Abstract

Optical tomography has become an indispensable tool for combustion diagnostics due to its noninvasiveness. However, for a typical tomography system, multiple high-speed cameras are usually required to capture different perspectives simultaneously, which is costly and requires precise synchronization, especially for the diagnostics of supersonic/hypersonic flows. Recently, a single-camera endoscopic tomography system has been proposed to overcome the aforementioned problem [Opt. Commun. 437, 33 (2019) [CrossRef]  ]. This work aims to optimize the parameters of the single-camera tomography system such as the number of input ends of the fiber bundle and focal length of the lens. Simulative and experimental studies were conducted. The results show that it has the best performance to register nine projections onto a single camera.

© 2020 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  44. B. R. Halls, P. S. Hsu, N. B. Jiang, E. S. Legge, J. J. Felver, M. N. Slipchenko, S. Roy, T. R. Meyer, and J. R. Gord, “kHz-rate four-dimensional fluorescence tomography using an ultraviolet-tunable narrowband burst-mode optical parametric oscillator,” Optica 4, 897–902 (2017).
    [Crossref]
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    [Crossref]
  46. T. Li, J. Pareja, F. Fuest, M. Schütte, Y. Zhou, A. Dreizler, and B. Böhm, “Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames,” Meas. Sci. Technol. 29, 015206 (2018).
    [Crossref]

2019 (13)

H. Liu, Q. Wang, and W. Cai, “Assessment of plenoptic imaging for reconstruction of 3D discrete and continuous luminous fields,” J. Opt. Soc. Am. A 36, 149–158 (2019).
[Crossref]

Y. Gao, X. Yang, C. Fu, Y. Yang, Z. Li, H. Zhang, and F. Qi, “10 kHz simultaneous PIV/PLIF study of the diffusion flame response to periodic acoustic forcing,” Appl. Opt. 58, C112–C120 (2019).
[Crossref]

N. A. Worth and J. R. Dawson, “Characterisation of flame surface annihilation events in self excited interacting flames,” Combust. Flame 199, 338–351 (2019).
[Crossref]

A. Unterberger, A. Kempf, and K. Mohri, “3D evolutionary reconstruction of scalar fields in the gas-phase,” Energies 12, 2075 (2019).
[Crossref]

J. Huang, H. Liu, and W. Cai, “Online in situ prediction of 3-D flame evolution from its history 2-D projections via deep learning,” J. Fluid Mech. 875, R2 (2019).
[Crossref]

Y. Tao, L. Ziming, R. Can, C. Feier, L. Xingcai, and C. Weiwei, “Development of an absorption-corrected method for three-dimensional computed tomography of chemiluminescence,” Meas. Sci. Technol. 30, 045403 (2019).
[Crossref]

J. Zhao, H. Liu, and W. Cai, “Numerical and experimental validation of a single-camera 3D velocimetry based on endoscopic tomography,” Appl. Opt. 58, 1363–1373 (2019).
[Crossref]

Q. Qu, Z. Cao, L. Xu, C. Liu, L. Chang, and H. McCann, “Reconstruction of two-dimensional velocity distribution in scramjet by laser absorption spectroscopy tomography,” Appl. Opt. 58, 205–212 (2019).
[Crossref]

C. Ruan, T. Yu, F. E. Chen, S. X. Wang, W. W. Cai, and X. C. Lu, “Experimental characterization of the spatiotemporal dynamics of a turbulent flame in a gas turbine model combustor using computed tomography of chemiluminescence,” Energy 170, 744–751 (2019).
[Crossref]

H. C. Liu, B. Sun, and W. W. Cai, “kHz-rate volumetric flame imaging using a single camera,” Opt. Commun. 437, 33–43 (2019).
[Crossref]

Y. Jin, W. Zhang, Y. Song, X. Qu, Z. Li, Y. Ji, and A. He, “Three-dimensional rapid flame chemiluminescence tomography via deep learning,” Opt. Express 27, 27308–27334 (2019).
[Crossref]

D. Mei, J. F. Ding, S. X. Shi, T. H. New, and J. Soria, “High resolution volumetric dual-camera light-field PIV,” Exp. Fluids 60, 132–152 (2019).
[Crossref]

H. C. Liu, J. N. Zhao, C. Y. Shui, and W. W. Cai, “Reconstruction and analysis of non-premixed turbulent swirl flames based on kHz-rate multi-angular endoscopic volumetric tomography,” Aerosp. Sci. Technol. 91, 422–433 (2019).
[Crossref]

2018 (1)

T. Li, J. Pareja, F. Fuest, M. Schütte, Y. Zhou, A. Dreizler, and B. Böhm, “Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames,” Meas. Sci. Technol. 29, 015206 (2018).
[Crossref]

2017 (10)

B. R. Halls, P. S. Hsu, N. B. Jiang, E. S. Legge, J. J. Felver, M. N. Slipchenko, S. Roy, T. R. Meyer, and J. R. Gord, “kHz-rate four-dimensional fluorescence tomography using an ultraviolet-tunable narrowband burst-mode optical parametric oscillator,” Optica 4, 897–902 (2017).
[Crossref]

H. Liu, T. Yu, M. Zhang, and W. Cai, “Demonstration of 3D computed tomography of chemiluminescence with a restricted field of view,” Appl. Opt. 56, 7107–7115 (2017).
[Crossref]

T. Yu and W. Cai, “Benchmark evaluation of inversion algorithms for tomographic absorption spectroscopy,” Appl. Opt. 56, 2183–2194 (2017).
[Crossref]

K. Wang, F. Li, H. Zeng, and X. Yu, “Three-dimensional flame measurements with large field angle,” Opt. Express 25, 21008–21018 (2017).
[Crossref]

K. Mohri, S. Görs, J. Schöler, A. Rittler, T. Dreier, C. Schulz, and A. Kempf, “Instantaneous 3D imaging of highly turbulent flames using computed tomography of chemiluminescence,” Appl. Opt. 56, 7385–7395 (2017).
[Crossref]

H. M. Lang, K. Oberleithner, C. O. Paschereit, and M. Sieber, “Measurement of the fluctuating temperature field in a heated swirling jet with BOS tomography,” Exp. Fluids 58, 88–108 (2017).
[Crossref]

C. Liu, Z. Cao, F. Y. Li, Y. Z. Lin, and L. J. Xu, “Flame monitoring of a model swirl injector using 1D tunable diode laser absorption spectroscopy tomography,” Meas. Sci. Technol. 28, 054002 (2017).
[Crossref]

Y. Jin, Y. Song, X. Qu, Z. Li, Y. Ji, and A. He, “Three-dimensional dynamic measurements of CH* and C2* concentrations in flame using simultaneous chemiluminescence tomography,” Opt. Express 25, 4640–4654 (2017).
[Crossref]

S. M. Wiseman, M. J. Brear, R. L. Gordon, and I. Marusic, “Measurements from flame chemiluminescence tomography of forced laminar premixed propane flames,” Combust. Flame 183, 1–14 (2017).
[Crossref]

W. W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
[Crossref]

2016 (6)

L. Ma, Y. Wu, Q. Lei, W. Xu, and C. D. Carter, “3D flame topography and curvature measurements at 5 kHz on a premixed turbulent Bunsen flame,” Combust. Flame 166, 66–75 (2016).
[Crossref]

M. Lin, Q. Lei, W. Yue, 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]

L. Xu, C. Liu, W. Jing, Z. Cao, X. Xue, and Y. Lin, “Tunable diode laser absorption spectroscopy-based tomography system for on-line monitoring of two-dimensional distributions of temperature and H2O mole fraction,” Rev. Sci. Instrum. 87, 013101 (2016).
[Crossref]

Y. Jin, Y. Song, X. Qu, Z. Li, Y. Ji, and A. He, “Hybrid algorithm for three-dimensional flame chemiluminescence tomography based on imaging overexposure compensation,” Appl. Opt. 55, 5917–5923 (2016).
[Crossref]

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. Transfer 172, 58–74 (2016).
[Crossref]

B. R. Halls, D. J. Thul, D. Michaelis, S. Roy, T. R. Meyer, and J. R. Gord, “Single-shot, volumetrically illuminated, three-dimensional, tomographic laser-induced-fluorescence imaging in a gaseous free jet,” Opt. Express 24, 10040–10049 (2016).
[Crossref]

2015 (2)

M. Zhang, J. H. Wang, W. Jin, Z. H. Huang, H. Kobayashi, and L. Ma, “Estimation of 3D flame surface density and global fuel consumption rate from 2D PLIF images of turbulent premixed flame,” Combust. Flame 162, 2087–2097 (2015).
[Crossref]

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

2014 (1)

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

2013 (1)

N. A. Worth and J. R. Dawson, “Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames,” Meas. Sci. Technol. 24, 24013–24023 (2013).
[Crossref]

2012 (3)

G. Qi, H. P. Wang, and J. J. Wang, “A single camera volumetric particle image velocimetry and its application,” Sci. China Technol. Sci. 55, 2501–2510 (2012).
[Crossref]

N. B. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of 2D-OH *-chemiluminescence distributions in turbulent diffusion flames,” Appl. Phys. B 107, 591–602 (2012).
[Crossref]

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]

2011 (2)

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]

2006 (1)

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

1998 (1)

P. C. Hanson, “Rank-deficient and discrete ill-posed problems,” Am. Math. Monthly 4, 491 (1998).

1988 (1)

1970 (1)

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theoret. Biol. 29, 471–481 (1970).
[Crossref]

Anikin, N. B.

N. B. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of 2D-OH *-chemiluminescence distributions in turbulent diffusion flames,” Appl. Phys. B 107, 591–602 (2012).
[Crossref]

Bender, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theoret. Biol. 29, 471–481 (1970).
[Crossref]

Bockhorn, H.

N. B. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of 2D-OH *-chemiluminescence distributions in turbulent diffusion flames,” Appl. Phys. B 107, 591–602 (2012).
[Crossref]

Böhm, B.

T. Li, J. Pareja, F. Fuest, M. Schütte, Y. Zhou, A. Dreizler, and B. Böhm, “Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames,” Meas. Sci. Technol. 29, 015206 (2018).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

Brear, M. J.

S. M. Wiseman, M. J. Brear, R. L. Gordon, and I. Marusic, “Measurements from flame chemiluminescence tomography of forced laminar premixed propane flames,” Combust. Flame 183, 1–14 (2017).
[Crossref]

Cai, W.

Cai, W. W.

H. C. Liu, J. N. Zhao, C. Y. Shui, and W. W. Cai, “Reconstruction and analysis of non-premixed turbulent swirl flames based on kHz-rate multi-angular endoscopic volumetric tomography,” Aerosp. Sci. Technol. 91, 422–433 (2019).
[Crossref]

H. C. Liu, B. Sun, and W. W. Cai, “kHz-rate volumetric flame imaging using a single camera,” Opt. Commun. 437, 33–43 (2019).
[Crossref]

C. Ruan, T. Yu, F. E. Chen, S. X. Wang, W. W. Cai, and X. C. Lu, “Experimental characterization of the spatiotemporal dynamics of a turbulent flame in a gas turbine model combustor using computed tomography of chemiluminescence,” Energy 170, 744–751 (2019).
[Crossref]

W. W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
[Crossref]

Can, R.

Y. Tao, L. Ziming, R. Can, C. Feier, L. Xingcai, and C. Weiwei, “Development of an absorption-corrected method for three-dimensional computed tomography of chemiluminescence,” Meas. Sci. Technol. 30, 045403 (2019).
[Crossref]

Cao, Z.

Q. Qu, Z. Cao, L. Xu, C. Liu, L. Chang, and H. McCann, “Reconstruction of two-dimensional velocity distribution in scramjet by laser absorption spectroscopy tomography,” Appl. Opt. 58, 205–212 (2019).
[Crossref]

C. Liu, Z. Cao, F. Y. Li, Y. Z. Lin, and L. J. Xu, “Flame monitoring of a model swirl injector using 1D tunable diode laser absorption spectroscopy tomography,” Meas. Sci. Technol. 28, 054002 (2017).
[Crossref]

L. Xu, C. Liu, W. Jing, Z. Cao, X. Xue, and Y. Lin, “Tunable diode laser absorption spectroscopy-based tomography system for on-line monitoring of two-dimensional distributions of temperature and H2O mole fraction,” Rev. Sci. Instrum. 87, 013101 (2016).
[Crossref]

Carter, C. D.

L. Ma, Y. Wu, Q. Lei, W. Xu, and C. D. Carter, “3D flame topography and curvature measurements at 5 kHz on a premixed turbulent Bunsen flame,” Combust. Flame 166, 66–75 (2016).
[Crossref]

M. Lin, Q. Lei, W. Yue, 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]

Chang, L.

Chen, F. E.

C. Ruan, T. Yu, F. E. Chen, S. X. Wang, W. W. Cai, and X. C. Lu, “Experimental characterization of the spatiotemporal dynamics of a turbulent flame in a gas turbine model combustor using computed tomography of chemiluminescence,” Energy 170, 744–751 (2019).
[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. Transfer 172, 58–74 (2016).
[Crossref]

Dawson, J. R.

N. A. Worth and J. R. Dawson, “Characterisation of flame surface annihilation events in self excited interacting flames,” Combust. Flame 199, 338–351 (2019).
[Crossref]

N. A. Worth and J. R. Dawson, “Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames,” Meas. Sci. Technol. 24, 24013–24023 (2013).
[Crossref]

Ding, J. F.

D. Mei, J. F. Ding, S. X. Shi, T. H. New, and J. Soria, “High resolution volumetric dual-camera light-field PIV,” Exp. Fluids 60, 132–152 (2019).
[Crossref]

Dreier, T.

Dreizler, A.

T. Li, J. Pareja, F. Fuest, M. Schütte, Y. Zhou, A. Dreizler, and B. Böhm, “Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames,” Meas. Sci. Technol. 29, 015206 (2018).
[Crossref]

Elsinga, G. E.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[Crossref]

Faris, G. W.

Feier, C.

Y. Tao, L. Ziming, R. Can, C. Feier, L. Xingcai, and C. Weiwei, “Development of an absorption-corrected method for three-dimensional computed tomography of chemiluminescence,” Meas. Sci. Technol. 30, 045403 (2019).
[Crossref]

Felver, J. J.

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Zhou, Y.

T. Li, J. Pareja, F. Fuest, M. Schütte, Y. Zhou, A. Dreizler, and B. Böhm, “Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames,” Meas. Sci. Technol. 29, 015206 (2018).
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Ziming, L.

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Aerosp. Sci. Technol. (1)

H. C. Liu, J. N. Zhao, C. Y. Shui, and W. W. Cai, “Reconstruction and analysis of non-premixed turbulent swirl flames based on kHz-rate multi-angular endoscopic volumetric tomography,” Aerosp. Sci. Technol. 91, 422–433 (2019).
[Crossref]

Am. Math. Monthly (1)

P. C. Hanson, “Rank-deficient and discrete ill-posed problems,” Am. Math. Monthly 4, 491 (1998).

Appl. Opt. (7)

Appl. Phys. B (1)

N. B. Anikin, R. Suntz, and H. Bockhorn, “Tomographic reconstruction of 2D-OH *-chemiluminescence distributions in turbulent diffusion flames,” Appl. Phys. B 107, 591–602 (2012).
[Crossref]

Combust. Flame (7)

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]

N. A. Worth and J. R. Dawson, “Characterisation of flame surface annihilation events in self excited interacting flames,” Combust. Flame 199, 338–351 (2019).
[Crossref]

M. Zhang, J. H. Wang, W. Jin, Z. H. Huang, H. Kobayashi, and L. Ma, “Estimation of 3D flame surface density and global fuel consumption rate from 2D PLIF images of turbulent premixed flame,” Combust. Flame 162, 2087–2097 (2015).
[Crossref]

S. M. Wiseman, M. J. Brear, R. L. Gordon, and I. Marusic, “Measurements from flame chemiluminescence tomography of forced laminar premixed propane flames,” Combust. Flame 183, 1–14 (2017).
[Crossref]

L. Ma, Y. Wu, Q. Lei, W. Xu, and C. D. Carter, “3D flame topography and curvature measurements at 5 kHz on a premixed turbulent Bunsen flame,” Combust. Flame 166, 66–75 (2016).
[Crossref]

M. Lin, Q. Lei, W. Yue, 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]

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

Energies (1)

A. Unterberger, A. Kempf, and K. Mohri, “3D evolutionary reconstruction of scalar fields in the gas-phase,” Energies 12, 2075 (2019).
[Crossref]

Energy (1)

C. Ruan, T. Yu, F. E. Chen, S. X. Wang, W. W. Cai, and X. C. Lu, “Experimental characterization of the spatiotemporal dynamics of a turbulent flame in a gas turbine model combustor using computed tomography of chemiluminescence,” Energy 170, 744–751 (2019).
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Exp. Fluids (3)

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Figures (11)

Fig. 1.
Fig. 1. Illustration of an endoscopic system with (a) single and (b) multiple input end(s), respectively.
Fig. 2.
Fig. 2. Phantoms with (a) high and (b) low swirl strength reconstructed by CTC.
Fig. 3.
Fig. 3. Projections of (a) Phantom 1 and (b) Phantom 2 when ${N={3}}$.
Fig. 4.
Fig. 4. Evolution of RMSE and SSIM as a function of $N$ for (a) Phantom 1 and (b) Phantom 2.
Fig. 5.
Fig. 5. Evolution of RMSE as a function of noise level for (a) Phantom 1 and (b) Phantom 2. The evolution of SSIM as a function of noise level for (c) Phantom 1 and (d) Phantom 2.
Fig. 6.
Fig. 6. Three-dimensional rendering of reconstructions for (a) Phantom 1 and (b) Phantom 2 at different noise levels when $N={3}$.
Fig. 7.
Fig. 7. Evolution of RMSE as a function of $R$ for (a) Phantom 1 and (b) Phantom 2. The evolution of SSIM as a function of $R$ for (c) Phantom 1 and (d) Phantom 2.
Fig. 8.
Fig. 8. RMSE and SSIM of reconstructions for Phantom 1 with different lens distortion coefficients.
Fig. 9.
Fig. 9. Layout of the experimental setup.
Fig. 10.
Fig. 10. (a) Benchmark. (b)–(d) Reconstructions for $N={1}\sim{3}$, respectively.
Fig. 11.
Fig. 11. SSIM and RMSE between reconstructions and benchmark for $N={1}\sim{3}$, respectively.

Tables (1)

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Table 1. Distortion Coefficients for Different Lenses

Equations (5)

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A N v × N p x N p × 1 = p N p × 1 ,
x ( k + 1 , i ) = x ( k , i ) λ A R T × A i × x ( k , i ) p i A i 2 2 × A i T ,
M = 1024 N × H p H v ,
R M S E = i = 1 Q ( x i P h a n x i R e c ) 2 Q ,
S S I M = ( 2 × μ P h a n × μ R e c + c 1 ) × ( 2 × σ P h a n R e c + c 2 ) ( ( μ P h a n ) 2 × ( μ R e c ) 2 + c 1 ) × ( ( σ P h a n ) 2 × ( σ R e c ) 2 + c 2 ) ,

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