Abstract

A non-intrusive OSNR measurement technique relying on the detailed spectral comparison of an optical signal with its “noise-free” spectrum is described, including mathematical basis, validity conditions and algorithmic steps. The technique’s performance is experimentally demonstrated with 100G PM-QPSK and 200G PM-16QAM signals subject to fiber non-linearity induced by 100G PM-QPSK and 10G NRZ-OOK neighbors. The OSNR measurement performance is also demonstrated when root-raised cosine spectral shaping is applied to the signals, with channel spacings of 50GHz and 37.5GHz. Experimental results for OSNR levels up to 30dB and launch powers up to 3dB above the optimum BER launch conditions are shown for different system and signal configurations.

© 2016 Optical Society of America

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References

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  1. Optical monitoring for dense wavelength division multiplexing systems: ITU-T Recommendation G.697 (02/12).
  2. Optical signal-to-noise ratio measurement for dense wavelength-division multiplexed systems: IEC 61280–2-9 (Edition 2.0 2009–02).
  3. M. Rasztovist-Wiech, M. Danner, and W. R. Leeb, “Optical signal-to-noise ratio measurement in WDM networks using polarization extinction,”in ECOC 1998 (1998), pp. 549–550.
  4. J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37(15), 792–793 (2001).
    [Crossref]
  5. D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.
  6. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express 20(2), 1022–1032 (2012).
    [Crossref] [PubMed]
  7. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the Impact of Nonlinear Propagation Effects in Uncompensated Optical Coherent Transmission Links,” J. Lightwave Technol. 30(10), 1524–1539 (2012).
    [Crossref]
  8. Z. Dong, F. N. Khan, Q. Sui, K. Zhong, C. Lu, and A. P. T. Lau, “Optical performance monitoring: A review of current and future technologies,” J. Lightwave Technol. 34(2), 525–543 (2016).
    [Crossref]
  9. M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.
  10. Y. C. Chung, S. K. Shin, and K. J. Park, “A novel optical signal-to-noise ratio monitoring technique for WDM networks,” in OFC (2000), paper WK6.
  11. T. Saida, I. Ogawa, T. Mizuno, K. Sano, H. Fukuyama, Y. Muramoto, Y. Hashizume, H. Nosaka, S. Yamamoto, and K. Murata, “In-band OSNR monitor with high-speed integrated Stokes polarimeter for polarization division multiplexed signal,” Opt. Express 20(26), B165–B170 (2012).
    [Crossref] [PubMed]
  12. L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
    [Crossref]
  13. H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
    [Crossref]
  14. D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
    [Crossref]
  15. D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
    [Crossref]
  16. D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

2016 (1)

2012 (3)

2011 (1)

D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
[Crossref]

2001 (1)

J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37(15), 792–793 (2001).
[Crossref]

Antona, J.-C.

Aoki, Y.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Bigo, S.

Bononi, A.

Bosco, G.

Breton, Y.

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

Carena, A.

Chang, J. H.

H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
[Crossref]

Chang, Y. C.

H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
[Crossref]

Chitgarha, M. R.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Choi, H. G.

H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
[Crossref]

Chung, Y. C.

J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37(15), 792–793 (2001).
[Crossref]

Y. C. Chung, S. K. Shin, and K. J. Park, “A novel optical signal-to-noise ratio monitoring technique for WDM networks,” in OFC (2000), paper WK6.

Curri, V.

Daab, W.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Danner, M.

M. Rasztovist-Wiech, M. Danner, and W. R. Leeb, “Optical signal-to-noise ratio measurement in WDM networks using polarization extinction,”in ECOC 1998 (1998), pp. 549–550.

Dery, B.

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

Dong, Z.

Dou, L.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Forghieri, F.

Fukuyama, H.

Gariépy, D.

D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
[Crossref]

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
[Crossref]

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

Grellier, E.

Hashizume, Y.

He, G.

D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
[Crossref]

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
[Crossref]

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

Hoshida, T.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Khaleghi, S.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Khan, F. N.

Kim, H.

H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
[Crossref]

Lau, A. P. T.

Lee, J. H.

J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37(15), 792–793 (2001).
[Crossref]

Leeb, W. R.

M. Rasztovist-Wiech, M. Danner, and W. R. Leeb, “Optical signal-to-noise ratio measurement in WDM networks using polarization extinction,”in ECOC 1998 (1998), pp. 549–550.

Lorcy, L.

Lu, C.

Mizuno, T.

Mohajerin-Ariaei, A.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Muramoto, Y.

Murata, K.

Nosaka, H.

Oda, S.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Ogawa, I.

Park, K. J.

Y. C. Chung, S. K. Shin, and K. J. Park, “A novel optical signal-to-noise ratio monitoring technique for WDM networks,” in OFC (2000), paper WK6.

Poggiolini, P.

Rasmussen, J. C.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Rasztovist-Wiech, M.

M. Rasztovist-Wiech, M. Danner, and W. R. Leeb, “Optical signal-to-noise ratio measurement in WDM networks using polarization extinction,”in ECOC 1998 (1998), pp. 549–550.

Rival, O.

Rogawski, D.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Saida, T.

Sano, K.

Schinn, G. W.

D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
[Crossref]

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

Searcy, S.

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
[Crossref]

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

Shin, S. K.

Y. C. Chung, S. K. Shin, and K. J. Park, “A novel optical signal-to-noise ratio monitoring technique for WDM networks,” in OFC (2000), paper WK6.

Simonneau, C.

Sui, Q.

Tao, Z.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Tibuleac, S.

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
[Crossref]

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

Touch, J. D.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Tur, M.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Vacondio, F.

Vusirikala, V.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Willner, A. E.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Yamamoto, S.

Zhao, W.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Zhao, Y.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

Zhong, K.

Ziyadi, M.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Electron. Lett. (1)

J. H. Lee and Y. C. Chung, “Improved OSNR monitoring technique based on polarization-nulling method,” Electron. Lett. 37(15), 792–793 (2001).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (2)

Opt. Fiber Technol. (1)

D. Gariépy, G. He, and G. W. Schinn, “Non-intrusive measurement of In-band OSNR of high bitrate polarization-multiplexed signals,” Opt. Fiber Technol. 17(5), 518–522 (2011).
[Crossref]

Other (10)

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Non-intrusive In-band OSNR Measurement of Polarization Multiplexed Signals Operating in the Non-Linear Regime,” in Proc. OFC (2015), paper W4D.6.
[Crossref]

D. Gariépy, S. Searcy, G. He, and S. Tibuleac, “Demonstration of non-intrusive in-band OSNR measurement technique for PM-16QAM signals with spectral shaping and subject to fiber nonlinearity,” in OFC (2016), paper Tu3G.5.

M. R. Chitgarha, S. Khaleghi, W. Daab, M. Ziyadi, A. Mohajerin-Ariaei, D. Rogawski, M. Tur, J. D. Touch, V. Vusirikala, W. Zhao, and A. E. Willner, “ Demonstration of WDM OSNR Performance Monitoring and Operating Guidelines for Pol-Muxed 200-Gbit/s 16-QAM and 100-Gbit/s QPSK Data Channels,” in OFC/NFOEC (2013), paper OTh3B.6.

Y. C. Chung, S. K. Shin, and K. J. Park, “A novel optical signal-to-noise ratio monitoring technique for WDM networks,” in OFC (2000), paper WK6.

D. Gariépy, G. He, Y. Breton, B. Dery, and G. W. Schinn, “Novel OSA-based method for in-band OSNR measurement,” in OFC (2010), paper JThA15.

L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Proc. OFC (2015), paper W4D.3.
[Crossref]

H. G. Choi, J. H. Chang, H. Kim, and Y. C. Chang, “Nonlinearity-tolerant OSNR estimation technique for coherent optical systems,” in Proc. OFC (2015), paper W4D.2.
[Crossref]

Optical monitoring for dense wavelength division multiplexing systems: ITU-T Recommendation G.697 (02/12).

Optical signal-to-noise ratio measurement for dense wavelength-division multiplexed systems: IEC 61280–2-9 (Edition 2.0 2009–02).

M. Rasztovist-Wiech, M. Danner, and W. R. Leeb, “Optical signal-to-noise ratio measurement in WDM networks using polarization extinction,”in ECOC 1998 (1998), pp. 549–550.

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Figures (6)

Fig. 1
Fig. 1 Simplified flowchart of algorithm.
Fig. 2
Fig. 2 Schematic of experimental fiber transmission link.
Fig. 3
Fig. 3 a) Back-to-back OSNRNI results for 10 unshaped QPSK channels for 0.1nm OSNR levels of 10 to 30dB. b) Same channels after transmission while varying launch power and thus non-linear conditions.
Fig. 4
Fig. 4 OSNRNI deviation results for 3 channels for different system configurations with and without CDC. The test channels are indicated by matching color arrows in the inset spectra.
Fig. 5
Fig. 5 a) Back-to back OSNRNI results for 5 shaping conditions of two tests channels for 0.1nm OSNR levels ranging from 10 to 30dB. b) Same channels after 8 spans of SSMF for varied launch power.
Fig. 6
Fig. 6 a) Back-to back OSNRNI results 100G PM-QPSK RRC shaped 37.5GHz spaced channel for 0.1nm OSNR levels from 13 to 30dB. b) Same channel after transmission while varying launch power and after adding ASE.

Tables (1)

Tables Icon

Table 1 Summary of Various Experimental Test Conditions for OSNR Measurement

Equations (9)

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

κ(λ)= κ L (λ)× κ NL (λ) = κ 0 ×[1+Δ κ L (λ)]×[1+Δ κ NL (λ)]
OSD( λ )= P Meas ( λ ) κ 0 P ref ( λ ) κ 0 × P Ref ( λ p )  =OS D S ( λ )+OS D ASE ( λ )
OS D S ( λ )= P Sig ( λ ) P Sig ( λ p ) P Ref ( λ ) P Ref ( λ p ) =Δκ× P Ref ( λ ) P Ref ( λ p )
OS D ASE ( λ )= N ASE ( λ ) P Sig ( λ p ) = 1 OSN R ASE (λ)
OSN R ASE (λ)= 1 OS D ASE ( λ ) = 1 OSD( λ )OS D S ( λ )
κ 0Est = P Meas ( λ 1 ) P Meas ( λ 2 ) P Ref ( λ 1 ) P Ref ( λ 2 ) = κ 0
OSN R Est (λ)= 1 OSD(λ) = κ 0Est × P Ref ( λ p ) P Meas (λ) κ 0Est × P Ref (λ) =OSN R ASE (λ)
1 OSN R Est (λ)  = 1 OSN R ASE (λ)  + 1 ΔOSNR(λ)             
Rdev(λ) = d P Meas (λ) d P Ref (λ) =κ(λ)+ P Ref (λ)× dκ(λ) d P Ref (λ) + d N ASE (λ) d P Ref (λ) κ(λ)+ P Ref (λ)× dκ(λ) d P Ref (λ)

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