Abstract

This work reports the development and experimental validation of a reconstruction algorithm for three-dimensional (3D) nonlinear tomography problems. Many optical tomography problems encountered in practice are nonlinear, for example, due to significant absorption, multiple-scattering, or radiation trapping. Past research efforts have predominately focused on reconstruction algorithms for linear problems, and these algorithms are not readily extendable to nonlinear problems due to several challenges. These challenges include the computational cost caused by the nonlinearity (which was compounded by the large scale of the problems when they are 3D), the limited view angles available in many practical applications, and the measurement uncertainty. A new algorithm was therefore developed to overcome these challenges. The algorithm was validated both numerically and experimentally, and was demonstrated to be able to solve a range of nonlinear tomography problems with significantly enhanced efficiency and accuracy compared to existing algorithms.

© 2016 Optical Society of America

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References

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2016 (1)

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (4)

2012 (2)

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(8), 1588–1595 (2012).
[Crossref]

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61(5), 1417–1425 (2012).
[Crossref]

2011 (4)

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(12), 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(2), 376–391 (2011).
[Crossref]

J. Floyd and A. 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]

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(4), A29–A37 (2011).
[Crossref] [PubMed]

2009 (2)

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47(4-5), 553–568 (2009).
[Crossref]

2008 (2)

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt. 47(21), 3751–3759 (2008).
[Crossref] [PubMed]

2006 (2)

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

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(1), 34–40 (2005).
[Crossref]

2004 (2)

D. Mishra, J. P. Longtin, R. P. Singh, and V. Prasad, “Performance evaluation of iterative tomography algorithms for incomplete projection data,” Appl. Opt. 43(7), 1522–1532 (2004).
[Crossref] [PubMed]

W. Fang, “A nonlinear image reconstruction algorithm for electrical capacitance tomography,” Meas. Sci. Technol. 15(10), 2124–2132 (2004).
[Crossref]

2003 (1)

W. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol. 14(1), R1–R13 (2003).
[Crossref]

2002 (1)

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

2001 (1)

C.-T. Hsiao, G. Chahine, and N. Gumerov, “Application of a hybrid genetic/Powell algorithm and a boundary element method to electrical impedance tomography,” J. Comput. Phys. 173(2), 433–454 (2001).
[Crossref]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

1998 (1)

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

1996 (1)

1992 (1)

M. Moghaddam and W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30(1), 147–156 (1992).
[Crossref]

1991 (1)

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

1988 (1)

1987 (1)

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

1981 (1)

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

1980 (1)

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[Crossref]

1977 (1)

W. Swindell and H. H. Barrett, “Computerized tomography: taking sectional x rays,” Phys. Today 30(12), 32–41 (1977).
[Crossref]

An, X.

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

Atkinson, C.

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47(4-5), 553–568 (2009).
[Crossref]

Barrett, H. H.

W. Swindell and H. H. Barrett, “Computerized tomography: taking sectional x rays,” Phys. Today 30(12), 32–41 (1977).
[Crossref]

Belkebir, K.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

Best, P.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

Blott, B. H.

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

Bolomey, J.-C.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

Broquetas, A.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

Cai, W.

Carangelo, R.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

Carter, C. D.

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Caswell, A. W.

Chahine, G.

C.-T. Hsiao, G. Chahine, and N. Gumerov, “Application of a hybrid genetic/Powell algorithm and a boundary element method to electrical impedance tomography,” J. Comput. Phys. 173(2), 433–454 (2001).
[Crossref]

Chaumet, P. C.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

Chew, W. C.

M. Moghaddam and W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30(1), 147–156 (1992).
[Crossref]

Chien, P.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

Corana, A.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

Cox, S. J.

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

Danchak, M.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

Daniell, G. J.

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

Drsek, F.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Emmerman, P.

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[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(12), 5754–5767 (2011).
[Crossref]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

Fang, W.

W. Fang, “A nonlinear image reconstruction algorithm for electrical capacitance tomography,” Meas. Sci. Technol. 15(10), 2124–2132 (2004).
[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(2), 376–391 (2011).
[Crossref]

J. Floyd and A. 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]

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(2), 376–391 (2011).
[Crossref]

Giovannini, H.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Girard, J.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Gord, J. R.

Goulard, R.

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[Crossref]

Gumerov, N.

C.-T. Hsiao, G. Chahine, and N. Gumerov, “Application of a hybrid genetic/Powell algorithm and a boundary element method to electrical impedance tomography,” J. Comput. Phys. 173(2), 433–454 (2001).
[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(5), 1417–1425 (2012).
[Crossref]

Hsiao, C.-T.

C.-T. Hsiao, G. Chahine, and N. Gumerov, “Application of a hybrid genetic/Powell algorithm and a boundary element method to electrical impedance tomography,” J. Comput. Phys. 173(2), 433–454 (2001).
[Crossref]

Ibrahim, S.

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Ilovici, I.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[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(1), 34–40 (2005).
[Crossref]

Jiang, H.

Joachimowicz, N.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

Kang, M.

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.

J. Floyd and A. 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]

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(2), 376–391 (2011).
[Crossref]

Konan, D.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Kraetschmer, T.

Lei, Q.

Li, F.

Li, X.

Longtin, J. P.

Lu, G.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61(5), 1417–1425 (2012).
[Crossref]

Ma, L.

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Y. Wu, W. Xu, Q. Lei, and L. Ma, “Single-shot volumetric laser induced fluorescence (VLIF) measurements in turbulent flows seeded with iodine,” Opt. Express 23(26), 33408–33418 (2015).
[Crossref] [PubMed]

Y. Wu, Q. Lei, and L. Ma, “Experimental demonstration of 4D imaging in two-phase flows based on computed tomography at 5 kHz,” Appl. Opt. 53(24), 5547–5553 (2014).
[Crossref] [PubMed]

Q. Lei, Y. Wu, H. Xiao, and L. Ma, “Analysis of four-dimensional Mie imaging using fiber-based endoscopes,” Appl. Opt. 53(28), 6389–6398 (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]

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]

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(1), 1152–1162 (2013).
[Crossref] [PubMed]

W. Cai, X. Li, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21(6), 7050–7064 (2013).
[Crossref] [PubMed]

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(8), 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(12), 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(4), A29–A37 (2011).
[Crossref] [PubMed]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt. 47(21), 3751–3759 (2008).
[Crossref] [PubMed]

Maire, G.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Mallorqui, J. J.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

Manaf, M. S.

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

Martini, C.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

Mishra, D.

Moghaddam, M.

M. Moghaddam and W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30(1), 147–156 (1992).
[Crossref]

Mohamad, E. J.

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Molinari, M.

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

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(1), 34–40 (2005).
[Crossref]

Ombrello, T. M.

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Peng, L.

W. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol. 14(1), R1–R13 (2003).
[Crossref]

Plemmons, D. H.

Pogue, B. W.

Prasad, V.

Rahim, R. A.

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Ridella, S.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

Roy, S.

Sanders, S. T.

Santoro, R.

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[Crossref]

Scarano, F.

F. Scarano, “Tomographic PIV: principles and practice,” Meas. Sci. Technol. 24(1), 012001 (2013).
[Crossref]

Semerjian, H.

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[Crossref]

Sentenac, A.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

Singh, R. P.

Snyder, R.

Solomon, P.

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[Crossref]

Soria, J.

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47(4-5), 553–568 (2009).
[Crossref]

Sulaiman, S.

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Swindell, W.

W. Swindell and H. H. Barrett, “Computerized tomography: taking sectional x rays,” Phys. Today 30(12), 32–41 (1977).
[Crossref]

Takami, K.

Talneau, A.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Wu, Y.

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Y. Wu, W. Xu, Q. Lei, and L. Ma, “Single-shot volumetric laser induced fluorescence (VLIF) measurements in turbulent flows seeded with iodine,” Opt. Express 23(26), 33408–33418 (2015).
[Crossref] [PubMed]

Y. Wu, Q. Lei, and L. Ma, “Experimental demonstration of 4D imaging in two-phase flows based on computed tomography at 5 kHz,” Appl. Opt. 53(24), 5547–5553 (2014).
[Crossref] [PubMed]

Q. Lei, Y. Wu, H. Xiao, and L. Ma, “Analysis of four-dimensional Mie imaging using fiber-based endoscopes,” Appl. Opt. 53(28), 6389–6398 (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]

Xiao, H.

Xu, W.

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Y. Wu, W. Xu, Q. Lei, and L. Ma, “Single-shot volumetric laser induced fluorescence (VLIF) measurements in turbulent flows seeded with iodine,” Opt. Express 23(26), 33408–33418 (2015).
[Crossref] [PubMed]

Yan, Y.

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61(5), 1417–1425 (2012).
[Crossref]

Yang, W.

W. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol. 14(1), R1–R13 (2003).
[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(8), 1588–1595 (2012).
[Crossref]

ACM Trans. Math. Softw. (1)

A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corrigenda for this article is available here,” ACM Trans. Math. Softw. 13(3), 262–280 (1987).
[Crossref]

Appl. Math. Comput. (1)

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(12), 5754–5767 (2011).
[Crossref]

Appl. Opt. (6)

Combust. Flame (4)

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]

P. Best, P. Chien, R. Carangelo, P. Solomon, M. Danchak, and I. Ilovici, “Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame: species concentrations and temperatures,” Combust. Flame 85(3-4), 309–318 (1991).
[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(2), 376–391 (2011).
[Crossref]

L. Ma, Q. Lei, Y. Wu, W. Xu, T. M. Ombrello, and C. D. Carter, “From ignition to stable combustion in a cavity flameholder studied via 3D tomographic chemiluminescence at 20 kHz,” Combust. Flame 165, 1–10 (2016).
[Crossref]

Comput. Phys. Commun. (2)

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(8), 1588–1595 (2012).
[Crossref]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

Exp. Fluids (1)

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47(4-5), 553–568 (2009).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

M. Moghaddam and W. C. Chew, “Nonlinear two-dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sens. 30(1), 147–156 (1992).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

M. M. Hossain, G. Lu, and Y. Yan, “Optical fiber imaging based tomographic reconstruction of burner flames,” IEEE Trans. Instrum. Meas. 61(5), 1417–1425 (2012).
[Crossref]

IEEE Trans. Med. Imaging (1)

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, “Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography,” IEEE Trans. Med. Imaging 17(4), 562–570 (1998).
[Crossref] [PubMed]

Int. J. Heat Mass Transfer (1)

R. Santoro, H. Semerjian, P. Emmerman, and R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24(7), 1139–1150 (1981).
[Crossref]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

J. Comput. Phys. (1)

C.-T. Hsiao, G. Chahine, and N. Gumerov, “Application of a hybrid genetic/Powell algorithm and a boundary element method to electrical impedance tomography,” J. Comput. Phys. 173(2), 433–454 (2001).
[Crossref]

J. Energy (1)

P. Emmerman, R. Goulard, R. Santoro, and H. Semerjian, “Multiangular absorption diagnostics of a turbulent argon-methane jet,” J. Energy 4(2), 70–77 (1980).
[Crossref]

J. Opt. Soc. Am. A (2)

JSME Int. J. Ser. B (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(1), 34–40 (2005).
[Crossref]

Meas. Sci. Technol. (3)

W. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol. 14(1), R1–R13 (2003).
[Crossref]

F. Scarano, “Tomographic PIV: principles and practice,” Meas. Sci. Technol. 24(1), 012001 (2013).
[Crossref]

W. Fang, “A nonlinear image reconstruction algorithm for electrical capacitance tomography,” Meas. Sci. Technol. 15(10), 2124–2132 (2004).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Phys. Today (1)

W. Swindell and H. H. Barrett, “Computerized tomography: taking sectional x rays,” Phys. Today 30(12), 32–41 (1977).
[Crossref]

Physiol. Meas. (1)

M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, “Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction,” Physiol. Meas. 23(1), 95–104 (2002).
[Crossref] [PubMed]

Proc. Combust. Inst. (1)

J. Floyd and A. 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]

Sens. Actuators A Phys. (1)

E. J. Mohamad, R. A. Rahim, S. Ibrahim, S. Sulaiman, and M. S. Manaf, “Flame imaging using laser-based transmission tomography,” Sens. Actuators A Phys. 127(2), 332–339 (2006).
[Crossref]

Other (3)

J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Siam, 1970).

C. A. DiMarzio, Optics for Engineers (Crc Press, 2011).

G. Herman, Image Reconstruction from Projections: the Fundamentals of Computerized Tomography (Academic, 1980).

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Figures (9)

Fig. 1
Fig. 1 Mathematical formulation of a nonlinear tomography problem.
Fig. 2
Fig. 2 Panel (a): experimental setup from the top view. Panel (b): the spatial profile of illumination laser intensity at X = 25 mm.
Fig. 3
Fig. 3 Experimental results obtained from the controlled dye cell. Panel (a): projection of the volumetric LIF signal from the top view. Panel (b): intensity of signal along the laser propagation direction at three different Y locations (Y = −5, 0 and 5 mm). Panel (c): the reconstructed concentration distribution at three difference planes (Z = 10, 20 and 30 mm). Panel (d): reconstructed dye concentration along three lines.
Fig. 4
Fig. 4 Numerical validation using a uniform phantom. Panel (a): reconstructed distribution on the central plane (i.e., Y = 0) using simulated projections with 4% artificial noises added. Panel (b): reconstructed distribution along 3 lines.
Fig. 5
Fig. 5 Comparison of reconstruction accuracy and computational time among different algorithms.
Fig. 6
Fig. 6 A set of example projections on the turbulent flow.
Fig. 7
Fig. 7 Application of NIRT on 3D measurement of I2 concentration in turbulent flows using VLIF. Panel (a): 3D rendering of the reconstruction. Panel (b): three planar slices of the 3D reconstruction. Panel(c): a planar slice taken out of 3D reconstruction at Y = 5 mm. Panel (d): projection measured by camera 5.
Fig. 8
Fig. 8 Reconstruction error using simulated projections based on turbulent phantoms.
Fig. 9
Fig. 9 The quantitative comparison from several slices and lines between phantom and reconstruction on turbulent V-flow phantom

Equations (10)

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

P=PSF( ΓC )
[ P 1 P 2 P m P M ]=[ PS F 1,1 PS F 1,2 PS F 1,n PS F 1,N PS F 2,1 PS F 2,2 PS F 2,n PS F 2,N PS F m,1 PS F M,1 PS F m,2 PS F M,2 PS F m,n PS F M,n PS F m,N PS F M,N ][ Γ 1 C 1 Γ 2 C 2 Γ n C n Γ N C N ]
[ Γ 1 Γ 2 Γ n Γ N ]=[ I 0,1 e α C l dl I 0,2 e α C l dl I 0,n e α C l dl I 0,N e α C l dl ]
P=PSFdiag(Γ)C
NPSF=[ PS F 1,1 Γ 1 PS F 1,2 Γ 2 PS F 1,n Γ n PS F 1,N Γ N PS F 2,1 Γ 1 PS F 2,2 Γ 2 PS F 2,n Γ n PS F 2,N Γ N PS F m,1 Γ 1 PS F M,1 Γ 1 PS F m,2 Γ 2 PS F M,2 Γ 2 PS F m,n Γ n PS F M,n Γ n PS F m,N Γ N PS F M,N Γ N ]
P=NPSFC
D m q = P m P m q
C n q+1 = C n q +β D m q NPS F m,n q ||NPS F q | | 2
| n=1 N C n q n=1 N C n q1 |Δβ n=1 N C n q
e R = n=1 N | C n rec C n true | n=1 N C n true

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