Abstract

Optical fiber Fabry-Perot (F-P) sensors have been used in various on-line monitoring of physical parameters such as acoustics, temperature and pressure. In this paper, a wavelet phase extracting demodulation algorithm for optical fiber F-P sensing is first proposed. In application of this demodulation algorithm, search range of scale factor is determined by estimated cavity length which is obtained by fast Fourier transform (FFT) algorithm. Phase information of each point on the optical interference spectrum can be directly extracted through the continuous complex wavelet transform without de-noising. And the cavity length of the optical fiber F-P sensor is calculated by the slope of fitting curve of the phase. Theorical analysis and experiment results show that this algorithm can greatly reduce the amount of computation and improve demodulation speed and accuracy.

© 2016 Optical Society of America

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References

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  1. J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
    [Crossref]
  2. S. A. Taya and T. M. El-Agez, “Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure,” Optik (Stuttg.) 123(5), 417–421 (2012).
    [Crossref]
  3. J. Wang, M. Wang, J. Xu, L. Peng, M. Yang, M. Xia, and D. Jiang, “Underwater blast wave pressure sensor based on polymer film fiber Fabry-Perot cavity,” Appl. Opt. 53(28), 6494–6502 (2014).
    [Crossref] [PubMed]
  4. A. Lamberti, S. Vanlanduit, B. De Pauw, and F. Berghmans, “A novel fast phase correlation algorithm for peak wavelength detection of Fiber Bragg Grating sensors,” Opt. Express 22(6), 7099–7112 (2014).
    [Crossref] [PubMed]
  5. L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24(13), 905–907 (1999).
    [Crossref] [PubMed]
  6. L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
    [Crossref]
  7. M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
    [Crossref]
  8. M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
    [Crossref]
  9. A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41(12), 3209–3216 (2002).
    [Crossref]
  10. J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
    [Crossref]
  11. S. M. Musa, R. O. Claus, J. H. Reed, R. L. Simpson, and A. Wang, Real-time Signal Processing and Hardware Development for a Wavelength Modulated Optical Fiber Sensor System (Virginia Polytechnic Institute and State University, 1997).
  12. B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

2014 (3)

2012 (2)

L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[Crossref]

S. A. Taya and T. M. El-Agez, “Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure,” Optik (Stuttg.) 123(5), 417–421 (2012).
[Crossref]

2009 (1)

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

2003 (1)

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

2002 (2)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41(12), 3209–3216 (2002).
[Crossref]

1999 (1)

Abid, A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Afifi, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Barnes, T. H.

Berghmans, F.

Burton, D. R.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

De Pauw, B.

Duan, Y.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

El-Agez, T. M.

S. A. Taya and T. M. El-Agez, “Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure,” Optik (Stuttg.) 123(5), 417–421 (2012).
[Crossref]

Fassi-Fihri, A.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Federico, A.

A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41(12), 3209–3216 (2002).
[Crossref]

Gao, X. R.

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Gdeisat, M. A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Hua, J. L.

J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
[Crossref]

Huang, Z.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Huo, W.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Jiang, D.

Kaufmann, G. H.

A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41(12), 3209–3216 (2002).
[Crossref]

Lalor, M. J.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Lamberti, A.

Li, J. L.

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Lilley, F.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Luo, L.

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Luo, M. Z.

J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
[Crossref]

Marjane, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

May, R. G.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Moore, C.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Nassim, K.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Peng, L.

Peng, W.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Pickrell, G. R.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Qi, B.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Qudeisat, M.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Rachafi, S.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Shi, Y. K.

J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
[Crossref]

Sidki, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Tan, S. M.

Taya, S. A.

S. A. Taya and T. M. El-Agez, “Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure,” Optik (Stuttg.) 123(5), 417–421 (2012).
[Crossref]

Vanlanduit, S.

Wang, A.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Wang, J.

Wang, M.

Wang, Z. Y.

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Watkins, L. R.

L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[Crossref]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24(13), 905–907 (1999).
[Crossref] [PubMed]

Xia, M.

Xiao, H.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Xu, J.

J. Wang, M. Wang, J. Xu, L. Peng, M. Yang, M. Xia, and D. Jiang, “Underwater blast wave pressure sensor based on polymer film fiber Fabry-Perot cavity,” Appl. Opt. 53(28), 6494–6502 (2014).
[Crossref] [PubMed]

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Yang, M.

Zhang, P.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Zhao, J. H.

J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
[Crossref]

Zhao, Q. K.

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Appl. Opt. (1)

Opt. Commun. (1)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, “Wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
[Crossref]

Opt. Eng. (2)

A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41(12), 3209–3216 (2002).
[Crossref]

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).

Opt. Express (1)

Opt. Lasers Eng. (2)

L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[Crossref]

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47(12), 1348–1361 (2009).
[Crossref]

Opt. Lett. (1)

Optik (Stuttg.) (1)

S. A. Taya and T. M. El-Agez, “Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure,” Optik (Stuttg.) 123(5), 417–421 (2012).
[Crossref]

Proc. SPIE (1)

J. L. Li, X. R. Gao, Z. Y. Wang, Q. K. Zhao, and L. Luo, “Three dimensional detection of rail shape based on self-adaptive filtering,” Proc. SPIE 9282, 928211 (2014).
[Crossref]

Other (2)

S. M. Musa, R. O. Claus, J. H. Reed, R. L. Simpson, and A. Wang, Real-time Signal Processing and Hardware Development for a Wavelength Modulated Optical Fiber Sensor System (Virginia Polytechnic Institute and State University, 1997).

J. H. Zhao, M. Z. Luo, Y. K. Shi, and J. L. Hua, “Detection of impact induced stress waves using a novel optical fiber Fabry-Perot sensor,” in Proceedings of IEEE Conference on Measuring Technology and Mechatronics Automation (IEEE, 2010), pp. 1093–1096.
[Crossref]

Supplementary Material (2)

NameDescription
» Data File 1: CSV (16 KB)      The underlying values of Figure 2
» Data File 2: CSV (1 KB)      The underlying values of Figure 3

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Figures (3)

Fig. 1
Fig. 1 The experimental setup for pressure sensing.
Fig. 2
Fig. 2 Cavity length of 800 times continuous measurement with (a) wavelet phase extracting cavity length demodulation algorithm and (b) DGT method. The pressure is 750 kPa. See Data File 1 for underlying values.
Fig. 3
Fig. 3 The results of the pressure calibration experiment demodulated by (a) wavelet phase extracting cavity length demodulation algorithm and (b) single peak algorithm. The pressure was from 60 kPa to 1000 kPa. The step was set to 50 kPa. See Data File 2 for underlying values.

Equations (10)

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ψ( x )= 1 π F b exp( j2π F c x )exp( 1 F b x 2 )
I( k )=A( k )+B( k )cosφ( k )=A+ 1 2 Bexp[ jφ( k ) ]+ 1 2 Bexp[ jφ( k ) ]
W( a,b )= 1 2 a Bexp{ { π F c F b [ φ ( b )a 2π F c 1 ] } 2 }exp[ jφ( b ) ]
| W(a,b) |=| 1 2 a Bexp{ { π F c F b [ φ ( b )a 2π F c 1 ] } 2 } |
a m ( b )= π F b F c + ( π F b F c ) 2 + F b F b φ ( b )
φ=4πdk+ φ 0 = φ k+ φ 0
a m ( b )= π F b F c + ( π F b F c ) 2 + F b 4π F b d
W r ( a m ,b )= 1 2 a m Bexp{ { π F c F b [ π F b F c + ( π F b F c ) 2 + F b 2π F b F c 1 ] } 2 }×exp[ jφ( b ) ]
φ( b )=arctan{ Im[ W r ( a m ,b ) ] Re[ W r ( a m ,b ) ] }
d= φ ( b ) 4π

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