Abstract

We experimentally demonstrate parallel Fabry-Perot interferometers (FPIs) fabrication in multicore-fiber with individually variable cavity length, for the purpose of discriminative sensing of temperature and strain. First, we theoretically find that, in order to obtain a small condition number of sensitivity matrix, it is necessary to fabricate parallel FPIs with large cavity difference in single multicore fiber. Then, parallel FPIs are inscribed by femtosecond laser selective micro-holes drilling on the seven-core fiber facet, together with fiber fusion splicing process. By the use of image processing algorithm, individual core position is precisely locked, and then parallel FPIs can be obtained on arbitrary two cores of seven-core fiber. With the location of parallel micro-holes and duration time of fiber fusion splicing adjusted, parallel FPIs with different cavity length of 26µm and 61µm can be simultaneously obtained at the central core and surrounding core, respectively. Consequently, each FPI possesses different sensitivity towards environmental temperature and strain. Finally, a proof-of-concept experiment verifies that relative measurement errors of both temperature and strain discriminative sensing are less than 0.5% and 2.5%, respectively.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (5)

2018 (1)

2017 (4)

2016 (1)

2015 (1)

2014 (2)

2013 (2)

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

2012 (1)

2008 (1)

Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-optic pressure and temperature sensor system for down hole measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008).
[Crossref]

2007 (1)

E. Chehura, S. W. James, and R. P. Tatam, “Temperature and strain discrimination using a single titled fibre Bragg grating,” Opt. Commun. 275(2), 344–347 (2007).
[Crossref]

1997 (1)

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Andre, R. M.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Antunes, P.

Araujo, F.

Biazoli, C. R.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Braga, A.

Bruno, A.

Carvalho, I.

Chehura, E.

E. Chehura, S. W. James, and R. P. Tatam, “Temperature and strain discrimination using a single titled fibre Bragg grating,” Opt. Commun. 275(2), 344–347 (2007).
[Crossref]

Chen, L.

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

Chen, N.

Chen, Z.

Cordeiro, C. M.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Costa, G.

Culshaw, B.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Dang, Y.

Dinh, X.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Favero, F.

Frazao, O.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Fu, S.

Z. Zhao, Y. Dang, M. Tang, L. Wang, L. Gan, S. Fu, C. Yang, W. Tong, and C. Lu, “Enabling simultaneous DAS and DTS through space-division multiplexing based on multicore fiber,” J. Lightwave Technol. 36(24), 5707–5713 (2018).
[Crossref]

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Gan, L.

Z. Zhao, Y. Dang, M. Tang, L. Wang, L. Gan, S. Fu, C. Yang, W. Tong, and C. Lu, “Enabling simultaneous DAS and DTS through space-division multiplexing based on multicore fiber,” J. Lightwave Technol. 36(24), 5707–5713 (2018).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Gouvêa, P.

Guo, X.

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Han, M.

He, P.

He, X.

He, Z.

Hu, T.

James, S. W.

E. Chehura, S. W. James, and R. P. Tatam, “Temperature and strain discrimination using a single titled fibre Bragg grating,” Opt. Commun. 275(2), 344–347 (2007).
[Crossref]

Jiang, X.

Jin, W.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Jing, Z.

Konstantaki, M.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Li, J.

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

Li, Z.

Liao, C.

Liu, D.

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Liu, G.

Liu, S.

Liu, Y.

S. Zhang, Z. Zhao, N. Chen, F. Pang, Z. Chen, Y. Liu, and T. Wang, “Temperature characteristic of silicon core optical fiber Fabry-Perot interferometer,” Opt. Lett. 40(7), 1362–1365 (2015).
[Crossref]

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

Liu, Z.

Low, C.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Lu, C.

Lu, P.

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

Luo, Z.

Ma, J.

Marques, M. B.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Michie, W. C.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Min, F.

Paixao, T.

Palffy-Muhoray, P.

Pang, F.

S. Zhang, Z. Zhao, N. Chen, F. Pang, Z. Chen, Y. Liu, and T. Wang, “Temperature characteristic of silicon core optical fiber Fabry-Perot interferometer,” Opt. Lett. 40(7), 1362–1365 (2015).
[Crossref]

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

Peng, W.

Pereira, J.

Qiao, X.

Qin, B.

Ran, Z.

Rao, Y.

Shao, X.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Shen, L.

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Sheng, Q.

Shum, P.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Silva, S. O.

R. M. Andre, C. R. Biazoli, S. O. Silva, M. B. Marques, C. M. Cordeiro, and O. Frazao, “Strain-temperature discrimination using multimode interference in tapered fiber,” IEEE Photonics Technol. Lett. 25(2), 155–158 (2013).
[Crossref]

Soares, L.

Sun, C.

Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-optic pressure and temperature sensor system for down hole measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008).
[Crossref]

Tang, J.

Tang, M.

Z. Zhao, Y. Dang, M. Tang, L. Wang, L. Gan, S. Fu, C. Yang, W. Tong, and C. Lu, “Enabling simultaneous DAS and DTS through space-division multiplexing based on multicore fiber,” J. Lightwave Technol. 36(24), 5707–5713 (2018).
[Crossref]

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Tatam, R. P.

E. Chehura, S. W. James, and R. P. Tatam, “Temperature and strain discrimination using a single titled fibre Bragg grating,” Opt. Commun. 275(2), 344–347 (2007).
[Crossref]

Thursby, G.

W. Jin, W. C. Michie, G. Thursby, M. Konstantaki, and B. Culshaw, “Simultaneous measurement of strain and temperature: error analysis,” Opt. Eng. 36(2), 598–610 (1997).
[Crossref]

Tian, M.

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

Tong, W.

Z. Zhao, Y. Dang, M. Tang, L. Wang, L. Gan, S. Fu, C. Yang, W. Tong, and C. Lu, “Enabling simultaneous DAS and DTS through space-division multiplexing based on multicore fiber,” J. Lightwave Technol. 36(24), 5707–5713 (2018).
[Crossref]

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Wang, D.

Wang, G.

Wang, L.

Wang, Q.

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref]

Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-optic pressure and temperature sensor system for down hole measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008).
[Crossref]

Wang, R.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Wang, T.

S. Zhang, Z. Zhao, N. Chen, F. Pang, Z. Chen, Y. Liu, and T. Wang, “Temperature characteristic of silicon core optical fiber Fabry-Perot interferometer,” Opt. Lett. 40(7), 1362–1365 (2015).
[Crossref]

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

Wang, W.

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

Wang, Y.

Wu, J.

Wu, Y.

Wu, Z.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Xia, L.

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Xie, Z.

Xu, Z.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Yang, C.

Z. Zhao, Y. Dang, M. Tang, L. Wang, L. Gan, S. Fu, C. Yang, W. Tong, and C. Lu, “Enabling simultaneous DAS and DTS through space-division multiplexing based on multicore fiber,” J. Lightwave Technol. 36(24), 5707–5713 (2018).
[Crossref]

L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

Yang, J.

Yang, K.

Yang, M.

M. Tian, P. Lu, L. Chen, D. Liu, and M. Yang, “Micro-multicavity Fabry-Perot interferometers sensor in SMFs machined by femtosecond laser,” IEEE Photonics Technol. Lett. 25(16), 1609–1612 (2013).
[Crossref]

Yang, T.

Yang, Y.

Yu, H.

Yu, Q.

Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-optic pressure and temperature sensor system for down hole measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008).
[Crossref]

Yuan, L.

Yuan, P.

Zhang, H.

H. Zhang, Z. Wu, P. Shum, X. Dinh, C. Low, Z. Xu, R. Wang, X. Shao, S. Fu, W. Tong, and M. Tang, “Highly sensitive strain sensor based on helical structure combined with Mach-Zehnder interferometer in multicore fiber,” Sci. Rep. 7(1), 46633 (2017).
[Crossref]

Zhang, L.

Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-optic pressure and temperature sensor system for down hole measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008).
[Crossref]

Zhang, S.

Zhang, X.

J. Li, X. Zhang, W. Wang, F. Pang, Y. Liu, and T. Wang, “Direct inscription of intrinsic Fabry-Perot interferometers in optical fiber tapers with a femtosecond laser,” in Passive Components and Fiber-based Devices, B. Pal, ed., Vol. 8307 of Proceedings of SPIE (OSA, 2011), paper 83070F.

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L. Gan, J. Zhou, L. Shen, X. Guo, Y. Wang, C. Yang, W. Tong, L. Xia, S. Fu, M. Tang, and D. Liu, “Ultra-low crosstalk fused taper type Fan-in/Fan-out devices for multicore fiber,” in Optical Fiber Communication Conference (OFC)2019, OSA Technical Digest, paper Th3D.3.

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Figures (6)

Fig. 1.
Fig. 1. Experimental setup for parallel FPIs based discriminative sensing for both temperature and strain.
Fig. 2.
Fig. 2. Experiment setup for parallel micro-holes drilling.
Fig. 3.
Fig. 3. Image correlation analysis between (a) multicore fiber with calibration point, (b) multicore fiber to be processed.
Fig. 4.
Fig. 4. (a)-(d) End view of four kinds of parallel micro-holes arrangements on the cleaved seven-core fiber facet. (e)-(h) Optical microscopic image of the fabricated parallel FPIs.
Fig. 5.
Fig. 5. Optical spectral of parallel FPIs.
Fig. 6.
Fig. 6. Temperature response of parallel FPIs on (a) core 1, and (b) core 2. Strain response of parallel FPIs at (c) core 1, and (d) core 2, insets are the corresponding spectrum shifting.

Tables (1)

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Table 1. Discriminative temperature and strain measurement.

Equations (12)

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( Δ ε Δ T ) = ( C ε 1 C T 1 C ε 2 C T 2 ) 1 ( Δ λ 1 Δ λ 2 ) = A 1 ( Δ λ 1 Δ λ 2 )
C o n d 2 ( A ) = | | A | | 2 | | A 1 | | 2
| | A | | 2  =  ( i | a i | 2 ) 1 / 2
C o n d 2 ( A ) = | | A | | 2 | | A 1 | | 2  =  ( C ε 1 ) 2 + ( C T 1 ) 2 + ( C ε 2 ) 2 + ( C T 2 ) 2 | C ε 1 C T 2 C ε 2 C T 1 |
D = | C ε 1 C T 2 C ε 2 C T 1 |
I = I 1 + I 2 + 2 I 1 I 2 cos ( 4 π n L λ + φ 0 )
4 π n L λ m + φ 0 = ( 2 m + 1 ) π
C T = d λ m d T = 4 2 m + 1 ( d n d T L + d L d T n )
C ε = d λ m d S = 4 2 m + 1 ( d n d S L + d L d S n )
C T = d λ m d T = 4 2 m + 1 d L d T n
C ε = d λ m d S = 4 2 m + 1 d L d S n
( Δ ε Δ T ) = ( C ε 1 C T 1 C ε 2 C T 2 ) 1 ( Δ λ c o r e 1 Δ λ c o r e 2 ) = ( 8.3 0.74 3.7 1.37 ) 1 ( Δ λ c o r e 1 Δ λ c o r e 2 )

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