Abstract

Instantaneous three-dimensional (3D) measurements have been long desired to resolve the spatial structures of turbulent flows and flame. Previous efforts have demonstrated tomography as a promising technique to enable such measurements. To facilitate the practical application, this work investigated four practical aspects for implementing 3D tomographic under the context of volumetric combustion diagnostics. Both numerical simulations and controlled experiments were performed to study: (1) the termination criteria of the inversion algorithm; (2) the effects of regularization and the determination of the optimal regularization factor; (3) the effects of a number of views; and (4) the impact of the resolution of the projection measurements. The results obtained have illustrated the effects of these practical aspects on the accuracy and spatial resolution of volumetric tomography. Furthermore, all these aspects are related to the complexity and implementing cost (both hardware cost and computational cost). Therefore, the results obtained in this work are expected to be valuable for the design and implementation of practical 3D diagnostics.

© 2013 Optical Society of America

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  1. G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
    [CrossRef]
  2. R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. 31, 49–75 (2007).
    [CrossRef]
  3. L. Ma, “High speed imaging in reactive flows using hyperspectral tomography and photodissociation spectroscopy,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2010), paper LWA3.
  4. L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.
  5. R. Wellander, M. Richter, and M. Alden, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express 19, 21508–21514 (2011).
    [CrossRef]
  6. J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
    [CrossRef]
  7. D. P. Correia, P. Ferrao, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163, 1–24 (2001).
    [CrossRef]
  8. R. Snyder and L. Hesselink, “Measurement of mixing fluid-flows with optical tomography,” Opt. Lett. 13, 87–89 (1988).
    [CrossRef]
  9. 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]
  10. X. Li, W. Cai, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21, 7050–7064 (2013).
    [CrossRef]
  11. C. T. Herman, Image reconstruction from projections—the fundamentals of computerized tomography (Academic, 1980).
  12. L. Ma and W. Cai, “Determination of the optimal regularization parameters in hyperspectral tomography,” Appl. Opt. 47, 4186 (2008).
    [CrossRef]
  13. E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).
  14. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
    [CrossRef]
  15. X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
    [CrossRef]
  16. L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009).
    [CrossRef]
  17. L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express 21, 1152–1162 (2013).
    [CrossRef]
  18. Q. Huang, F. Wang, J. Yan, and Y. Chi, “Simultaneous estimation of the 3-D soot temperature and volume fraction distributions in asymmetric flames using high-speed stereoscopic images,” Appl. Opt. 51, 2968–2978 (2012).
    [CrossRef]
  19. 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, 751–758 (2011).
    [CrossRef]
  20. M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
    [CrossRef]
  21. W. Cai, A. J. Wickersham, and L. Ma, “Three-dimensional combustion diagnostics based on computed tomography of chemiluminescence,” presented at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Dallas Region, Texas, 7–10 January2013.
  22. L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
    [CrossRef]
  23. W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
    [CrossRef]
  24. Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
    [CrossRef]
  25. R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
    [CrossRef]
  26. H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
    [CrossRef]
  27. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).
  28. W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comp. Phys. Commun. 181, 1974–1981 (2010).
    [CrossRef]
  29. X. Li and L. Ma, “Minimizing binary functions with simulated annealing algorithm with applications to binary tomography,” Comput. Phys. Commun. 183, 309–315 (2012).
    [CrossRef]
  30. Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J. 48, 34–40 (2005).
    [CrossRef]
  31. N. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames,” Appl. Phys. 100, 675–694 (2010).
    [CrossRef]
  32. J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (2011).
    [CrossRef]
  33. W. Cai and L. Ma, “Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm,” Comput. Phys. Commun. 181, 11–16 (2010).
    [CrossRef]
  34. W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
    [CrossRef]
  35. A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
    [CrossRef]
  36. W. Cai and L. Ma, “Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows,” Appl. Opt. 49, 601–610 (2010).
    [CrossRef]
  37. D. Verhoeven, “Limited-data computed-tomography algorithms for the physical sciences,” Appl. Opt. 32, 3736–3754 (1993).
    [CrossRef]
  38. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef]
  39. P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-Curve,” Siam Rev. 34, 561–580 (1992).
    [CrossRef]
  40. G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33, 189–211 (1971).
    [CrossRef]
  41. G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction technique: an experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol. 33, 213–223 (1971).
    [CrossRef]

2013

2012

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Simultaneous estimation of the 3-D soot temperature and volume fraction distributions in asymmetric flames using high-speed stereoscopic images,” Appl. Opt. 51, 2968–2978 (2012).
[CrossRef]

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
[CrossRef]

Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
[CrossRef]

X. Li and L. Ma, “Minimizing binary functions with simulated annealing algorithm with applications to binary tomography,” Comput. Phys. Commun. 183, 309–315 (2012).
[CrossRef]

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

2011

J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (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, 751–758 (2011).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
[CrossRef]

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]

X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
[CrossRef]

R. Wellander, M. Richter, and M. Alden, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express 19, 21508–21514 (2011).
[CrossRef]

2010

W. Cai and L. Ma, “Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows,” Appl. Opt. 49, 601–610 (2010).
[CrossRef]

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

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comp. Phys. Commun. 181, 1974–1981 (2010).
[CrossRef]

W. Cai and L. Ma, “Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm,” Comput. Phys. Commun. 181, 11–16 (2010).
[CrossRef]

2009

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009).
[CrossRef]

A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
[CrossRef]

2008

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
[CrossRef]

L. Ma and W. Cai, “Determination of the optimal regularization parameters in hyperspectral tomography,” Appl. Opt. 47, 4186 (2008).
[CrossRef]

2007

R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. 31, 49–75 (2007).
[CrossRef]

2006

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

2005

Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J. 48, 34–40 (2005).
[CrossRef]

2002

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

2001

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

1994

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef]

1993

1992

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-Curve,” Siam Rev. 34, 561–580 (1992).
[CrossRef]

1988

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

1971

G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33, 189–211 (1971).
[CrossRef]

G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction technique: an experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol. 33, 213–223 (1971).
[CrossRef]

1970

R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
[CrossRef]

Alden, M.

R. Wellander, M. Richter, and M. Alden, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express 19, 21508–21514 (2011).
[CrossRef]

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Alwahabi, Z. T.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

An, X.

X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
[CrossRef]

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

Anikin, N.

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

Axelsson, B.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Baba, J.

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

Barlow, R. S.

R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. 31, 49–75 (2007).
[CrossRef]

Bengtsson, P. E.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Bockhorn, H.

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

Bruecker, C.

J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (2011).
[CrossRef]

Cai, W.

X. Li, W. Cai, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21, 7050–7064 (2013).
[CrossRef]

X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
[CrossRef]

W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comp. Phys. Commun. 181, 1974–1981 (2010).
[CrossRef]

W. Cai and L. Ma, “Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm,” Comput. Phys. Commun. 181, 11–16 (2010).
[CrossRef]

W. Cai and L. Ma, “Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows,” Appl. Opt. 49, 601–610 (2010).
[CrossRef]

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009).
[CrossRef]

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
[CrossRef]

L. Ma and W. Cai, “Determination of the optimal regularization parameters in hyperspectral tomography,” Appl. Opt. 47, 4186 (2008).
[CrossRef]

W. Cai, A. J. Wickersham, and L. Ma, “Three-dimensional combustion diagnostics based on computed tomography of chemiluminescence,” presented at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Dallas Region, Texas, 7–10 January2013.

Caldeira-Pires, A.

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

Caswell, A.

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

Caswell, A. W.

Chan, Q. N.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

Chi, Y.

Collin, R.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Correia, D. P.

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

Crowther, R.

R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
[CrossRef]

Dally, B. B.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

DeRosier, D.

R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
[CrossRef]

Ewing, D. J.

W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
[CrossRef]

Ferrao, P.

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

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).

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, 751–758 (2011).
[CrossRef]

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]

Frieder, G.

G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33, 189–211 (1971).
[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]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Gord, J. R.

Hansen, P. C.

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-Curve,” Siam Rev. 34, 561–580 (1992).
[CrossRef]

Herman, C. T.

C. T. Herman, Image reconstruction from projections—the fundamentals of computerized tomography (Academic, 1980).

Herman, G. T.

G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction technique: an experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol. 33, 213–223 (1971).
[CrossRef]

G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33, 189–211 (1971).
[CrossRef]

Hesselink, L.

Hossain, M. M.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
[CrossRef]

Huang, Q.

Hudson, H. M.

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef]

Hult, J.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[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. 48, 34–40 (2005).
[CrossRef]

Kaipio, J. P.

A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
[CrossRef]

Kalt, P. A. M.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

Kaminski, C. F.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Kao, C. M.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

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]

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, 751–758 (2011).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Kitzhofer, J.

J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (2011).
[CrossRef]

Klug, A.

R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
[CrossRef]

Kraetschmer, T.

Kranendonk, L.

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

Larkin, R. S.

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef]

Lee, T.

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

Li, F.

Li, X.

X. Li, W. Cai, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21, 7050–7064 (2013).
[CrossRef]

L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express 21, 1152–1162 (2013).
[CrossRef]

Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
[CrossRef]

X. Li and L. Ma, “Minimizing binary functions with simulated annealing algorithm with applications to binary tomography,” Comput. Phys. Commun. 183, 309–315 (2012).
[CrossRef]

X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
[CrossRef]

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

Lu, G.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
[CrossRef]

Ma, L.

L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express 21, 1152–1162 (2013).
[CrossRef]

X. Li, W. Cai, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21, 7050–7064 (2013).
[CrossRef]

X. Li and L. Ma, “Minimizing binary functions with simulated annealing algorithm with applications to binary tomography,” Comput. Phys. Commun. 183, 309–315 (2012).
[CrossRef]

Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
[CrossRef]

X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50, A29–A37 (2011).
[CrossRef]

W. Cai and L. Ma, “Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm,” Comput. Phys. Commun. 181, 11–16 (2010).
[CrossRef]

W. Cai and L. Ma, “Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows,” Appl. Opt. 49, 601–610 (2010).
[CrossRef]

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comp. Phys. Commun. 181, 1974–1981 (2010).
[CrossRef]

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009).
[CrossRef]

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
[CrossRef]

L. Ma and W. Cai, “Determination of the optimal regularization parameters in hyperspectral tomography,” Appl. Opt. 47, 4186 (2008).
[CrossRef]

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

L. Ma, “High speed imaging in reactive flows using hyperspectral tomography and photodissociation spectroscopy,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2010), paper LWA3.

W. Cai, A. J. Wickersham, and L. Ma, “Three-dimensional combustion diagnostics based on computed tomography of chemiluminescence,” presented at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Dallas Region, Texas, 7–10 January2013.

Medwell, P. R.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

Nathan, G. J.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

Nonn, T.

J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (2011).
[CrossRef]

Nygren, J.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

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. 48, 34–40 (2005).
[CrossRef]

Omrane, A.

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

Pan, X. H.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

Plemmons, D.

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

Plemmons, D. H.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).

Richter, M.

Rowland, S.

G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction technique: an experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol. 33, 213–223 (1971).
[CrossRef]

Roy, S.

Sanders, S. T.

Seppanen, A.

A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
[CrossRef]

Sidky, E. Y.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

Snyder, R.

Suntz, R.

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

Takami, K.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Verhoeven, D.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).

Voutilainen, A.

A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
[CrossRef]

Wang, F.

Wellander, R.

Wickersham, A. J.

W. Cai, A. J. Wickersham, and L. Ma, “Three-dimensional combustion diagnostics based on computed tomography of chemiluminescence,” presented at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Dallas Region, Texas, 7–10 January2013.

Yan, J.

Yan, Y.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
[CrossRef]

Zhao, Y.

Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
[CrossRef]

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

Appl. Math. Comput.

W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217, 5754–5767 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys.

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

Combust. Flame

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]

Combust. Sci. Technol.

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

Comp. Phys. Commun.

W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comp. Phys. Commun. 181, 1974–1981 (2010).
[CrossRef]

Comput. Phys. Commun.

X. Li and L. Ma, “Minimizing binary functions with simulated annealing algorithm with applications to binary tomography,” Comput. Phys. Commun. 183, 309–315 (2012).
[CrossRef]

W. Cai, L. Kranendonk, T. Lee, and L. Ma, “Characterization of composite nanoparticles using an improved light scattering program for coated spheres,” Comput. Phys. Commun. 181, 978–984 (2010).
[CrossRef]

Y. Zhao, X. Li, and L. Ma, “Multidimensional Monte Carlo model for two-photon laser-induced fluorescence and amplified spontaneous emission,” Comput. Phys. Commun. 183, 1588–1595 (2012).
[CrossRef]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179, 250 (2008).
[CrossRef]

W. Cai and L. Ma, “Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm,” Comput. Phys. Commun. 181, 11–16 (2010).
[CrossRef]

Exp. Fluids

J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33, 265–269 (2002).
[CrossRef]

J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51, 1471–1492 (2011).
[CrossRef]

IEEE Trans. Instrum. Meas.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61, 1417–1425 (2012).
[CrossRef]

IEEE Trans. Med. Imaging

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef]

Inverse Probl.

A. Seppanen, A. Voutilainen, and J. P. Kaipio, “State estimation in process tomography-reconstruction of velocity fields using EIT,” Inverse Probl. 25, 085009 (2009).
[CrossRef]

J. Aerosol Sci.

L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 40, 588–596 (2009).
[CrossRef]

J. Theor. Biol.

G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33, 189–211 (1971).
[CrossRef]

G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction technique: an experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol. 33, 213–223 (1971).
[CrossRef]

J. X-Ray Sci. Technol.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

JSME Int. J.

Y. Ishino and N. Ohiwa, “Three-dimensional computerized tomographic reconstruction of instantaneous distribution of chemiluminescence of a turbulent premixed flame,” JSME Int. J. 48, 34–40 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Combust. Inst.

R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. 31, 49–75 (2007).
[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, 751–758 (2011).
[CrossRef]

Proc. R. Soc. London

R. Crowther, D. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. R. Soc. London 317, 319–340 (1970).
[CrossRef]

Prog. Energy Combust. Sci.

G. J. Nathan, P. A. M. Kalt, Z. T. Alwahabi, B. B. Dally, P. R. Medwell, and Q. N. Chan, “Recent advances in the measurement of strongly radiating, turbulent reacting flows,” Prog. Energy Combust. Sci. 38, 41–61 (2012).
[CrossRef]

Science

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Siam Rev.

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the L-Curve,” Siam Rev. 34, 561–580 (1992).
[CrossRef]

Other

C. T. Herman, Image reconstruction from projections—the fundamentals of computerized tomography (Academic, 1980).

L. Ma, “High speed imaging in reactive flows using hyperspectral tomography and photodissociation spectroscopy,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2010), paper LWA3.

L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of high speed imaging in practical propulsion systems using hyperspectral tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, OSA Technical Digest (Optical Society of America, 2012), paper LM1B.5.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge, 1992).

W. Cai, A. J. Wickersham, and L. Ma, “Three-dimensional combustion diagnostics based on computed tomography of chemiluminescence,” presented at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Dallas Region, Texas, 7–10 January2013.

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Figures (12)

Fig. 1.
Fig. 1.

Mathematical formulation of the TC problem and example flames used to validate the TC technique experimentally.

Fig. 2.
Fig. 2.

Phantoms used for numerical simulations.

Fig. 3.
Fig. 3.

Insensitivity to initial guess.

Fig. 4.
Fig. 4.

Evolution of e and normalized residual illustrating issues with termination criterion in the ART algorithm.

Fig. 5.
Fig. 5.

Evolution of e and normalized F illustrating the monotonic decrease of e in the RHybrid algorithm.

Fig. 6.
Fig. 6.

Application of regularization in the TC technique. Projections from eight random views were used with 5% Gaussian noise added (these same conditions were used in the results in Figs. 7 and 8).

Fig. 7.
Fig. 7.

L curve for phantom 2 (a smooth flame).

Fig. 8.
Fig. 8.

Application of regularization to phantom 4 (a turbulent flame).

Fig. 9.
Fig. 9.

Layer 1 of the reconstructions from experimentally measured projections.

Fig. 10.
Fig. 10.

Reconstruction of experimental data with and without binning the measured projections.

Fig. 11.
Fig. 11.

Layer 1 of the reconstructions from simulated projections.

Fig. 12.
Fig. 12.

Reconstruction of experimental data with and without binning the simulated projections.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P(r,θ,ϕ)=ixNxiyNyizNzF(xi,yi,zi)·PSF(xi,yi,zi;r,θ,ϕ),
minimizeD=r,θ,ϕ[Pm(r,θ,ϕ)Pc(r,θ,ϕ)]2with respect toF(x,y,z),
e=ixiyiz|Fix,iy,izrecFix,iy,iz|ixiyiz|Fix,iy,iz|,
|ixNxiyNyizNzFk(xi,yi,zi)ixNxiyNyizNzFk1(xi,yi,zi)|ε·β·ixNxiyNyizNzFk(xi,yi,zi),
D=r,θ,ϕ|Pmk(r,θ,ϕ)Pck(r,θ,ϕ)|2,
|DkDk1|ε·Dk,
RTV(F)=ix,iy,iz(Fix,iy,izFix1,iy,iz)2+(Fix,iy,izFix,iy1,iz)2+(Fix,iy,izFix,iy,iz1)2.
minf=D+γ·RTV,

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