Abstract

We describe the combination of a polarimetric pressure sensor with a two-wavelength passive quadrature demodulation system allowing for dynamic pressure sensing in the 10-MPa range with unambiguous fringe counting. Furthermore, continuous phase measurement with the arctan method applied to the quadrature interference signals after automatic offset subtraction is demonstrated for the first time, to our knowledge. A single low-coherent superluminescent diode is used as a light source, and a polarizing beam splitter in combination with two adjustable interference filters of slightly different central wavelengths serves for the creation of the quadrature signals. Results of initial experiments with 60-ms pressure relaxation-time constants with the fringe-counting technique demonstrate the performance that was predicted theoretically. The measured pressure sensitivity exhibits excellent agreement with the previous research of Bock and Urbanczyk [IEEE Trans. Instrum. Meas. 44, 694–697 (1995)] using a polarimetric readout. The fringe-contrast variation and the measurement range obtained experimentally show the fiber dispersion to influence dephasing (deviation from quadrature) and visibility decrease significantly with increasing pressure.

© 1998 Optical Society of America

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References

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  1. W. J. Bock, W. Urbanczyk, “Temperature-hydrostatic pressure cross-sensitivity effect in elliptical-core highly birefringent fibers,” Appl. Opt. 35, 6267–6270 (1996).
    [CrossRef] [PubMed]
  2. W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
    [CrossRef]
  3. W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
    [CrossRef]
  4. A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
    [CrossRef]
  5. R. D. Turner, D. G. Laurin, R. M. Measures, “Localized dual-wavelength fiber-optic polarimeter for the measurement of structural strain and orientation,” Appl. Opt. 31, 2994–3003 (1992).
    [CrossRef] [PubMed]
  6. S. K. Sheem, T. G. Giallorenzi, K. Koo, “Optical techniques to solve the signal fading problem in fiber interferometers,” Appl. Opt. 21, 689–693 (1982).
    [CrossRef] [PubMed]
  7. N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
    [CrossRef]
  8. A. Ezbiri, R. P. Tatam, “Passive signal processing for a miniature Fabry–Perot interferometric sensor with a multimode laser-diode source,” Opt. Lett. 20, 1818–1820 (1995).
    [CrossRef] [PubMed]
  9. N. Fürstenau, W. Schmidt, H.-C. Goetting, “Simultaneous interferometric and polarimetric strain measurements on composites using a fiber-optic strain gauge,” Appl. Opt. 31, 2987–2993 (1992).
    [CrossRef] [PubMed]
  10. N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, New York, 1975), p. 316ff.
  12. Infrared Engineering Ltd., Optical Filters and Coatings, technical note (The Causeway, Maldon, Essex, CM9 7XD, England, 1996), p. 28.

1997 (1)

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

1996 (2)

W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
[CrossRef]

W. J. Bock, W. Urbanczyk, “Temperature-hydrostatic pressure cross-sensitivity effect in elliptical-core highly birefringent fibers,” Appl. Opt. 35, 6267–6270 (1996).
[CrossRef] [PubMed]

1995 (2)

A. Ezbiri, R. P. Tatam, “Passive signal processing for a miniature Fabry–Perot interferometric sensor with a multimode laser-diode source,” Opt. Lett. 20, 1818–1820 (1995).
[CrossRef] [PubMed]

W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
[CrossRef]

1993 (1)

N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
[CrossRef]

1992 (2)

1984 (1)

A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
[CrossRef]

1982 (1)

Barwicz, A.

W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
[CrossRef]

Bock, W. J.

W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
[CrossRef]

W. J. Bock, W. Urbanczyk, “Temperature-hydrostatic pressure cross-sensitivity effect in elliptical-core highly birefringent fibers,” Appl. Opt. 35, 6267–6270 (1996).
[CrossRef] [PubMed]

W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, New York, 1975), p. 316ff.

Corke, M.

A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
[CrossRef]

Ezbiri, A.

Fürstenau, N.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
[CrossRef]

N. Fürstenau, W. Schmidt, H.-C. Goetting, “Simultaneous interferometric and polarimetric strain measurements on composites using a fiber-optic strain gauge,” Appl. Opt. 31, 2987–2993 (1992).
[CrossRef] [PubMed]

Giallorenzi, T. G.

Goetting, H.-C.

Goetze, W.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

Horack, H.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

Jackson, D. A.

A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
[CrossRef]

Janzen, D. D.

N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
[CrossRef]

Kersey, A. D.

A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
[CrossRef]

Koo, K.

Laurin, D. G.

Measures, R. M.

Schmidt, M.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

Schmidt, W.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
[CrossRef]

N. Fürstenau, W. Schmidt, H.-C. Goetting, “Simultaneous interferometric and polarimetric strain measurements on composites using a fiber-optic strain gauge,” Appl. Opt. 31, 2987–2993 (1992).
[CrossRef] [PubMed]

Sheem, S. K.

Tatam, R. P.

Turner, R. D.

Urbanczyk, W.

W. J. Bock, W. Urbanczyk, “Temperature-hydrostatic pressure cross-sensitivity effect in elliptical-core highly birefringent fibers,” Appl. Opt. 35, 6267–6270 (1996).
[CrossRef] [PubMed]

W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
[CrossRef]

W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
[CrossRef]

Wojcik, J.

W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, New York, 1975), p. 316ff.

Appl. Opt. (4)

Electron. Lett. (1)

A. D. Kersey, M. Corke, D. A. Jackson, “Linearized polarimetric fibre sensor using a heterodyne-type signal recovery scheme,” Electron. Lett. 20, 209–210 (1984).
[CrossRef]

IEE Proc.: Optoelectron. (1)

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc.: Optoelectron. 144, 134–144 (1997).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

W. J. Bock, W. Urbanczyk, A. Barwicz, “Performance analysis of fiber-optic transducer for measuring low pressures,” IEEE Trans. Instrum. Meas. 45, 556–560 (1996).
[CrossRef]

W. J. Bock, W. Urbanczyk, J. Wojcik, “White-light interferometric pressure transducer,” IEEE Trans. Instrum. Meas. 44, 694–697 (1995).
[CrossRef]

Opt. Lett. (1)

Smart Mater. Struct. (1)

N. Fürstenau, D. D. Janzen, W. Schmidt, “In-flight strain measurements on structurally integrated composite plates using fiber-optic interferometric strain gauges,” Smart Mater. Struct. 2, 147–156 (1993).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, New York, 1975), p. 316ff.

Infrared Engineering Ltd., Optical Filters and Coatings, technical note (The Causeway, Maldon, Essex, CM9 7XD, England, 1996), p. 28.

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Figures (9)

Fig. 1
Fig. 1

Experimental setup of the polarimetric pressure sensor connected to a SLD light source by means of a fiber-optic polarizer and to 2λ passive quadrature readout unit by means of the PM downlead: PB, polarizing beam splitter; PM, polarization maintaining fiber; PF, polarizing fiber; Fi, bandpass filter; PD, photodiode.

Fig. 2
Fig. 2

(a) Numerical evaluation of Eq. (1) for two wavelengths λ1 = 815.4 nm, λ2 = 820 nm, and p max = 5 MPa versus pressure for a nondispersive sensing fiber. (b) Lissajou representation demonstrating the deviation from quadrature condition (horizontal ellipse, large diameter) with increasing fiber elongation and pressure (tilted ellipse, small diameter).

Fig. 3
Fig. 3

(a) Numerical evaluation of Eq. (1) for two wavelengths λ1 = 815.4 nm and λ2 = 820 nm versus time (exponential pressure drop, τ = 60 ms, p max = 5 MPa) for dispersive sensing fiber. (b) Lissajou representation. Dispersion increases the decrease of fringe visibility (decrease of ellipse diameter) and dephasing (tilting of ellipse axes) with pressure.

Fig. 4
Fig. 4

Measurement with the polarimetric pressure sensor under pressure increasing to 5 MPa with the precision pressure chamber. Data are taken with 4-kHz sampling rate. Top graph: Output voltages of 2λ unit versus time; bottom graph: Lissajou plot showing a gradual tilting of initially horizontal (equal quadrature condition) I 2 versus I 1 ellipse corresponding to increasing deviation of I 1I 2 phase difference ΔΦ12.

Fig. 5
Fig. 5

Measurement with the polarimetric pressure sensor after the opening of the valve of the pressure chamber with initial pressure p max = 5 MPa. (a) Output voltages of 2λ unit versus time; (b) Lissajou plot showing gradual tilting of an initially skewed I 2 versus I 1 ellipse corresponding to approach of I 1I 2 phase difference toward quadrature condition (π/2-phase difference).

Fig. 6
Fig. 6

Measurement with the polarimetric pressure sensor after the opening of the valve of the pressure chamber with initial pressure p max = 10 MPa. (a) Output voltages of 2λ unit versus time; (b) Lissajou plot showing a gradual tilting of initially skewed I 2 versus I 1 ellipse corresponding to the approach of the I 1I 2 phase difference toward the quadrature condition (π/2-phase difference).

Fig. 7
Fig. 7

Plot of fringe number versus time depicting the exponential decay of pressure after the opening of the precision pressure chamber valve at 10-MPa (upper curve) and 5-MPa maximum pressure (lower curve). The linear fit to data with exponential curve yields time constants of τ = 61 and 64 ms. First and last (not visible) experimental values not used in fit.

Fig. 8
Fig. 8

Maximum pressure versus fringe number. The linear fit to data yields an incremental pressure resolution of 0.268 MPa/π rad [i.e., per half-fringe = distance between 0V and crossings of Fig. 5(a)].

Fig. 9
Fig. 9

Normalized and smoothed interference signals (left vertical axis) and evaluation of 10-MPa measurement (Fig. 6) when the arctan(I 1/I 2) procedure for phase calculation (dotted curve, right vertical axis) is used. Inset shows periodic deviation of the calculated phase from fit-to-phase data (solid curve) with the exponential pressure relaxation model.

Equations (11)

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I ± = 0.5 I 0 1 + μ   cos Φ + Δ Φ ± ,
μ = exp - π   R λ δ λ 2 2 λ 2 ,
ϕ λ 1 = 2 π Δ n Δ L λ 1 + 2 π L S λ 1 Δ n p   p ,
R λ 1 = Δ N Δ L + L S Δ N p   p ,
Δ Φ 12 p = Φ λ 1 - Φ λ 2 = 2 π   Δ L Δ N λ Δ λ λ + 2 π   L S λ Δ N p   p   Δ λ λ + π ,
Δ N p = Δ n p - λ   2 Δ n λ p .
Δ λ Q λ = K - 1 2 λ 2 Δ N Δ L .
λ θ = λ 0 1 - n 0 n * 2 sin 2   θ 1 / 2 .
π / 2 > | Δ Φ 12 p | ,
U 1 = U 01 sin   Φ t , U 2 = U 02 cos Φ t + Δ Δ Φ 12 ,
Φ   =   arctan U ˆ 1 U ˆ 2 ± m π ,

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