Abstract

A system for three-dimensional computed tomography of chemiluminescence was developed to measure flames over a large field angle. Nine gradient-index rods, with a 9 × 1 endoscope and only one camera are used. Its large field of view, simplicity, and low cost make it attractive for inner flow field diagnostics. To study the bokeh effect caused by the imaging system on reconstruction solutions, fluorescent beads were used to determine the blurring function. Experiments using a steady diffusion flame were conducted to validate the system. Three models, namely the clear-imaging, out-of-focus imaging, and deconvolution models, were utilized. Taking the bokeh effect into account, the results suggest that based on run-times the deconvolution model provides the best reconstruction accuracy without increasing computational time.

© 2017 Optical Society of America

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References

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2016 (1)

K. J. Daun, S. J. Grauer, and P. J. Hadwin, “Chemical species tomography of turbulent flows: discrete ill-posed and rank deficient problems and the use of prior information,” J. Quant. Spectrosc. Radiat. Transf. 172, 58–74 (2016).
[Crossref]

2015 (5)

M. Kang, X. Li, and L. Ma, “Three-dimensional flame measurements using fiber-based endoscopes,” Proc. Combust. Inst. 35(3), 3821–3828 (2015).
[Crossref]

L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
[Crossref]

M. Gamba and M. G. Mungal, “Ignition, flame structure and near-wall burning in transverse hydrogen jets in supersonic crossflow,” J. Fluid Mech. 780, 226–273 (2015).
[Crossref]

T. Fiala and T. Sattelmayer, “Heat release and uv–vis radiation in non-premixed hydrogen–oxygen flames,” Exp. Fluids 56(7), 144 (2015).
[Crossref]

J. Wang, Y. Song, Z. H. Li, A. Kempf, and A. Z. He, “Multi-directional 3d flame chemiluminescence tomography based on lens imaging,” Opt. Lett. 40(7), 1231–1234 (2015).
[Crossref] [PubMed]

2014 (3)

X. Li and L. Ma, “Volumetric imaging of turbulent reactive flows at kHz based on computed tomography,” Opt. Express 22(4), 4768–4778 (2014).
[Crossref] [PubMed]

M. Kang, Y. Wu, and L. Ma, “Fiber-based endoscopes for 3d combustion measurements: view registration and spatial resolution,” Combust. Flame 161(12), 3063–3072 (2014).
[Crossref]

T. García-Armingol, Y. Hardalupas, A. M. K. P. Taylor, and J. Ballester, “Effect of local flame properties on chemiluminescence-based stoichiometry measurement,” Exp. Therm. Fluid Sci. 53, 93–103 (2014).
[Crossref]

2013 (1)

2012 (2)

K. R. Gosselin and M. W. Renfro, “Reconstruction of three-dimensional chemiluminescence images with a maximum entropy deconvolution algorithm,” Appl. Opt. 51(11), 1671–1680 (2012).
[Crossref] [PubMed]

T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

2011 (2)

M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
[Crossref]

J. Floyd and A. M. Kempf, “Computed tomography of chemiluminescence (ctc): high resolution and instantaneous 3-d measurements of a matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

2010 (1)

N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the oh*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100(3), 675–694 (2010).
[Crossref]

2008 (1)

2005 (1)

B. D. Stojkovic, T. D. Fansler, M. C. Drake, and V. Sick, “High-speed imaging of oh* and soot temperature and concentration in a stratified-charge direct-injection gasoline engine,” Proc. Combust. Inst. 30(2), 2657–2665 (2005).
[Crossref]

2002 (2)

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

N. Docquier, F. Lacas, and S. Candel, “Closed-loop equivalence ratio control of premixed combustors using spectrally resolved chemiluminescence measurements,” Proc. Combust. Inst. 29(1), 139–145 (2002).
[Crossref]

2001 (1)

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31(5), 1076–1078 (2001).
[PubMed]

2000 (1)

J. G. Lee, K. Kim, and D. Santavicca, “Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion,” Proc. Combust. Inst. 28(1), 415–421 (2000).
[Crossref]

1985 (1)

1984 (1)

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13(1), 191–219 (1984).
[Crossref] [PubMed]

1983 (1)

M. P. Rimmer, “Ray tracing in inhomogeneous media,” Proc. SPIE 399, 339–344 (1983).
[Crossref]

1974 (1)

R. Gordon, “A tutorial on ART (algebraic reconstruction techniques),” IEEE Trans. Nucl. Sci. 21(3), 78–93 (1974).
[Crossref]

1971 (1)

Agard, D. A.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13(1), 191–219 (1984).
[Crossref] [PubMed]

Anikin, N.

N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the oh*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100(3), 675–694 (2010).
[Crossref]

Aul, C. J.

M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
[Crossref]

Ballester, J.

T. García-Armingol, Y. Hardalupas, A. M. K. P. Taylor, and J. Ballester, “Effect of local flame properties on chemiluminescence-based stoichiometry measurement,” Exp. Therm. Fluid Sci. 53, 93–103 (2014).
[Crossref]

Ben-Li, Y.

Y. Ying-Hai, H. Wei-Tong, Y. Ben-Li, L. Zu-Ning, and L. Peng, “Imaging properties and measurement of SELFOC lens and SLA,” in Proc. IEEE Int. Conf. Industrial Technology (IEEE, 1994), pp. 422–425.
[Crossref]

Bockhorn, H.

N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the oh*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100(3), 675–694 (2010).
[Crossref]

Cai, W.

Candel, S.

N. Docquier, F. Lacas, and S. Candel, “Closed-loop equivalence ratio control of premixed combustors using spectrally resolved chemiluminescence measurements,” Proc. Combust. Inst. 29(1), 139–145 (2002).
[Crossref]

Carter, C. D.

L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
[Crossref]

Chen, X.

Crosley, D. R.

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

Daun, K. J.

K. J. Daun, S. J. Grauer, and P. J. Hadwin, “Chemical species tomography of turbulent flows: discrete ill-posed and rank deficient problems and the use of prior information,” J. Quant. Spectrosc. Radiat. Transf. 172, 58–74 (2016).
[Crossref]

Docquier, N.

N. Docquier, F. Lacas, and S. Candel, “Closed-loop equivalence ratio control of premixed combustors using spectrally resolved chemiluminescence measurements,” Proc. Combust. Inst. 29(1), 139–145 (2002).
[Crossref]

Drake, M. C.

B. D. Stojkovic, T. D. Fansler, M. C. Drake, and V. Sick, “High-speed imaging of oh* and soot temperature and concentration in a stratified-charge direct-injection gasoline engine,” Proc. Combust. Inst. 30(2), 2657–2665 (2005).
[Crossref]

Fansler, T. D.

B. D. Stojkovic, T. D. Fansler, M. C. Drake, and V. Sick, “High-speed imaging of oh* and soot temperature and concentration in a stratified-charge direct-injection gasoline engine,” Proc. Combust. Inst. 30(2), 2657–2665 (2005).
[Crossref]

Fiala, T.

T. Fiala and T. Sattelmayer, “Heat release and uv–vis radiation in non-premixed hydrogen–oxygen flames,” Exp. Fluids 56(7), 144 (2015).
[Crossref]

Floyd, J.

J. Floyd and A. M. Kempf, “Computed tomography of chemiluminescence (ctc): high resolution and instantaneous 3-d measurements of a matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

J. Floyd, “Computed tomography of chemiluminescence: a 3d time resolved sensor for turbulent combustion,” (2009).

Gamba, M.

M. Gamba and M. G. Mungal, “Ignition, flame structure and near-wall burning in transverse hydrogen jets in supersonic crossflow,” J. Fluid Mech. 780, 226–273 (2015).
[Crossref]

García-Armingol, T.

T. García-Armingol, Y. Hardalupas, A. M. K. P. Taylor, and J. Ballester, “Effect of local flame properties on chemiluminescence-based stoichiometry measurement,” Exp. Therm. Fluid Sci. 53, 93–103 (2014).
[Crossref]

George, N.

Gordon, R.

R. Gordon, “A tutorial on ART (algebraic reconstruction techniques),” IEEE Trans. Nucl. Sci. 21(3), 78–93 (1974).
[Crossref]

Gosselin, K. R.

Grauer, S. J.

K. J. Daun, S. J. Grauer, and P. J. Hadwin, “Chemical species tomography of turbulent flows: discrete ill-posed and rank deficient problems and the use of prior information,” J. Quant. Spectrosc. Radiat. Transf. 172, 58–74 (2016).
[Crossref]

Guo, Q.

T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

Hadwin, P. J.

K. J. Daun, S. J. Grauer, and P. J. Hadwin, “Chemical species tomography of turbulent flows: discrete ill-posed and rank deficient problems and the use of prior information,” J. Quant. Spectrosc. Radiat. Transf. 172, 58–74 (2016).
[Crossref]

Hardalupas, Y.

T. García-Armingol, Y. Hardalupas, A. M. K. P. Taylor, and J. Ballester, “Effect of local flame properties on chemiluminescence-based stoichiometry measurement,” Exp. Therm. Fluid Sci. 53, 93–103 (2014).
[Crossref]

He, A. Z.

Jeffries, J. B.

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

Joshi, N.

N. Joshi, R. Szeliski, and D. Kriegman, “PSF estimation using sharp edge prediction,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (2008), pp. 1–8.

Kang, M.

M. Kang, X. Li, and L. Ma, “Three-dimensional flame measurements using fiber-based endoscopes,” Proc. Combust. Inst. 35(3), 3821–3828 (2015).
[Crossref]

M. Kang, Y. Wu, and L. Ma, “Fiber-based endoscopes for 3d combustion measurements: view registration and spatial resolution,” Combust. Flame 161(12), 3063–3072 (2014).
[Crossref]

Kempf, A.

Kempf, A. M.

J. Floyd and A. M. Kempf, “Computed tomography of chemiluminescence (ctc): high resolution and instantaneous 3-d measurements of a matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

Kim, K.

J. G. Lee, K. Kim, and D. Santavicca, “Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion,” Proc. Combust. Inst. 28(1), 415–421 (2000).
[Crossref]

Kriegman, D.

N. Joshi, R. Szeliski, and D. Kriegman, “PSF estimation using sharp edge prediction,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (2008), pp. 1–8.

Lacas, F.

N. Docquier, F. Lacas, and S. Candel, “Closed-loop equivalence ratio control of premixed combustors using spectrally resolved chemiluminescence measurements,” Proc. Combust. Inst. 29(1), 139–145 (2002).
[Crossref]

Lauer, M.

M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
[Crossref]

Lauer, T. R.

T. R. Lauer, “Deconvolution with a spatially-variant PSF,” in Proc. of the SPIE,Astronomical Data Analysis II (2002), pp. 167–173.
[Crossref]

Lee, J. G.

J. G. Lee, K. Kim, and D. Santavicca, “Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion,” Proc. Combust. Inst. 28(1), 415–421 (2000).
[Crossref]

Lei, Q.

L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
[Crossref]

Li, X.

Li, Z. H.

Luque, J.

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

Ma, L.

M. Kang, X. Li, and L. Ma, “Three-dimensional flame measurements using fiber-based endoscopes,” Proc. Combust. Inst. 35(3), 3821–3828 (2015).
[Crossref]

L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
[Crossref]

M. Kang, Y. Wu, and L. Ma, “Fiber-based endoscopes for 3d combustion measurements: view registration and spatial resolution,” Combust. Flame 161(12), 3063–3072 (2014).
[Crossref]

X. Li and L. Ma, “Volumetric imaging of turbulent reactive flows at kHz based on computed tomography,” Opt. Express 22(4), 4768–4778 (2014).
[Crossref] [PubMed]

W. Cai, X. Li, and L. Ma, “Practical aspects of implementing three-dimensional tomography inversion for volumetric flame imaging,” Appl. Opt. 52(33), 8106–8116 (2013).
[Crossref] [PubMed]

Mungal, M. G.

M. Gamba and M. G. Mungal, “Ignition, flame structure and near-wall burning in transverse hydrogen jets in supersonic crossflow,” J. Fluid Mech. 780, 226–273 (2015).
[Crossref]

Ombrello, T. M.

L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
[Crossref]

Park, C.

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

Paxton, K. B.

Peng, L.

Y. Ying-Hai, H. Wei-Tong, Y. Ben-Li, L. Zu-Ning, and L. Peng, “Imaging properties and measurement of SELFOC lens and SLA,” in Proc. IEEE Int. Conf. Industrial Technology (IEEE, 1994), pp. 422–425.
[Crossref]

Renfro, M. W.

Rimmer, M. P.

M. P. Rimmer, “Ray tracing in inhomogeneous media,” Proc. SPIE 399, 339–344 (1983).
[Crossref]

Santavicca, D.

J. G. Lee, K. Kim, and D. Santavicca, “Measurement of equivalence ratio fluctuation and its effect on heat release during unstable combustion,” Proc. Combust. Inst. 28(1), 415–421 (2000).
[Crossref]

Sattelmayer, T.

T. Fiala and T. Sattelmayer, “Heat release and uv–vis radiation in non-premixed hydrogen–oxygen flames,” Exp. Fluids 56(7), 144 (2015).
[Crossref]

M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
[Crossref]

Schaefer, L. H.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31(5), 1076–1078 (2001).
[PubMed]

Sharma, A.

Sick, V.

B. D. Stojkovic, T. D. Fansler, M. C. Drake, and V. Sick, “High-speed imaging of oh* and soot temperature and concentration in a stratified-charge direct-injection gasoline engine,” Proc. Combust. Inst. 30(2), 2657–2665 (2005).
[Crossref]

Smith, G. P.

G. P. Smith, J. Luque, C. Park, J. B. Jeffries, and D. R. Crosley, “Low pressure flame determinations of rate constants for oh(a) and ch(a) chemiluminescence,” Combust. Flame 131(1-2), 59–69 (2002).
[Crossref]

Song, X.

T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

Song, Y.

Stojkovic, B. D.

B. D. Stojkovic, T. D. Fansler, M. C. Drake, and V. Sick, “High-speed imaging of oh* and soot temperature and concentration in a stratified-charge direct-injection gasoline engine,” Proc. Combust. Inst. 30(2), 2657–2665 (2005).
[Crossref]

Streifer, W.

Suntz, R.

N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the oh*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100(3), 675–694 (2010).
[Crossref]

Swedlow, J. R.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31(5), 1076–1078 (2001).
[PubMed]

Szeliski, R.

N. Joshi, R. Szeliski, and D. Kriegman, “PSF estimation using sharp edge prediction,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (2008), pp. 1–8.

Taylor, A. M. K. P.

T. García-Armingol, Y. Hardalupas, A. M. K. P. Taylor, and J. Ballester, “Effect of local flame properties on chemiluminescence-based stoichiometry measurement,” Exp. Therm. Fluid Sci. 53, 93–103 (2014).
[Crossref]

Wallace, W.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31(5), 1076–1078 (2001).
[PubMed]

Wang, J.

Wei-Tong, H.

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L. Ma, Q. Lei, Y. Wu, T. M. Ombrello, and C. D. Carter, “3d measurements of ignition processes at 20 khz in a supersonic combustor,” Appl. Phys. B 119(2), 313–318 (2015).
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M. Kang, Y. Wu, and L. Ma, “Fiber-based endoscopes for 3d combustion measurements: view registration and spatial resolution,” Combust. Flame 161(12), 3063–3072 (2014).
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Ying-Hai, Y.

Y. Ying-Hai, H. Wei-Tong, Y. Ben-Li, L. Zu-Ning, and L. Peng, “Imaging properties and measurement of SELFOC lens and SLA,” in Proc. IEEE Int. Conf. Industrial Technology (IEEE, 1994), pp. 422–425.
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T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

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M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
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T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

Zhou, Z.

T. Zhang, Q. Guo, X. Song, Z. Zhou, and G. Yu, “The chemiluminescence and structure properties of normal/inverse diffusion Flames,” Spectroscopy (Springf.) 2013, 1–7 (2012).

Zu-Ning, L.

Y. Ying-Hai, H. Wei-Tong, Y. Ben-Li, L. Zu-Ning, and L. Peng, “Imaging properties and measurement of SELFOC lens and SLA,” in Proc. IEEE Int. Conf. Industrial Technology (IEEE, 1994), pp. 422–425.
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[Crossref]

N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the oh*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. B 100(3), 675–694 (2010).
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M. Kang, Y. Wu, and L. Ma, “Fiber-based endoscopes for 3d combustion measurements: view registration and spatial resolution,” Combust. Flame 161(12), 3063–3072 (2014).
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T. Fiala and T. Sattelmayer, “Heat release and uv–vis radiation in non-premixed hydrogen–oxygen flames,” Exp. Fluids 56(7), 144 (2015).
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M. Lauer, M. Zellhuber, T. Sattelmayer, and C. J. Aul, “Determination of the heat release distribution in turbulent flames by a model based correction of oh*chemiluminescence,” J. Eng. Gas Turbines Power 133(12), 121501 (2011).
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M. Gamba and M. G. Mungal, “Ignition, flame structure and near-wall burning in transverse hydrogen jets in supersonic crossflow,” J. Fluid Mech. 780, 226–273 (2015).
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J. Floyd and A. M. Kempf, “Computed tomography of chemiluminescence (ctc): high resolution and instantaneous 3-d measurements of a matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
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M. Kang, X. Li, and L. Ma, “Three-dimensional flame measurements using fiber-based endoscopes,” Proc. Combust. Inst. 35(3), 3821–3828 (2015).
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Other (4)

J. Floyd, “Computed tomography of chemiluminescence: a 3d time resolved sensor for turbulent combustion,” (2009).

Y. Ying-Hai, H. Wei-Tong, Y. Ben-Li, L. Zu-Ning, and L. Peng, “Imaging properties and measurement of SELFOC lens and SLA,” in Proc. IEEE Int. Conf. Industrial Technology (IEEE, 1994), pp. 422–425.
[Crossref]

T. R. Lauer, “Deconvolution with a spatially-variant PSF,” in Proc. of the SPIE,Astronomical Data Analysis II (2002), pp. 167–173.
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N. Joshi, R. Szeliski, and D. Kriegman, “PSF estimation using sharp edge prediction,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (2008), pp. 1–8.

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Figures (11)

Fig. 1
Fig. 1 Physical coordinate system of the 3D-CTC setup.
Fig. 2
Fig. 2 (a) Multi-directional imaging system; (b) Blurring circle from a point light source.
Fig. 3
Fig. 3 Intensity distributions (a) at a 65-mm objective distance for various radial distances relative to the on-axis, and (b) along the optical axis for various objective depths.
Fig. 4
Fig. 4 (a) Coordinate systems defining the various transformations; (b) 3D calibration setup.
Fig. 5
Fig. 5 Jet nozzle and CH4 diffusion flames.
Fig. 6
Fig. 6 (a) Simultaneous projections of the ten diffusion flames; (b) Intensity distribution along the red line.
Fig. 7
Fig. 7 Schematic diagram of the projection processing models. Model (a): clear-imaging model; Model (b): out-of-focus imaging model; Model (c): deconvolution model.
Fig. 8
Fig. 8 Top views of the reconstructed flames based on: (left) model (a), (center) model (b), and (right) model (c).
Fig. 9
Fig. 9 Normalized intensity between the red concentric circles in Fig. 7.
Fig. 10
Fig. 10 Difference between the measured and reconstructed projections.
Fig. 11
Fig. 11 Cross-sections of reconstructed flame at different y positions by the projection processing model (a) (the four left images) and model (c) (the four right images).

Tables (2)

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Table 1 Coordinates Calibration Results

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Table 2 Procedure settings and run-times for each projection model.

Equations (6)

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I q ( x m , y n ) = x i , y j , z k F ( x i , y j , z k ) W ( x i , y j , z k ; q ; m , n ) ,
y = 4.9 3.9 π / 2 e 2 ( x 16.1 3.9 ) 2 ,
[ x " y " z " ] = [ cos ε sin ε 0 sin ε cos ε 0 0 0 1 ] [ 1 0 1 0 cos ϕ sin ϕ 0 sin ϕ cos ϕ ] [ cos θ 0 sin θ 0 1 cos θ sin θ 0 0 ] [ x y z ] + [ T x T y T z ] ,
F ( k + 1 ) = F ( k ) + λ W I p q W F ( k ) W W .
e r r o r = i j k | F r e c ( x , y , z ) F ( x , y , z ) | i j k | F ( x , y , z ) ,
D i f f k = | p m e a s u r e m e n t p k c o m p u t e | ,

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