Abstract

A time division multiplexing of polarization-insensitive fiber-optic Michelson interferometric sensors (TDM–PIMI’s) with a 3 × 3 directional coupler is presented. The elimination of polarization-induced fading and the output intensities of the TDM–PIMI system are described and demonstrated. The output intensity of each sensor of the system can be demodulated by a passive homodyne method to increase the sensor bandwidth significantly. The sensor cross talk of the system having an optical gate with a finite extinction ratio is analyzed. The use of a laser source with an adequate coherence length to reduce the sensor cross talk is suggested. The delay-fiber cross talk of the system by Rayleigh backscattering is analyzed and demonstrated. We further suggest some methods that could possibly reduce the effect of the Rayleigh backscattered light. Finally a sophisticated design of a TDM–PIMI system with a 3 × 3 directional coupler is described.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. D. Kersey, “Recent progress in interferometric fiber sensor technology,” in Fiber Optic and Laser Sensors VIII, R. P. Depaula, E. Udd, eds., Proc. SPIE1367, 2–12 (1990).
    [CrossRef]
  2. J. P. Dakin, “Multiplexed and distributed optical fibre sensors,” in The Distributed Fibre Optic Sensing Handbook, J. P. Dakin, ed. (IFS Publications, Bedford, UK, 1990), pp. 3–20.
  3. A. D. Kersey, “Multiplexed fiber optic sensors,” in Distributed and Multiplexed Fiber Optic sensors II, J. P. Dakin, A. D. Kersey, eds., Proc. SPIE1797, 161–185 (1993).
    [CrossRef]
  4. J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
    [CrossRef]
  5. A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
    [CrossRef]
  6. M. Martinelli, “A universal compensator for polarisation change induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
    [CrossRef]
  7. M. J. Marrone, A. D. Kersey, A. Dandridge, “Fiber optic Michelson array with passive elimination of polarization fading and source feedback isolation,” in Proceedings of the Eighth Optic Fiber Sensors Conference (1992), pp. 69–72.
  8. S. C. Huang, W. W. Lin, M. H. Chen, “Time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” Opt. Lett. 20, 1244–1246 (1995).
    [CrossRef] [PubMed]
  9. A. Dandridge, A. B. Tveten, “Phase noise of single mode diode laser in interferometer system,” Appl. Phys. Lett. 39, 530–532 (1981).
    [CrossRef]
  10. K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
    [CrossRef]
  11. C. B. Cameron, R. M. Keolian, S. L. Garrett, “A symmetric analogue demodulator for optical fiber interferometric sensor,” presented at the 34th Midwest Symposium on Circuits and Systems, Monterey, Calif., May 1991.
  12. S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
    [CrossRef]
  13. A. M. Yurek, A. Dandridge, A. D. Kersey, “Coherent backscatter induced excess noise in reflective interferometric fiber sensors,” in Optical Fiber Sensors, Vol. 2 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 72–75.
  14. C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
    [CrossRef]
  15. R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
    [CrossRef]
  16. L. Sun, P. Ye, “General analysis of [3 × 3] optical-fiber directional couplers,” Microwave Opt. Technol. Lett. 2, 52–54 (1989).
    [CrossRef]
  17. P. Gysel, R. K. Staubli, “Statistical properties of Rayleigh backscattering in single mode fibers,” J. Lightwave Technol. 8, 561–567 (1990).
    [CrossRef]
  18. A. Dandridge, “Fiber optic sensors based on the Mach–Zehnder and Michelson interferometers,” in Fiber Optic Sensors, E. Udd, ed. (Wiley, New York, 1991), pp. 271–323.
  19. E. Brinkmeyer, “Backscattering in single-mode fibers,” Electron. Lett. 16, 329–330 (1980).
    [CrossRef]
  20. M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
    [CrossRef]

1996 (1)

S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
[CrossRef]

1995 (1)

1994 (1)

C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
[CrossRef]

1992 (1)

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

1991 (1)

A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
[CrossRef]

1990 (1)

P. Gysel, R. K. Staubli, “Statistical properties of Rayleigh backscattering in single mode fibers,” J. Lightwave Technol. 8, 561–567 (1990).
[CrossRef]

1989 (2)

L. Sun, P. Ye, “General analysis of [3 × 3] optical-fiber directional couplers,” Microwave Opt. Technol. Lett. 2, 52–54 (1989).
[CrossRef]

M. Martinelli, “A universal compensator for polarisation change induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

1987 (1)

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

1983 (1)

R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

1982 (1)

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

1981 (1)

A. Dandridge, A. B. Tveten, “Phase noise of single mode diode laser in interferometer system,” Appl. Phys. Lett. 39, 530–532 (1981).
[CrossRef]

1980 (1)

E. Brinkmeyer, “Backscattering in single-mode fibers,” Electron. Lett. 16, 329–330 (1980).
[CrossRef]

Boslehi, B.

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

Brinkmeyer, E.

E. Brinkmeyer, “Backscattering in single-mode fibers,” Electron. Lett. 16, 329–330 (1980).
[CrossRef]

Brooks, J. L.

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

Cameron, C. B.

C. B. Cameron, R. M. Keolian, S. L. Garrett, “A symmetric analogue demodulator for optical fiber interferometric sensor,” presented at the 34th Midwest Symposium on Circuits and Systems, Monterey, Calif., May 1991.

Chen, M. H.

S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
[CrossRef]

S. C. Huang, W. W. Lin, M. H. Chen, “Time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” Opt. Lett. 20, 1244–1246 (1995).
[CrossRef] [PubMed]

Dakin, J. P.

J. P. Dakin, “Multiplexed and distributed optical fibre sensors,” in The Distributed Fibre Optic Sensing Handbook, J. P. Dakin, ed. (IFS Publications, Bedford, UK, 1990), pp. 3–20.

Dandridge, A.

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

A. Dandridge, A. B. Tveten, “Phase noise of single mode diode laser in interferometer system,” Appl. Phys. Lett. 39, 530–532 (1981).
[CrossRef]

A. M. Yurek, A. Dandridge, A. D. Kersey, “Coherent backscatter induced excess noise in reflective interferometric fiber sensors,” in Optical Fiber Sensors, Vol. 2 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 72–75.

A. Dandridge, “Fiber optic sensors based on the Mach–Zehnder and Michelson interferometers,” in Fiber Optic Sensors, E. Udd, ed. (Wiley, New York, 1991), pp. 271–323.

Davis, M. A.

A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
[CrossRef]

Garrett, S. L.

C. B. Cameron, R. M. Keolian, S. L. Garrett, “A symmetric analogue demodulator for optical fiber interferometric sensor,” presented at the 34th Midwest Symposium on Circuits and Systems, Monterey, Calif., May 1991.

Gysel, P.

P. Gysel, R. K. Staubli, “Statistical properties of Rayleigh backscattering in single mode fibers,” J. Lightwave Technol. 8, 561–567 (1990).
[CrossRef]

Huang, S. C.

S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
[CrossRef]

S. C. Huang, W. W. Lin, M. H. Chen, “Time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” Opt. Lett. 20, 1244–1246 (1995).
[CrossRef] [PubMed]

Jackson, D. A.

C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
[CrossRef]

Keolian, R. M.

C. B. Cameron, R. M. Keolian, S. L. Garrett, “A symmetric analogue demodulator for optical fiber interferometric sensor,” presented at the 34th Midwest Symposium on Circuits and Systems, Monterey, Calif., May 1991.

Kersey, A. D.

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
[CrossRef]

A. D. Kersey, “Multiplexed fiber optic sensors,” in Distributed and Multiplexed Fiber Optic sensors II, J. P. Dakin, A. D. Kersey, eds., Proc. SPIE1797, 161–185 (1993).
[CrossRef]

A. D. Kersey, “Recent progress in interferometric fiber sensor technology,” in Fiber Optic and Laser Sensors VIII, R. P. Depaula, E. Udd, eds., Proc. SPIE1367, 2–12 (1990).
[CrossRef]

A. M. Yurek, A. Dandridge, A. D. Kersey, “Coherent backscatter induced excess noise in reflective interferometric fiber sensors,” in Optical Fiber Sensors, Vol. 2 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 72–75.

Kim, B. Y.

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

Kirkendall, C. K.

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

Koo, K. P.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Lin, W. W.

S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
[CrossRef]

S. C. Huang, W. W. Lin, M. H. Chen, “Time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” Opt. Lett. 20, 1244–1246 (1995).
[CrossRef] [PubMed]

MaGarrity, C.

C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
[CrossRef]

Marrone, M. J.

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
[CrossRef]

Martinelli, M.

M. Martinelli, “A universal compensator for polarisation change induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Pechstedt, R. D.

C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
[CrossRef]

Shaw, H. J.

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

Staubli, R. K.

P. Gysel, R. K. Staubli, “Statistical properties of Rayleigh backscattering in single mode fibers,” J. Lightwave Technol. 8, 561–567 (1990).
[CrossRef]

Stokes, L. F.

R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

Sun, L.

L. Sun, P. Ye, “General analysis of [3 × 3] optical-fiber directional couplers,” Microwave Opt. Technol. Lett. 2, 52–54 (1989).
[CrossRef]

Tveten, A. B.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

A. Dandridge, A. B. Tveten, “Phase noise of single mode diode laser in interferometer system,” Appl. Phys. Lett. 39, 530–532 (1981).
[CrossRef]

Villarruel, C. A.

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

Ye, P.

L. Sun, P. Ye, “General analysis of [3 × 3] optical-fiber directional couplers,” Microwave Opt. Technol. Lett. 2, 52–54 (1989).
[CrossRef]

Youngquist, R. C.

R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

Yurek, A. M.

A. M. Yurek, A. Dandridge, A. D. Kersey, “Coherent backscatter induced excess noise in reflective interferometric fiber sensors,” in Optical Fiber Sensors, Vol. 2 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 72–75.

Appl. Phys. Lett. (2)

A. Dandridge, A. B. Tveten, “Phase noise of single mode diode laser in interferometer system,” Appl. Phys. Lett. 39, 530–532 (1981).
[CrossRef]

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometer using (3 × 3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Electron. Lett. (3)

A. D. Kersey, M. J. Marrone, M. A. Davis, “Polarisation-insensitive fiber optic Michelson interferometer,” Electron. Lett. 27, 518–520 (1991).
[CrossRef]

E. Brinkmeyer, “Backscattering in single-mode fibers,” Electron. Lett. 16, 329–330 (1980).
[CrossRef]

M. J. Marrone, A. D. Kersey, C. A. Villarruel, C. K. Kirkendall, A. Dandridge, “Elimination of coherent Rayleigh backscatter induced noise in fibre Michelson interferometers,” Electron. Lett. 28, 1803–1804 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. C. Youngquist, L. F. Stokes, H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

J. Lightwave Technol. (3)

J. L. Brooks, B. Boslehi, B. Y. Kim, H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Lightwave Technol. LT-5, 1014–1023 (1987).
[CrossRef]

P. Gysel, R. K. Staubli, “Statistical properties of Rayleigh backscattering in single mode fibers,” J. Lightwave Technol. 8, 561–567 (1990).
[CrossRef]

S. C. Huang, W. W. Lin, M. H. Chen, “Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors,” J. Lightwave Technol. 14, 1488–1500 (1996).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

L. Sun, P. Ye, “General analysis of [3 × 3] optical-fiber directional couplers,” Microwave Opt. Technol. Lett. 2, 52–54 (1989).
[CrossRef]

Opt. Commun. (2)

C. MaGarrity, R. D. Pechstedt, D. A. Jackson, “Studies of Rayleigh interference in fiber illuminated by a long coherence laser,” Opt. Commun. 104, 259–265 (1994).
[CrossRef]

M. Martinelli, “A universal compensator for polarisation change induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Opt. Lett. (1)

Other (7)

A. Dandridge, “Fiber optic sensors based on the Mach–Zehnder and Michelson interferometers,” in Fiber Optic Sensors, E. Udd, ed. (Wiley, New York, 1991), pp. 271–323.

M. J. Marrone, A. D. Kersey, A. Dandridge, “Fiber optic Michelson array with passive elimination of polarization fading and source feedback isolation,” in Proceedings of the Eighth Optic Fiber Sensors Conference (1992), pp. 69–72.

A. D. Kersey, “Recent progress in interferometric fiber sensor technology,” in Fiber Optic and Laser Sensors VIII, R. P. Depaula, E. Udd, eds., Proc. SPIE1367, 2–12 (1990).
[CrossRef]

J. P. Dakin, “Multiplexed and distributed optical fibre sensors,” in The Distributed Fibre Optic Sensing Handbook, J. P. Dakin, ed. (IFS Publications, Bedford, UK, 1990), pp. 3–20.

A. D. Kersey, “Multiplexed fiber optic sensors,” in Distributed and Multiplexed Fiber Optic sensors II, J. P. Dakin, A. D. Kersey, eds., Proc. SPIE1797, 161–185 (1993).
[CrossRef]

A. M. Yurek, A. Dandridge, A. D. Kersey, “Coherent backscatter induced excess noise in reflective interferometric fiber sensors,” in Optical Fiber Sensors, Vol. 2 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 72–75.

C. B. Cameron, R. M. Keolian, S. L. Garrett, “A symmetric analogue demodulator for optical fiber interferometric sensor,” presented at the 34th Midwest Symposium on Circuits and Systems, Monterey, Calif., May 1991.

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 (10)

Fig. 1
Fig. 1

Bisensor TDM–PIMI system with a 3 × 3 directional coupler.

Fig. 2
Fig. 2

Experimental arrangement of the polarization-fading measurement in a bisensor TDM–PIMI system with a 3 × 3 directional coupler.

Fig. 3
Fig. 3

Upper trace Ref1 (vertical scale, 500 mV/div) is a light pulse received at a pulse detector (Dp). Lower trace Ref2 (vertical scale, 100 mV/div) is a light pulse train received at the second output detector (D2) in which the second pulse was the interference signal of the first sensor (horizontal scale, 400 ns/div).

Fig. 4
Fig. 4

Signal amplitude of the first sensor without the Faraday rotator mirror. Upper trace Ref1 differs from the lower tracer Ref2 whether PC1 is kept still or adjusted continually (vertical scale, 1 V/div; horizontal scale, 5 s/div).

Fig. 5
Fig. 5

Signal amplitude of the first sensor with the Faraday rotator mirror. Upper trace Ref1 differs from the lower tracer Ref2 whether PC1 is kept still or adjusted continually (vertical scale, 1 V/div; horizontal scale, 5 s/div).

Fig. 6
Fig. 6

(a) Spectrum of an output signal at the first sensor (SI1). The light pulse is adjusted with an extinction ratio of 27 dB, in which the 0.5-rad, 1-kHz effective output phase signal of SI1 is generated by PZT1, whereas the 0.5-rad, 1.5-kHz effective phase signal of the second sensor (SI2) is generated by PZT2. (b) Relative frequency response curve of SI2 cross talk at SI1 output.

Fig. 7
Fig. 7

(a) Spectrum of the output signal at the first sensor (SI1). The light pulse is adjusted with an extinction ratio of 10 dB in which the 0.5-rad, 1-kHz effective output phase signal of SI1 is generated by PZT1, whereas the 0.5-rad, 1.5-kHz effective phase signal of the second sensor (SI2) is generated by PZT2. (b) The relative frequency response curve of SI2 cross talk at the SI1 output.

Fig. 8
Fig. 8

(a) Spectrum of the output phase signal of SI1 (light pulse width, 250 ns), in which the 0.5-rad, 1-kHz effective phase signal of SI1 is generated by PZT1, whereas the 2-rad, 1.5-kHz effective phase signal of DF is generated by PZTD. (b) Similar in measurement to (a) but with a 350-ns light pulse width instead. (c) The relative frequency response curve of DF cross talk at SI1 output (light pulse width, 250 ns).

Fig. 9
Fig. 9

Array configuration for the TDM–PIMI system with N sensors and a compensating interferometer with a 3 × 3 coupler.

Fig. 10
Fig. 10

Sophisticated design (with a 3POC) for the TDM–PIMI system with N sensors and a compensating interferometer with a 3 × 3 coupler.

Equations (59)

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

Eo,1Eo,2=1/2expiπ/2/2expiπ/2/21/2Ei,1Ei,2,
Eo,1Eo,2Eo,3=uvvvuvvvuEi,1Ei,2Ei,3,
J0=Ax expiδxAy expiδy.
R=α0-1-10,
E1=Ex1Ey1=α10-1-10J0 expiωt1=-α1Ay expiδyAx expiδxexpiωt1,
E1=Ex1Ey1=α10-1-10J0 expiωt1+2ϕ1+π=-α1Ay expiδyAx expiδxexpiωt1+2ϕ1+π,
R0=α0q0g0-h0*h0g0*,
Ei,1=R0E1,
Ei,1=R0E1.
Er,3=αc0-1-10vR0E1 expiωtc+2ϕc,
Er,2=αc0-1-10vR0E1 expiωtc,
Eo,1=v2αcα11/2 expiωt+2ϕc×0-1-10R00-1-10J0,
Eo,1=v2αcα11/2 expiωt+2ϕ1+π×0-1-10R00-1-10J0.
JT=0-1-10R00-1-10J0.
ET,1=Eo,1+Eo,1=v2α expiωt+2ϕc×JT+v2α expiωt+2ϕ1+πJT,
ET,2=Eo,2+Eo,2=v2α expiωt+2ϕc×JT+uvα expiωt+2ϕ1+πJT,
ET,3=Eo,3+Eo,3=uvα expiωt+2ϕc×JT+v2α expiωt+2ϕ1+πJT.
E=ExEy,
IT,1=ηET,1*·ET,1=ηα2A22v*v2+2v*v2 cos2ϕ1+π-2ϕc.
IT,1=2/9ηα2A21+cos2ϕ1+π-2ϕc,
IT,2=2/9ηα2A21+cos2ϕ1+π-2ϕc+2π/3,
IT,3=2/9ηα2A21+cos2ϕ1+π-2ϕc+4π/3.
EH1=1/4bEH expiπ,
EH1=1/4bEH expi2π+2ϕ1+ωΔtL=1/4bEH expi2ϕ1+ωΔtL,
EL2=1/4bEL,
EL2=1/4bEL expiπ+2ϕ2t,
EH1=1/4b2bpv2EH expiπ+2ϕc+ωΔtL,
EL2=1/4b2bpv2EL expi2ϕc+ωΔtL,
EL2=1/4b2bpv2EL expiπ+2ϕ2t+2ϕc+ωΔtL.
EH1=1/4b2bpv2EH expi2ϕ1+ωΔtL.
EL2=1/4b2bpv2ELexpiωΔtL+expi2ϕc+ωΔtL,
EL2=1/8b2bpv2EL expiπ+2ϕ2t+ΔtL+ωΔtL+1/8b2bpv2EL expiπ+2ϕc+2ϕ2t+ωΔtL.
ET,1=EH1+EH1+EL2+EL2.
IT,1=ηET,1*·ET,1=1/16ηb4bp2v*v2×2EH2+4EL2-2EH2 cos2ϕ1-2ϕc+2EL2 cos-2ϕc+2EL2 cos-2Δϕ2-2ϕc-2EL2 cos2ϕ2t+ΔtL-2EL2 cos2ϕ2t-2EL2 cos2ϕ2t+ΔtL-2ϕc-2EL2 cos-2ϕ2t-2ϕc-2EHEL cos-2ϕc+2EHEL cos2ϕ2t+ΔtL-2ϕc+2EHEL cos2ϕ1-2EHEL×cos2ϕ1-2ϕ2t+ΔtL-2EHEL+2EHEL cos2ϕ2t+2EHEL cos2ϕ1-2ϕc-2EHEL cos2ϕ1-2ϕ2t-2ϕc.
S1=1/36gηb4bp2EH2ϕ1-EL2Δϕ2+EL2ϕ2t+ΔtL+EL2-ϕ2t+EHELϕ2t+ΔtL+EHELϕ1+EHELϕ1-ϕ2t=1/36gηb4bp2EH2+2EHEL×ϕ1-2EL2+EHELΔϕ2,
Δϕ2=a2 cosω2t-a2 cosω2t+Δ tLa2ω2ΔtL sinω2t.
Asensor=20 log2EL2+EHELω2ΔtLEH2+2EHEL 20 logEHELω2ΔtLEH2 20 logEL/EH+20 logω2ΔtL=10 logpL/pH+20 logω2ΔtL.
Asensor=-ER+20 logω2ΔtL.
Ib1=1/4αsSIs exp-2αfL1-d×1-exp-αfLp/2αf,
Ir1=1/16b2Is exp-2αfL.
Ib1=1/8αsSIsLp,
Ir1=1/16b2Is.
Eb1=Ib/η1/2 expiϕd,i+ϕd,ot,
Eb1=Ib/η1/2 expiϕd,i+ϕd,ot+ΔtL+ωΔtL,
Er1=Ir/η1/2 expiπ,
Er1=Ir/η1/2 expi2π+2ϕ1+ωΔtL=Ir/η1/2 expi2ϕ1+ωΔtL.
Eb1=bbpv2Ib/η1/2 expiϕd,i+ϕd,ot+2ϕc+ωΔtL,
Eb1=bbpv2Ib/η1/2 expiϕd,i+ϕd,o×t+ΔtL+ωΔtL,
Er1=bbpv2Ir/η1/2 expiπ+2ϕc+ωΔtL,
Er1=bbpv2Ir/η1/2 expi2ϕ1+ωΔtL.
ETB,1=Eb1+Eb1+Er1+Er1.
ITB,1=ηETB,1*·ETB,1=b2bp2v*v2×2Ir+2Ib-2Ir cos2ϕ1-2ϕc+2Ibcosϕd,ot+ΔtL-ϕd,ot-2ϕc-2IbIr1/2 cosϕd,i+ϕd,ot+2IbIr1/2 cos2ϕ1-ϕd,i-ϕd,ot-2ϕc-2IbIr1/2 cosϕd,i+ϕd,ot+ΔtL-2ϕc+2IbIr1/2 cos2ϕ1-ϕd,i-ϕd,ot+ΔtL.
S1B=2/9gb2bp22Irϕ1+Ibϕd,ot+ΔtL-ϕd,ot+IbIr1/22ϕ1-ϕd,i-ϕd,ot+IbIr1/2×ϕd,i+ϕd,ot+ΔtL=2/9gb2bp22Ir+2IbIr1/2ϕ1-IbIr1/2+IbΔϕd.
ΔϕdadωdΔtL sinωdt.
ARB=20 logIbIr1/2+IbωdΔtL2Ir+2IbIr1/210 logIbIr+20 logωdΔtL-6=10 log2αsSLp/b2+20 logωdΔtL-6.
1XN-K+12=a2XN-K+1-1XN-K+121XN-K2.
Xm=1-am-1am-21-a+1am-2.
Asensor20 log1-10-x/20EHEL/EH2=20 log1-10-x/20-ER.
ARB20 log1-10-x/20IbIr1/2/Ir=20 log1-10-x/20+10 log2αsSLp/b2.

Metrics