ2,iλ26exp(C2λ2Ti)].
Pnoise=Pexact·(ψ·ξ+1),
{cr=Ir(T)/Rcg=Ig(T)/G,

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