Abstract

Compared with conventional camera, the light field camera takes the advantage of being capable of recording the direction and intensity information of each ray projected onto the CCD (charge couple device) sensor simultaneously. In this paper, a novel method is proposed for reconstructing three-dimensional (3-D) temperature field of a flame based on a single light field camera. A radiative imaging of a single light field camera is also modeled for the flame. In this model, the principal ray represents the beam projected onto the pixel of the CCD sensor. The radiation direction of the ray from the flame outside the camera is obtained according to thin lens equation based on geometrical optics. The intensities of the principal rays recorded by the pixels on the CCD sensor are mathematically modeled based on radiative transfer equation. The temperature distribution of the flame is then reconstructed by solving the mathematical model through the use of least square QR-factorization algorithm (LSQR). The numerical simulations and experiments are carried out to investigate the validity of the proposed method. The results presented in this study show that the proposed method is capable of reconstructing the 3-D temperature field of a flame.

© 2016 Optical Society of America

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References

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2015 (1)

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

2014 (1)

M. Saffaripour, A. Veshkini, M. Kholghy, and M. J. Thomson, “Experimental investigation and detailed modeling of soot aggregate formation and size distribution in laminar co-flow diffusion flames of Jet A-1, a synthetic kerosene, and n-decane,” Combust. Flame 161(3), 848–863 (2014).
[Crossref]

2013 (2)

M. M. Hossain, G. Lu, D. Sun, and Y. Yan, “Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-color pyrometric techniques,” Meas. Sci. Technol. 24(7), 074010 (2013).
[Crossref]

X. Wang, Z. Wu, Z. Zhou, Y. Wang, and W. Wu, “Temperature field reconstruction of combustion flame based on high dynamic range images,” Opt. Eng. 52(4), 043601 (2013).
[Crossref]

2012 (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]

2011 (1)

W. Li, C. Lou, Y. Sun, and H. Zhou, “Estimation of radiative properties and temperature distributions in coal-fired boiler furnaces by a portable image processing system,” Exp. Therm. Fluid Sci. 35(2), 416–421 (2011).
[Crossref]

2010 (3)

C. Lou, Y. Sun, and H. Zhou, “Measurement of temperature and soot concentration in a diffusion flame by image processing,” J. Eng. Thermophys. 31(9), 1595–1598 (2010).

J. Ballester and T. García-Armingol, “Diagnostic techniques for the monitoring and control of practical flames,” Prog. Energ. Combust. 36(4), 375–411 (2010).
[Crossref]

T. Georgiev and A. Lumsdaine, “Focused plenoptic camera and rendering,” J. Electron. Imaging 19(2), 021106 (2010).
[Crossref]

2009 (2)

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Determination of soot volume fraction and temperature distribution in ethylene/air non-premixed flame based on back-projection algorithm,” J. Comput. Sci. Technol. 15(3), 209–213 (2009).

2007 (2)

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46(1), 015601 (2007).
[Crossref]

2005 (1)

1992 (1)

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. 14(2), 99–106 (1992).
[Crossref]

1982 (1)

C. Paige and M. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

1973 (1)

J. Felske and C. Tien, “Calculation of the emissivity of luminous flames,” Combust. Sci. Technol. 7(1), 25–31 (1973).
[Crossref]

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. Camb. 18(1), 51–151 (1939).
[Crossref]

Adelson, E. H.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. 14(2), 99–106 (1992).
[Crossref]

Ayranci, I.

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

Ballester, J.

J. Ballester and T. García-Armingol, “Diagnostic techniques for the monitoring and control of practical flames,” Prog. Energ. Combust. 36(4), 375–411 (2010).
[Crossref]

Bessler, W. G.

Bolan, J. T.

J. T. Bolan, K. C. Johnson, and B. S. Thurow, “Preliminary investigation of three-dimensional flame measurements with a plenoptic camera,” InProceedings of 30th AIAA Aerodynamic Measurement Technology and Ground Testing Conference (AIAA, 2014), pp. 1–12.
[Crossref]

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Cai, X. S.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

Chi, Y.

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Determination of soot volume fraction and temperature distribution in ethylene/air non-premixed flame based on back-projection algorithm,” J. Comput. Sci. Technol. 15(3), 209–213 (2009).

Dany, E.

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

Deng, Y.

H. Zhou, X. Lou, and Y. Deng, “Measurement method of three-dimensional combustion temperature distribution in utility furnaces based on image processing radiative,” in Proceedings of the Chinese Society for Electrical Engineering (1997), pp. 1–4.

Doi, J.

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46(1), 015601 (2007).
[Crossref]

Dreier, T.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Felske, J.

J. Felske and C. Tien, “Calculation of the emissivity of luminous flames,” Combust. Sci. Technol. 7(1), 25–31 (1973).
[Crossref]

Frédéric, A.

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

García-Armingol, T.

J. Ballester and T. García-Armingol, “Diagnostic techniques for the monitoring and control of practical flames,” Prog. Energ. Combust. 36(4), 375–411 (2010).
[Crossref]

Georgiev, T.

T. Georgiev and A. Lumsdaine, “Focused plenoptic camera and rendering,” J. Electron. Imaging 19(2), 021106 (2010).
[Crossref]

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computational Photography (ICCP) (IEEE, 2009), pp. 1–8.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. Camb. 18(1), 51–151 (1939).
[Crossref]

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Hecht, C.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Hossain, M. M.

M. M. Hossain, G. Lu, D. Sun, and Y. Yan, “Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-color pyrometric techniques,” Meas. Sci. Technol. 24(7), 074010 (2013).
[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]

Huang, Q.

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Determination of soot volume fraction and temperature distribution in ethylene/air non-premixed flame based on back-projection algorithm,” J. Comput. Sci. Technol. 15(3), 209–213 (2009).

Jeffries, J. B.

Johnson, K. C.

J. T. Bolan, K. C. Johnson, and B. S. Thurow, “Preliminary investigation of three-dimensional flame measurements with a plenoptic camera,” InProceedings of 30th AIAA Aerodynamic Measurement Technology and Ground Testing Conference (AIAA, 2014), pp. 1–12.
[Crossref]

Kholghy, M.

M. Saffaripour, A. Veshkini, M. Kholghy, and M. J. Thomson, “Experimental investigation and detailed modeling of soot aggregate formation and size distribution in laminar co-flow diffusion flames of Jet A-1, a synthetic kerosene, and n-decane,” Combust. Flame 161(3), 848–863 (2014).
[Crossref]

Kronemayer, H.

Lee, T.

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Li, B.

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Li, W.

W. Li, C. Lou, Y. Sun, and H. Zhou, “Estimation of radiative properties and temperature distributions in coal-fired boiler furnaces by a portable image processing system,” Exp. Therm. Fluid Sci. 35(2), 416–421 (2011).
[Crossref]

Lou, C.

W. Li, C. Lou, Y. Sun, and H. Zhou, “Estimation of radiative properties and temperature distributions in coal-fired boiler furnaces by a portable image processing system,” Exp. Therm. Fluid Sci. 35(2), 416–421 (2011).
[Crossref]

C. Lou, Y. Sun, and H. Zhou, “Measurement of temperature and soot concentration in a diffusion flame by image processing,” J. Eng. Thermophys. 31(9), 1595–1598 (2010).

Lou, X.

H. Zhou, X. Lou, and Y. Deng, “Measurement method of three-dimensional combustion temperature distribution in utility furnaces based on image processing radiative,” in Proceedings of the Chinese Society for Electrical Engineering (1997), pp. 1–4.

Lu, G.

M. M. Hossain, G. Lu, D. Sun, and Y. Yan, “Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-color pyrometric techniques,” Meas. Sci. Technol. 24(7), 074010 (2013).
[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]

Lumsdaine, A.

T. Georgiev and A. Lumsdaine, “Focused plenoptic camera and rendering,” J. Electron. Imaging 19(2), 021106 (2010).
[Crossref]

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computational Photography (ICCP) (IEEE, 2009), pp. 1–8.

Nevin, S.

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR of Stanford University1–11 (2005).

Paige, C.

C. Paige and M. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

Qi, H.

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Rodolphe, V.

I. Ayrancı, V. Rodolphe, S. Nevin, A. Frédéric, and E. Dany, “Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry,” J. Quant. Spectrosc. Rad. 104(2), 266–276 (2007).
[Crossref]

Ruan, L.

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Saffaripour, M.

M. Saffaripour, A. Veshkini, M. Kholghy, and M. J. Thomson, “Experimental investigation and detailed modeling of soot aggregate formation and size distribution in laminar co-flow diffusion flames of Jet A-1, a synthetic kerosene, and n-decane,” Combust. Flame 161(3), 848–863 (2014).
[Crossref]

Sato, S.

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46(1), 015601 (2007).
[Crossref]

Saunders, M.

C. Paige and M. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” ACM Trans. Math. Softw. 8(1), 43–71 (1982).
[Crossref]

Schulz, C.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

T. Lee, W. G. Bessler, H. Kronemayer, C. Schulz, and J. B. Jeffries, “Quantitative temperature measurements in high-pressure flames with multiline NO-LIF thermometry,” Appl. Opt. 44(31), 6718–6728 (2005).
[Crossref] [PubMed]

Sun, D.

M. M. Hossain, G. Lu, D. Sun, and Y. Yan, “Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-color pyrometric techniques,” Meas. Sci. Technol. 24(7), 074010 (2013).
[Crossref]

Sun, Y.

W. Li, C. Lou, Y. Sun, and H. Zhou, “Estimation of radiative properties and temperature distributions in coal-fired boiler furnaces by a portable image processing system,” Exp. Therm. Fluid Sci. 35(2), 416–421 (2011).
[Crossref]

C. Lou, Y. Sun, and H. Zhou, “Measurement of temperature and soot concentration in a diffusion flame by image processing,” J. Eng. Thermophys. 31(9), 1595–1598 (2010).

Thomson, M. J.

M. Saffaripour, A. Veshkini, M. Kholghy, and M. J. Thomson, “Experimental investigation and detailed modeling of soot aggregate formation and size distribution in laminar co-flow diffusion flames of Jet A-1, a synthetic kerosene, and n-decane,” Combust. Flame 161(3), 848–863 (2014).
[Crossref]

Thurow, B. S.

J. T. Bolan, K. C. Johnson, and B. S. Thurow, “Preliminary investigation of three-dimensional flame measurements with a plenoptic camera,” InProceedings of 30th AIAA Aerodynamic Measurement Technology and Ground Testing Conference (AIAA, 2014), pp. 1–12.
[Crossref]

Tien, C.

J. Felske and C. Tien, “Calculation of the emissivity of luminous flames,” Combust. Sci. Technol. 7(1), 25–31 (1973).
[Crossref]

Veshkini, A.

M. Saffaripour, A. Veshkini, M. Kholghy, and M. J. Thomson, “Experimental investigation and detailed modeling of soot aggregate formation and size distribution in laminar co-flow diffusion flames of Jet A-1, a synthetic kerosene, and n-decane,” Combust. Flame 161(3), 848–863 (2014).
[Crossref]

Wang, F.

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Determination of soot volume fraction and temperature distribution in ethylene/air non-premixed flame based on back-projection algorithm,” J. Comput. Sci. Technol. 15(3), 209–213 (2009).

Wang, J. Y. A.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. 14(2), 99–106 (1992).
[Crossref]

Wang, S.

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Wang, X.

X. Wang, Z. Wu, Z. Zhou, Y. Wang, and W. Wu, “Temperature field reconstruction of combustion flame based on high dynamic range images,” Opt. Eng. 52(4), 043601 (2013).
[Crossref]

Wang, Y.

X. Wang, Z. Wu, Z. Zhou, Y. Wang, and W. Wu, “Temperature field reconstruction of combustion flame based on high dynamic range images,” Opt. Eng. 52(4), 043601 (2013).
[Crossref]

Wu, W.

X. Wang, Z. Wu, Z. Zhou, Y. Wang, and W. Wu, “Temperature field reconstruction of combustion flame based on high dynamic range images,” Opt. Eng. 52(4), 043601 (2013).
[Crossref]

Wu, Z.

X. Wang, Z. Wu, Z. Zhou, Y. Wang, and W. Wu, “Temperature field reconstruction of combustion flame based on high dynamic range images,” Opt. Eng. 52(4), 043601 (2013).
[Crossref]

Yan, J.

Q. Huang, F. Wang, J. Yan, and Y. Chi, “Determination of soot volume fraction and temperature distribution in ethylene/air non-premixed flame based on back-projection algorithm,” J. Comput. Sci. Technol. 15(3), 209–213 (2009).

Yan, Y.

M. M. Hossain, G. Lu, D. Sun, and Y. Yan, “Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-color pyrometric techniques,” Meas. Sci. Technol. 24(7), 074010 (2013).
[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]

Yang, B.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

Yang, H. N.

H. N. Yang, B. Yang, X. S. Cai, C. Hecht, T. Dreier, and C. Schulz, “Three-dimensional (3-D) temperature measurement in a low pressure flame reactor using multiplexed tunable diode laser absorption spectroscopy (TDLAS),” Laser. Eng. 31, 285–297 (2015).

Zhao, H.

L. Ruan, H. Qi, S. Wang, H. Zhao, B. Li, and L. Ruan, “Arbitrary directional radiative intensity by source six flux method in cylindrical coordinate,” Chin. J. Comput. Phys. 26(3), 437–443 (2009).

Zhou, H.

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Figures (13)

Fig. 1
Fig. 1 Schematic diagram of sampling of the rays with conventional camera and focused light field camera.
Fig. 2
Fig. 2 Schematic diagram of radiative imaging model for flames using a single light field camera.
Fig. 3
Fig. 3 Comparision of cone angles of the beam detected by the pixels of conventional and light field cameras.
Fig. 4
Fig. 4 Schematic diagram of ray tracing in focused light field camera.
Fig. 5
Fig. 5 Relationship between the blackbody furnace images and the corresponding radiation intensity.
Fig. 6
Fig. 6 Schematic diagram of the experimental setup.
Fig. 7
Fig. 7 Schematic of the co-flow diffusion burner.
Fig. 8
Fig. 8 Physical implementation of the flame imaging system.
Fig. 9
Fig. 9 Simuated gray level intensity distributions on CCD sensor plane.
Fig. 10
Fig. 10 Relative error of the reconstructed 3-D temperature field of the simulated flame.
Fig. 11
Fig. 11 Flame image captured by the light field camera (a) and (b), and corresponding schematic of division of voxels (c).
Fig. 12
Fig. 12 Reconstructed temperature distributions of flame over the cross-sections.
Fig. 13
Fig. 13 Reconstructed temperature variations of the radial voxels over the cross-sections.

Equations (11)

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

1 l m - 1 s v = 1 f m
P x - M x V x - M x = P y - M y V y - M y = l m s v
1 l+ s v - 1 s o = 1 f
V x -X O x -X = V y -Y O y -Y = l+ s v s o
d I λ ds = k λ I bλ - β λ I λ + σ λ 4π 4π I λ Φ( s ,s)dΩ
I nλ = I bλn (1exp(1 τ n ))+ i=1 n1 (exp( j=i+1 n τ j )exp( j=i n τ j )) I bλi
I ccd =AI B λ
T= c 2 /λln[ c 1 /( λ 5 π I bλ +1)]
I= c 1 λ -5 π(exp[ c 2 /(λT)]-1)
T(x,r)=2600( x 2 -0.04x+0.1)×(0.004- r 2 )+800(K)
σ i = | T i est - T i exa | T i exa ×100%

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