Abstract

Fiber optic interferometry is a common architecture in many optical sensing strategies and typically requires a demodulation scheme for phase (signal) extraction. For sensing applications, signal-to-noise and other statistical metrics are of great importance in characterizing system performance. In the context of a specific demodulation algorithm employing three-channel inputs, we analytically compute a probability density function of the demodulator output noise, given an arbitrary distribution of input intensity noise and arbitrary noise correlation among the three channels. We compare the analytical formulations with previously validated simulation data from a fiber Bragg grating sensor system, and we find excellent agreement within the specific example of Gaussian input noise.

© 2011 IEEE

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  1. Fiber Optic Smart Structures (Wiley Interscience, 1995).
  2. A. Othonos, K. Kalli, Fiber Bragg Gratings—Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999).
  3. Optical Fiber Sensor Technology-Volume 3: Applications and Systems (Kluwer Academic, 1999).
  4. Fiber Optic Sensors (Marcel Dekker, 2002).
  5. Handbook of Optical Fiber Sensing Technology (Wiley, 2002).
  6. A. Dandridge, A. B. Tveten, T. G. Giallorenzi, "Homodyne demodulation scheme using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).
  7. J. H. Cole, B. A. Danver, J. A. Bucaro, "Synthetic heterodyne interferometric demodulation," IEEE J. Quantum Electron. QE-18, 694-697 (1982).
  8. J. Proakis, M. Salehi, Communication Systems Engineering (Prentice-Hall, 1994).
  9. C. E. M. Strauss, "Synthetic-array heterodyne detection: A single-element detector acts as an array," Opt. Lett. 19, 1609-1611 (1994).
  10. B. Sklar, Digital Communications: Fundamentals and Applications (Prentice-Hall, 2001).
  11. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. Rashleigh, R. G. Priest, "Optical fiber sensor technology," IEEE J. Quantum Electron. QE-18, 626-666 (1982).
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  13. A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, "Quantum-noise-limited interferometer phase measurement," Appl. Opt. 32, 3481-3493 (1993).
  14. A. Arie, M. Tur, E. Goldstein, "Probability-density function of noise at the output of a two-beam interferometer," J. Opt. Soc. Am. A 8, 1936-1942 (1991).
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  16. G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984).
  17. K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).
  18. X. Zhang, Z. Qu, G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 28, 177-183 (2006).
  19. J. Minkoff, Signal Processing Fundamentals and Applications for Communications and Sensing Systems (Artech House, 2002).
  20. M. D. Todd, "Output noise statistical profile for digital phase demodulation systems with intensity-induced input noise," J. Lightw. Technol. 25, 747-756 (2007).
  21. M. D. Todd, "On the probability structure of output noise from a digital phase demodulation system subject to biased intensity-based input noise," J. Lightw. Technol. 26, 2291-2300 (2008).
  22. G. A. Johnson, M. D. Todd, B. L. Althouse, C. C. Chang, "Fiber Bragg grating interrogation and multiplexing with a 3x3 coupler and a scanning filter," J. Lightw. Technol. 18, 1105-1105 (2000).
  23. M. D. Todd, G. A. Johnson, B. L. Althouse, "A novel Bragg grating sensor interrogation system utilizing a scanning filter, a Mach-Zehnder interferometer, and a 3x3 coupler," Measure. Sci. Technol. 12, 771-777 (2001).
  24. M. D. Todd, M. Seaver, F. Bucholtz, "Improved, operationally-passive interferometric demodulation method using a 3x3 coupler," Electron. Lett. 38, 784-786 (2002).
  25. F. Schleip, R. Hereth, G. Schiffner, "Phase sensitive investigations of 3x3 single mode fibre directional couplers," Electron. Lett. 29, 68-70 (1993).
  26. M. D. Todd, J. M. Nichols, S. T. Trickey, M. Seaver, "Analysis of accuracy error and distortion in an operationally-passive interferometric demodulation technique," Proc. SPIE Smart Structures/NDE 6167 (2006).
  27. J. Bendat, A. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, 2000).

2008 (1)

M. D. Todd, "On the probability structure of output noise from a digital phase demodulation system subject to biased intensity-based input noise," J. Lightw. Technol. 26, 2291-2300 (2008).

2007 (1)

M. D. Todd, "Output noise statistical profile for digital phase demodulation systems with intensity-induced input noise," J. Lightw. Technol. 25, 747-756 (2007).

2006 (1)

X. Zhang, Z. Qu, G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 28, 177-183 (2006).

2004 (1)

K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).

2002 (1)

M. D. Todd, M. Seaver, F. Bucholtz, "Improved, operationally-passive interferometric demodulation method using a 3x3 coupler," Electron. Lett. 38, 784-786 (2002).

2001 (1)

M. D. Todd, G. A. Johnson, B. L. Althouse, "A novel Bragg grating sensor interrogation system utilizing a scanning filter, a Mach-Zehnder interferometer, and a 3x3 coupler," Measure. Sci. Technol. 12, 771-777 (2001).

2000 (1)

G. A. Johnson, M. D. Todd, B. L. Althouse, C. C. Chang, "Fiber Bragg grating interrogation and multiplexing with a 3x3 coupler and a scanning filter," J. Lightw. Technol. 18, 1105-1105 (2000).

1995 (1)

K.-P. Ho, J. M. Kahn, "Exact probability-density function for phase-measurement interferometry," J. Opt. Soc. Am. A 12, 1984-1989 (1995).

1994 (1)

C. E. M. Strauss, "Synthetic-array heterodyne detection: A single-element detector acts as an array," Opt. Lett. 19, 1609-1611 (1994).

1993 (2)

F. Schleip, R. Hereth, G. Schiffner, "Phase sensitive investigations of 3x3 single mode fibre directional couplers," Electron. Lett. 29, 68-70 (1993).

A. J. Stevenson, M. B. Gray, H.-A. Bachor, D. E. McClelland, "Quantum-noise-limited interferometer phase measurement," Appl. Opt. 32, 3481-3493 (1993).

1991 (1)

A. Arie, M. Tur, E. Goldstein, "Probability-density function of noise at the output of a two-beam interferometer," J. Opt. Soc. Am. A 8, 1936-1942 (1991).

1986 (1)

O. Sasaki, H. Okazaki, "Analysis of measurement accuracy in sinusoidal phase modulating interferometry," Appl. Opt. 25, 3152-3158 (1986).

1984 (1)

G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984).

1982 (3)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. Rashleigh, R. G. Priest, "Optical fiber sensor technology," IEEE J. Quantum Electron. QE-18, 626-666 (1982).

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, "Homodyne demodulation scheme using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).

J. H. Cole, B. A. Danver, J. A. Bucaro, "Synthetic heterodyne interferometric demodulation," IEEE J. Quantum Electron. QE-18, 694-697 (1982).

Appl. Opt. (1)

O. Sasaki, H. Okazaki, "Analysis of measurement accuracy in sinusoidal phase modulating interferometry," Appl. Opt. 25, 3152-3158 (1986).

Appl. Opt. (1)

Electron. Lett. (2)

F. Schleip, R. Hereth, G. Schiffner, "Phase sensitive investigations of 3x3 single mode fibre directional couplers," Electron. Lett. 29, 68-70 (1993).

G. Nicholson, "Probability of error for optical heterodyne DPSK system with quantum phase noise," Electron. Lett. 20, 1005-1007 (1984).

Electron. Lett. (1)

M. D. Todd, M. Seaver, F. Bucholtz, "Improved, operationally-passive interferometric demodulation method using a 3x3 coupler," Electron. Lett. 38, 784-786 (2002).

IEEE J. Quantum Electron. (1)

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, "Homodyne demodulation scheme using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).

IEEE J. Quantum Electron. (2)

J. H. Cole, B. A. Danver, J. A. Bucaro, "Synthetic heterodyne interferometric demodulation," IEEE J. Quantum Electron. QE-18, 694-697 (1982).

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. Rashleigh, R. G. Priest, "Optical fiber sensor technology," IEEE J. Quantum Electron. QE-18, 626-666 (1982).

IEEE J. Sel. Topics Quantum Electron. (1)

K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).

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

A. Arie, M. Tur, E. Goldstein, "Probability-density function of noise at the output of a two-beam interferometer," J. Opt. Soc. Am. A 8, 1936-1942 (1991).

J. Lightw. Technol. (3)

M. D. Todd, "Output noise statistical profile for digital phase demodulation systems with intensity-induced input noise," J. Lightw. Technol. 25, 747-756 (2007).

M. D. Todd, "On the probability structure of output noise from a digital phase demodulation system subject to biased intensity-based input noise," J. Lightw. Technol. 26, 2291-2300 (2008).

G. A. Johnson, M. D. Todd, B. L. Althouse, C. C. Chang, "Fiber Bragg grating interrogation and multiplexing with a 3x3 coupler and a scanning filter," J. Lightw. Technol. 18, 1105-1105 (2000).

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

K.-P. Ho, J. M. Kahn, "Exact probability-density function for phase-measurement interferometry," J. Opt. Soc. Am. A 12, 1984-1989 (1995).

Measure. Sci. Technol. (1)

M. D. Todd, G. A. Johnson, B. L. Althouse, "A novel Bragg grating sensor interrogation system utilizing a scanning filter, a Mach-Zehnder interferometer, and a 3x3 coupler," Measure. Sci. Technol. 12, 771-777 (2001).

Opt. Lett. (1)

C. E. M. Strauss, "Synthetic-array heterodyne detection: A single-element detector acts as an array," Opt. Lett. 19, 1609-1611 (1994).

Opt. Commun. (1)

X. Zhang, Z. Qu, G. Yang, "Probability density function of noise statistics for optically pre-amplified DPSK receivers with optical Mach-Zehnder interferometer demodulation," Opt. Commun. 28, 177-183 (2006).

Other (10)

J. Minkoff, Signal Processing Fundamentals and Applications for Communications and Sensing Systems (Artech House, 2002).

B. Sklar, Digital Communications: Fundamentals and Applications (Prentice-Hall, 2001).

J. Proakis, M. Salehi, Communication Systems Engineering (Prentice-Hall, 1994).

Fiber Optic Smart Structures (Wiley Interscience, 1995).

A. Othonos, K. Kalli, Fiber Bragg Gratings—Fundamentals and Applications in Telecommunications and Sensing (Artech House, 1999).

Optical Fiber Sensor Technology-Volume 3: Applications and Systems (Kluwer Academic, 1999).

Fiber Optic Sensors (Marcel Dekker, 2002).

Handbook of Optical Fiber Sensing Technology (Wiley, 2002).

M. D. Todd, J. M. Nichols, S. T. Trickey, M. Seaver, "Analysis of accuracy error and distortion in an operationally-passive interferometric demodulation technique," Proc. SPIE Smart Structures/NDE 6167 (2006).

J. Bendat, A. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, 2000).

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