Abstract

A white light temporal interferometric technique for measurement of the quasi-distributed birefringence dispersion (BD) in a polarization maintain (PM) device with high accuracy based on weighted least square (WLS) method is presented. It is verified theoretically and experimentally that the accuracy of WLS method and the conventional ordinary least square (OLS) method both are proportional to the signal-to-noise ratio (SNR) of interferogram, whereas the WLS method holds a higher scaling factor because it is more suitable for heteroscedastic model that has unequal error variance. The experiment results show a repeatability of ~4.6 × 10−5 ps/nm @ 1550 nm with WLS method for 100 sets of data, and ~4.3 × 10−4 ps/nm with OLS method, for an interferogram with SNR of 30 dB. Besides, WLS method without iterative operation is carried out by using power spectrum of interferogram as weight value. The feasibility of this technique is demonstrated by distinguishing the quasi-distributed BD of every part for a packaged Y-waveguide with two 1m-long PM pigtails.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry

Feng Tang, Xiang-zhao Wang, Yimo Zhang, and Wencai Jing
Appl. Opt. 46(19) 4073-4080 (2007)

Distributed measurement of birefringence dispersion in polarization-maintaining fibers

Feng Tang, Xiang-zhao Wang, Yimo Zhang, and Wencai Jing
Opt. Lett. 31(23) 3411-3413 (2006)

High-resolution distributed polarization crosstalk measurement for polarization maintaining fiber with considerable dispersion

Zhangjun Yu, Jun Yang, Yonggui Yuan, Hanyang Li, Changbo Hou, Chengcheng Hou, Haoliang Zhang, Shuaifei Tian, Xu Lu, Xiaojun Zhang, Fuqiang Jiang, Zheng Zhu, Jianzhong Zhang, Yu Zhang, Zhihai Liu, and Libo Yuan
Opt. Express 26(23) 29712-29723 (2018)

References

  • View by:
  • |
  • |
  • |

  1. W. Muguang and Y. Jianping, “Multitap microwave photonic filter with negative coefficients based on the inherent birefringence in a LiNbO3 phase modulator,” IEEE Photonics J. 5, 5500709 (2013).
    [Crossref]
  2. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
    [Crossref]
  3. W. Urbanczyk and W. J. Bock, “Analysis of dispersion effects for white-light interferometric fiber-optic sensors,” Appl. Opt. 33(1), 124–129 (1994).
    [Crossref] [PubMed]
  4. T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
    [Crossref]
  5. Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
    [Crossref]
  6. D. Deng, D. Sega, T. Cheng, W. Gao, X. Xue, T. Suzuki, and Y. Ohishi, “Dispersion characterization of two orthogonal modes in a birefringence tellurite microstructured optical fiber,” Opt. Express 22(20), 23920–23927 (2014).
    [Crossref] [PubMed]
  7. J. Y. Lee and D. Y. Kim, “Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry,” Opt. Express 14(24), 11608–11615 (2006).
    [Crossref] [PubMed]
  8. D. A. Flavin, R. McBride, and J. D. C. Jones, “Dispersion of birefringence and differential group delay in polarization-maintaining fiber,” Opt. Lett. 27(12), 1010–1012 (2002).
    [Crossref] [PubMed]
  9. F. Tang, X. Z. Wang, Y. Zhang, and W. Jing, “Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry,” Appl. Opt. 46(19), 4073–4080 (2007).
    [Crossref] [PubMed]
  10. K. Okamoto and T. Hosaka, “Polarization-dependent chromatic dispersion in birefringent optical fibers,” Opt. Lett. 12(4), 290–292 (1987).
    [Crossref] [PubMed]
  11. Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
    [Crossref]
  12. Z. Wenzin, “Automated fusion-splicing of polarization maintaining fibers,” J. Lightwave Technol. 15(1), 125–134 (1997).
    [Crossref]
  13. D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis (John Wiley & Sons, 2012), Chap. 5.
  14. T. Grósz, A. P. Kovács, M. Kiss, and R. Szipőcs, “Measurement of higher order chromatic dispersion in a photonic bandgap fiber: comparative study of spectral interferometric methods,” Appl. Opt. 53(9), 1929–1937 (2014).
    [Crossref] [PubMed]
  15. A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. Am. B 22(9), 1868–1874 (2005).
    [Crossref]
  16. S. Puntanen, G. P. Styan, and J. Isotalo, Matrix tricks for linear statistical models: our personal top twenty (Springer Science & Business Media, 2011), Chap. 15.
  17. J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
    [Crossref]

2014 (3)

2013 (1)

W. Muguang and Y. Jianping, “Multitap microwave photonic filter with negative coefficients based on the inherent birefringence in a LiNbO3 phase modulator,” IEEE Photonics J. 5, 5500709 (2013).
[Crossref]

2009 (1)

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2003 (1)

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

2002 (1)

1997 (1)

Z. Wenzin, “Automated fusion-splicing of polarization maintaining fibers,” J. Lightwave Technol. 15(1), 125–134 (1997).
[Crossref]

1995 (1)

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

1994 (1)

1987 (1)

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Ai, Z.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Bing, W.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Bock, W. J.

Braun, D. M.

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

Chao, L.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Cheng, T.

Chuang, L.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Dekai, Y.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Deng, D.

Fang, W.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Feng, P.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Flavin, D. A.

Fouquet, J. E.

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

Gao, W.

Gosteva, A.

Grósz, T.

Haiml, M.

Hosaka, T.

Jia, D.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Jianping, Y.

W. Muguang and Y. Jianping, “Multitap microwave photonic filter with negative coefficients based on the inherent birefringence in a LiNbO3 phase modulator,” IEEE Photonics J. 5, 5500709 (2013).
[Crossref]

Jing, W.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

F. Tang, X. Z. Wang, Y. Zhang, and W. Jing, “Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry,” Appl. Opt. 46(19), 4073–4080 (2007).
[Crossref] [PubMed]

Jones, J. D. C.

Jun, C.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Jun, Y.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Keller, U.

Kim, D. Y.

Kiss, M.

Kovács, A. P.

Lee, J. Y.

Lei, D.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Libo, Y.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Liu, K.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Ludowise, M. J.

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

McBride, R.

Muguang, W.

W. Muguang and Y. Jianping, “Multitap microwave photonic filter with negative coefficients based on the inherent birefringence in a LiNbO3 phase modulator,” IEEE Photonics J. 5, 5500709 (2013).
[Crossref]

Noda, J.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Ohishi, Y.

Okamoto, K.

K. Okamoto and T. Hosaka, “Polarization-dependent chromatic dispersion in birefringent optical fibers,” Opt. Lett. 12(4), 290–292 (1987).
[Crossref] [PubMed]

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Paschotta, R.

Sasaki, Y.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Sega, D.

Sheng, H.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Sorin, W. V.

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

Suzuki, T.

Szipocs, R.

Tang, F.

Trott, G. R.

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

Urbanczyk, W.

Wang, X. Z.

Wen-De, Z.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Wenzin, Z.

Z. Wenzin, “Automated fusion-splicing of polarization maintaining fibers,” J. Lightwave Technol. 15(1), 125–134 (1997).
[Crossref]

Xiaoke, Y.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Xiufeng, Y.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Xu, T.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Xue, X.

Yixin, W.

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

Yonggui, Y.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Yu, Z.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Zhang, H.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Zhang, Y.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

F. Tang, X. Z. Wang, Y. Zhang, and W. Jing, “Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry,” Appl. Opt. 46(19), 4073–4080 (2007).
[Crossref] [PubMed]

Zhihai, L.

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

J. E. Fouquet, G. R. Trott, W. V. Sorin, M. J. Ludowise, and D. M. Braun, “High-power semiconductor edge-emitting light-emitting diodes for optical low coherence reflectometry,” IEEE J. Quantum Electron. 31(8), 1494–1503 (1995).
[Crossref]

IEEE Photonics J. (1)

W. Muguang and Y. Jianping, “Multitap microwave photonic filter with negative coefficients based on the inherent birefringence in a LiNbO3 phase modulator,” IEEE Photonics J. 5, 5500709 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. Xiaoke, L. Chao, Y. Xiufeng, Z. Wen-De, W. Fang, D. Lei, and W. Yixin, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15(5), 754–756 (2003).
[Crossref]

J. Lightwave Technol. (3)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full Evaluation of Polarization Characteristics of Multifunctional Integrated Optic Chip With High Accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Z. Wenzin, “Automated fusion-splicing of polarization maintaining fibers,” J. Lightwave Technol. 15(1), 125–134 (1997).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Fiber Technol. (1)

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Opt. Lett. (2)

Other (2)

D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis (John Wiley & Sons, 2012), Chap. 5.

S. Puntanen, G. P. Styan, and J. Isotalo, Matrix tricks for linear statistical models: our personal top twenty (Springer Science & Business Media, 2011), Chap. 15.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Experiment setup of the measurement system.
Fig. 2
Fig. 2 The output signal of the measurement system. The four pairs of interferograms A, A’, B, B’, C, C’, D, and D’ are first order coupling crosstalk induced by the four splice points A, B, C, and D in Fig. 1, respectively. Polarization extinction capability of the Y-waveguide chip leads to the interferograms Y and Y’. The interferogram M is primarily resulted by the interference of excited mode in the probe arm and in the reference arm. The interferograms between B and Y, as well as interferograms between B’ and Y’, are second order coupling crosstalk which are beyond this paper.
Fig. 3
Fig. 3 Relationship between noise power and the measurement error of TBD (black) and SBD (blue) with OLS method (dash line) and WLS method (solid line) for 1000 sets simulation data, respectively. Inset: zoom out to show the results of OLS method at high noise power from −45 dB to −30 dB.
Fig. 4
Fig. 4 Comparison of measurement error variance between theory and 100 sets experimental data. (a) Measurement error of interferogram M with OLS method (red solid line) and corresponding theoretical error curve with spectral SNR of 60 dB (blue dash line), (b) error of M with WLS method and corresponding 60 dB theoretical error, (c) error of Y’ with OLS method and corresponding 30 dB theoretical error, (d) error of Y’ with WLS method and corresponding 30 dB theoretical error.
Fig. 5
Fig. 5 Comparison of the measurement results of BD for the interferometer. (a) Results of BD for the interferometer measured with two temporal methods and a spectral domain method. (b) The measurement error of these three methods calculated with 100 sets data. The error curves of OLS method and WLS method are actually the same as the experimental error curves in Fig. 4(a) and (b), respectively.
Fig. 6
Fig. 6 Measurement results for quasi-distributed BD of the four PM fibers. (a) PMF1, PMF3, and PMF4; (b) PMF2. Where, left means the curve is calculated by the data of interferograms on the left hand of interferogram M as shown in Fig. 2, and right means the right hand of M.
Fig. 7
Fig. 7 Measurement results for quasi-distributed BD of Y-waveguide chip with and without two pigtails of it.

Equations (11)

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

φ ( ω ) = φ ( ω 0 ) + L [ LB ( ω ω 0 ) + 1 2 SBD ( ω ω 0 ) 2 + 1 6 TBD ( ω ω 0 ) 3 ]
D ( λ ) = [ SBD + TBD ( 2 π c λ 2 π c λ 0 ) ] 2 π c λ 2
{ Δ D l 1 = ( D M D A ) / l 1 = ( D A ' D M ) / l 1 , Δ D l 2 = ( D A D B ) / l 2 = ( D B ' D A ' ) / l 2 , Δ D l 3 = ( D D D C ) / l 3 = ( D C ' D D ' ) / l 3 , Δ D l 4 = ( D M D D ) / l 4 = ( D D ' D M ) / l 4 , Δ D Y = ( D B D M D Y + D C ) / l Y = ( D Y ' D B ' D C ' + D M ) / l Y
φ = [ φ ( ω 1 ) φ ( ω 2 ) ... φ ( ω k ) ] T
φ = W ω B + ε
ω = [ 1 ω 1 ω 1 2 ω 1 3 1 ω 2 ω 2 2 ω 2 3 1 ω k ω k 2 ω k 3 ] , W = [ w 1 0 w 2 0 w k ] , B = [ B 0 B 1 B 2 B 3 ] T , ε = [ ε 1 ε 2 ε k ] T
σ ε 2 ( ω ) = 1 S [ a ( ω ) ] 2
B ^ wls = ( ω T W ω ) 1 ω T W φ
V = 1 S ( ω T W ω ) 1
V ols = 1 S ( ω T ω ) 1 ω T W 1 ω ( ω T ω ) 1
σ D 2 ( λ ) = ( 2 π c λ 2 ) 2 [ 4 V 3,3 + 36 ( 2 π c λ 2 π c λ 0 ) V 4 , 4 ] ,

Metrics