Abstract

A concept of the Young interference experiment has been applied in the design of a fiber optic homodyne phase demodulator. The system is based on a bicell-photodetector in the Fourier plane. The above system has been designed, described, and verified together with an estimation of the minimization of phase measurement error in connection with the distance between photodetectors, wavelength, and focal length of the Fourier lens. The fundamental investigation concerning the choice of a distance between photodetectors and its influence on the demodulator’s linearity has been presented and discussed as well.

© 2013 Optical Society of America

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References

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  1. E. Udd and W. B. Spillman, Fiber Optic Sensors: An Introduction for Engineering and Scientists, 2nd ed. (Wiley, 2006).
  2. J. M. Lopez-Higuera, Optical Fibre Sensing Technology (Wiley, 2006).
  3. N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
    [CrossRef]
  4. D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
    [CrossRef]
  5. V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
    [CrossRef]
  6. J. Zhang, A. N. Hone, and Th. E. Darcie, “Phase-modulated microwave–photonic link with optical-phase-looked-loop enhanced interferometric phase detection,” J. Lightwave Technol. 26, 2549–2556 (2008).
    [CrossRef]
  7. Th. R. Clark and M. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19, 1206–1208 (2007).
    [CrossRef]
  8. G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
    [CrossRef]
  9. M. Hicks and Ch. D. Reeve, “Acousto-optic system for automatic identification and decoding of digitally modulated signals,” Opt. Eng. 37, 931–941 (1998).
    [CrossRef]
  10. I. Merta and L. R. Jaroszewicz, “Demodulator of phase signal for single mode fiber-optics,” Proc. SPIE 6585, 65852B (2007).
    [CrossRef]
  11. S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
    [CrossRef]
  12. Y. Painchaud, M. Poulin, M. Morin, and M. Tetu, “Performance of balanced detection in a coherent receiver,” Opt. Express 17, 3659–3672 (2009).
    [CrossRef]
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    [CrossRef]
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  16. I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).
  17. Z. Hołdyński, “Modelowanie i badanie eksperymentalne swiatłowodowego demodulatora fazy z całkowaniem przestrzennym w płaszczyźnie Fouriera,” WAT (2010).
  18. O. Sasaki, H. Okazaki, and M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
    [CrossRef]
  19. A. Dubois, “Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets,” J. Opt. Soc. Am. A 18, 1972–1979 (2001).
    [CrossRef]

2010 (3)

N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
[CrossRef]

S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
[CrossRef]

I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).

2009 (1)

2008 (1)

2007 (6)

Th. R. Clark and M. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19, 1206–1208 (2007).
[CrossRef]

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

I. Merta and L. R. Jaroszewicz, “Demodulator of phase signal for single mode fiber-optics,” Proc. SPIE 6585, 65852B (2007).
[CrossRef]

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280, 1–9 (2007).
[CrossRef]

2001 (1)

1998 (1)

M. Hicks and Ch. D. Reeve, “Acousto-optic system for automatic identification and decoding of digitally modulated signals,” Opt. Eng. 37, 931–941 (1998).
[CrossRef]

1994 (1)

1987 (1)

Bellon, L.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280, 1–9 (2007).
[CrossRef]

Betts, G. E.

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

Bowers, J. E.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Bucholtz, F.

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

Chou, H.-F.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Clark, T. R.

S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
[CrossRef]

Clark, Th. R.

Th. R. Clark and M. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19, 1206–1208 (2007).
[CrossRef]

Darcie, Th. E.

Dennis, M.

Th. R. Clark and M. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19, 1206–1208 (2007).
[CrossRef]

Dennis, M. L.

S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
[CrossRef]

Dubois, A.

Fernandes, N.

N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert, 2005).

Gossner, K.

N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
[CrossRef]

Hicks, M.

M. Hicks and Ch. D. Reeve, “Acousto-optic system for automatic identification and decoding of digitally modulated signals,” Opt. Eng. 37, 931–941 (1998).
[CrossRef]

Holdynski, Z.

I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).

Z. Hołdyński, “Modelowanie i badanie eksperymentalne swiatłowodowego demodulatora fazy z całkowaniem przestrzennym w płaszczyźnie Fouriera,” WAT (2010).

Hone, A. N.

Jaroszewicz, L. R.

I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).

I. Merta and L. R. Jaroszewicz, “Demodulator of phase signal for single mode fiber-optics,” Proc. SPIE 6585, 65852B (2007).
[CrossRef]

Johansson, L. A.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Krisch, H.

N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
[CrossRef]

Krzewick, W.

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

Lopez-Higuera, J. M.

J. M. Lopez-Higuera, Optical Fibre Sensing Technology (Wiley, 2006).

McKinney, J. D.

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

Meers, B.

Merta, I.

I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).

I. Merta and L. R. Jaroszewicz, “Demodulator of phase signal for single mode fiber-optics,” Proc. SPIE 6585, 65852B (2007).
[CrossRef]

Morin, M.

Morrison, E.

O’Connor, S. R.

S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
[CrossRef]

Okazaki, H.

Painchaud, Y.

Paolino, P.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280, 1–9 (2007).
[CrossRef]

Poulin, M.

Ramaswamy, A.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Reeve, Ch. D.

M. Hicks and Ch. D. Reeve, “Acousto-optic system for automatic identification and decoding of digitally modulated signals,” Opt. Eng. 37, 931–941 (1998).
[CrossRef]

Robertson, D. I.

Rodwell, M.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Sakai, M.

Sasaki, O.

Spillman, W. B.

E. Udd and W. B. Spillman, Fiber Optic Sensors: An Introduction for Engineering and Scientists, 2nd ed. (Wiley, 2006).

Tetu, M.

Udd, E.

E. Udd and W. B. Spillman, Fiber Optic Sensors: An Introduction for Engineering and Scientists, 2nd ed. (Wiley, 2006).

Urick, V. J.

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

Ward, H.

Williams, K. J.

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

Wu, S.

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

Yu, P. K. L.

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

Zhang, J.

Zibar, D.

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (3)

D. Zibar, L. A. Johansson, H.-F. Chou, A. Ramaswamy, M. Rodwell, and J. E. Bowers, “Novel optical demodulator based on a sampling phase-looked loop,” IEEE Photon. Technol. Lett. 19, 686–688 (2007).
[CrossRef]

Th. R. Clark and M. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19, 1206–1208 (2007).
[CrossRef]

G. E. Betts, W. Krzewick, S. Wu, and P. K. L. Yu, “Experimental demonstration of linear phase detection,” IEEE Photon. Technol. Lett. 19, 993–995 (2007).
[CrossRef]

IEEE Photonics J (1)

S. R. O’Connor, M. L. Dennis, and T. R. Clark, “Optimal biasing of a self-homodyne optically coherent RF receiver,” IEEE Photonics J 2, 1–7 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

V. J. Urick, F. Bucholtz, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE Trans. Microw. Theory Tech. 55, 1978–1985 (2007).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280, 1–9 (2007).
[CrossRef]

Opt. Eng. (1)

M. Hicks and Ch. D. Reeve, “Acousto-optic system for automatic identification and decoding of digitally modulated signals,” Opt. Eng. 37, 931–941 (1998).
[CrossRef]

Opt. Express (1)

PAK (1)

I. Merta, L. R. Jaroszewicz, and Z. Hołdyński, “Fiber-optic phase demodulator based on spatial integration in Young fiber interferometer system,” PAK 56, 538–540 (2010).

Proc. SPIE (2)

I. Merta and L. R. Jaroszewicz, “Demodulator of phase signal for single mode fiber-optics,” Proc. SPIE 6585, 65852B (2007).
[CrossRef]

N. Fernandes, K. Gossner, and H. Krisch, “Low power signal processing for demodulation of wide dynamic range of interferometric optical fibre sensor signals,” Proc. SPIE 7653, 765328 (2010).
[CrossRef]

Other (4)

E. Udd and W. B. Spillman, Fiber Optic Sensors: An Introduction for Engineering and Scientists, 2nd ed. (Wiley, 2006).

J. M. Lopez-Higuera, Optical Fibre Sensing Technology (Wiley, 2006).

Z. Hołdyński, “Modelowanie i badanie eksperymentalne swiatłowodowego demodulatora fazy z całkowaniem przestrzennym w płaszczyźnie Fouriera,” WAT (2010).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert, 2005).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic diagram of the fiber optic diffraction demodulator of phase.

Fig. 2.
Fig. 2.

Diffraction pattern and its central section for 2b=125μm, d=4μm, f=11mm, λ=0,63μm, Tx=56μm: (a) general view and (b) central section of the pattern.

Fig. 3.
Fig. 3.

B-PD with gap q and fringe in the Fourier plane. SL, SR—signals from the left and right sides of the B-PD.

Fig. 4.
Fig. 4.

Sum and Diff as a function of the phase difference (Δφ) at different values of q/2 in the two-dimensional (a) and one-dimensional (b) geometries.

Fig. 5.
Fig. 5.

Coefficients ai, i=1, 2, 3 as a function of the distance (q/2) between the two PDs with different areas: (a) two-dimensional B-PD with dimensions along the xf and yf axes, respectively (RAq/2; 2RA) and (b) “one-dimensional B-PD” of dimensions along xf and yf axes, respectively (RAq/2; 1 px), where 1 pixel is equal to 4.65 μm.

Fig. 6.
Fig. 6.

Values of the sum and difference of signals from one-dimensional B-PD as a function of q/2.

Fig. 7.
Fig. 7.

Diagram of the measurement setup of the fiber optic homodyne phase demodulator.

Fig. 8.
Fig. 8.

Measured values of the Sum and Diff signals for three chosen values of the distance between PDs.

Fig. 9.
Fig. 9.

Measured and theoretically calculated values of a1, a2, a3.

Fig. 10.
Fig. 10.

Output characteristics of the homodyne phase demodulator for chosen values of q.

Fig. 11.
Fig. 11.

Coefficient of linear correlation of Pearson R2 for the phase characteristics.

Tables (1)

Tables Icon

Table 1. Values a2 and a3 and Their Mutual Relations

Equations (22)

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I(u,v)=|E0|2(πd24λf)2(2J1(πρd)πρd)2cos2(2πbu(φ2φ1)2),
u=xfλf;v=yfλf;ρ=(u2+v2)1/2.
SL=constq/2+I(xf/λf,yf/λf)dyfdxf,SR=constq/2+I(xf/λf,yf/λf)dyfdxf,
SL=a1+a2cosΔφ+a3sinΔφSR=a1+a2cosΔφa3sinΔφ.
a1=Cq/2+A2(ρ)dyfdxf;A2(ρ)=(2J1(πρd)πρd)2,
a2=Cq/2+A2(ρ)cos(4πbxf/λf)dyfdxf,
a3=Cq/2+A2(ρ)sin(4πbxf/λf)dyfdxf,
Sum(Δφ)=2(a1+a2cos(Δφ)),Diff(Δφ)=2a3sin(Δφ).
tan(Δφ)=[Diff(Δφ)a2a3(Sum(Δφ)2a1)].
nL2=nR2=σ2,nL=nR=0,|nL|SL,|nR|SR,
tan(Δφ+ε)=a2a3[Diff(Δφ)+(nLnR)(Sum(Δφ)+(nL+nR))2a1].
tan(Δφ+ε)=tan(Δφ)(1+NdiffDiff(Δφ))(1+NsumSum(Δφ)2a1),
ε=2σ2sin(Δφ)cos(Δφ)[1a221a32],
ε2=σ22[sin2(Δφ)a22+cos2(Δφ)a32].
ε2=σ22a2,
σε=ε2=σa2.
tan(Δφ)=Diff(Δφ)Sum(Δφ)2a1.
tan(Δφ+ε)=Diff(Δφ)Sum(Δφ)2a1.
tan(Δφ+ε)=tan(Δφ)a3a2.
tan(Δφ+ε)tan(Δφ)+ε(1+tan2(Δφ)).
ε=ρ12sin(2Δφ),
ε¯=12π02πε2(φ)dφ=|ρ1|22.

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