Abstract

A method for the phase detection of straight and equidistant fringes is applied to an optical sensor using a highly birefringent fiber. A birefringent wedge introduces a linear phase difference between orthogonally polarized light which emanates from the fiber, and Young’s fringes are formed on an image sensor. The phase difference between two orthogonal retardations of the fiber is proportional to the phase of Young’s fringes. The phase of Young’s fringes is calculated from Fourier cosine and sine integrals of the fringe profile. The experimental results of a fiber extension induced by a PZT expansion are presented with error estimations. The accuracy of a 2-m long fiber sensor is estimated to be higher than λ/200. A technique to extend the measurement range of the fiber sensor is also presented using two laser wavelengths, in which a new method for calculating the difference between two phases is used. The experimental results are presented with error estimations.

© 1988 Optical Society of America

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References

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  1. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
    [CrossRef]
  2. G. B. Hocker, “Fiber-Optic Sensing of Pressure and Temperature,” Appl. Opt. 18, 1445 (1979).
    [CrossRef] [PubMed]
  3. S. Nakadate, “Phase Detection of Equidistant Fringes for Highly Sensitive Optical Sensings. I: Principle and Error Analyses,” J. Opt. Soc. Am. A 5, 1258 (1988).
    [CrossRef]
  4. S. Nakadate, “Phase Detection of Equidistant Fringes for Highly Sensitive Optical Sensings. II: Experiments,” J. Opt. Soc. Am. A 5, 1265 (1988).
    [CrossRef]
  5. P. A. Leilabady, J. D. C. Jones, D. A. Jackson, “Monomode Fiber-Optic Strain Gauge With Simultaneous Phase- and Polarization-State Detection,” Opt. Lett. 10, 576 (1985).
    [CrossRef] [PubMed]
  6. A. D. Kersey, A. Dandrige, W. K. Burns, “Two-Wavelength Fibre Gyroscope with Wide Dynamic Range,” Electron. Lett. 22, 935 (1986).
    [CrossRef]

1988 (2)

1986 (1)

A. D. Kersey, A. Dandrige, W. K. Burns, “Two-Wavelength Fibre Gyroscope with Wide Dynamic Range,” Electron. Lett. 22, 935 (1986).
[CrossRef]

1985 (1)

1982 (1)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

1979 (1)

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Burns, W. K.

A. D. Kersey, A. Dandrige, W. K. Burns, “Two-Wavelength Fibre Gyroscope with Wide Dynamic Range,” Electron. Lett. 22, 935 (1986).
[CrossRef]

Cole, J. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Dandridge, A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Dandrige, A.

A. D. Kersey, A. Dandrige, W. K. Burns, “Two-Wavelength Fibre Gyroscope with Wide Dynamic Range,” Electron. Lett. 22, 935 (1986).
[CrossRef]

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Hocker, G. B.

Jackson, D. A.

Jones, J. D. C.

Kersey, A. D.

A. D. Kersey, A. Dandrige, W. K. Burns, “Two-Wavelength Fibre Gyroscope with Wide Dynamic Range,” Electron. Lett. 22, 935 (1986).
[CrossRef]

Leilabady, P. A.

Nakadate, S.

Priest, R. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Rashleigh, S. C.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

Sigel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of a basic birefringent fiber sensor using the phase detection of Young’s fringes.

Fig. 2
Fig. 2

Signal from the image sensor which detects Young’s fringes. The fringe frequency is 9.94 and the fringe contrast is 0.74.

Fig. 3
Fig. 3

Phase difference between two retardations of orthogonal polarization eigenmodes of the fiber, which is induced by the fiber extension due to the PZT expansion.

Fig. 4
Fig. 4

Phase fluctuation in the static states of the common path polarizing interferometers: (a) with a 2-m long fiber, and (b) without a fiber. The standard deviations are (a) 0.232° and (b) 0.026°.

Fig. 5
Fig. 5

Schematic diagram of a two-wavelength polarizing interferometer to widen the range of phase measurement.

Fig. 6
Fig. 6

Output signals from the image sensor for (a) 632.8 nm of a He–Ne laser and (b) 514.5 nm of an argon-ion laser. The fringe frequencies are (a) 8.0 and (b) 10.1.

Fig. 7
Fig. 7

Phase changes due to successive fiber extension of 20 μm for a, 632.8 nm; b, 514.5 nm; and c, the difference between two phases calculated from Eqs. (7), (8), and (4).

Fig. 8
Fig. 8

Phase fluctuation in the static state of the fiber interferometer shown in Fig. 5 for a wavelength of 514.5 nm: (a) original phase change during 50 s and (b) the difference between the original and the phase averaged over five sample points. The peak-to-peak phase change in (a) is 4.98°, and the standard deviation in (b) is 0.08°.

Equations (8)

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I ( x ) = W ( x ) [ 1 + cos ( 2 π f 0 x - φ ) ] ,
C = - I ( x ) cos ( 2 π f 0 x ) d x ,
S = - I ( x ) sin ( 2 π f 0 x ) d x .
φ = tan - 1 ( S C ) .
Δ ( φ f - φ s ) = 2 π λ ( δ n + 1 l δ n ) Δ l ,
Φ 2 - Φ 1 = 2 π ( λ 1 - λ 2 ) λ 1 λ 2 ( δ n + l l δ n ) Δ l ,
cos ( Φ 2 - Φ 1 ) C 1 C 2 + S 1 S 2 = C ,
sin ( Φ 2 - Φ 1 ) C 1 S 2 - S 1 C 2 = S .

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