Abstract

Active homodyne feedback control can be used to stabilize an interferometer against unwanted phase drifts introduced by, for example, temperature gradients. The technique is commonly used in fiber-optic sensors to maintain the fiber at its most sensitive (quadrature) position. We describe an extension of the technique to introduce stabilized, π/2-rad phase steps in a full-field interferometer. The technique was implemented in a single-mode, fiber-optic interference fringe projector used for shape measurement and can be easily applied to other fiber- or bulk-optic interferometers, for example, speckle pattern and holographic interferometers. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interfere at the fourth port of a directional coupler. The interference intensity (and hence phase) is maintained at quadrature by feedback control to a phase modulator in one of the fiber arms. Stepping between quadrature positions (separated by π rad for light undergoing a double pass) introduces stabilized phase steps in the projected fringes (separated by π/2 rad for a single pass). A root-mean-square phase stability of 0.61 mrad in a 50-Hz bandwidth and phase step accuracy of 1.17 mrad were measured.

© 2002 Optical Society of America

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References

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  2. D. A. Jackson, J. D. C. Jones, “Interferometers,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1990), Vol. 2, Chap. 10, pp. 329–380.
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    [CrossRef] [PubMed]
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    [CrossRef]
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2000 (1)

A. Brozeit, J. Burke, H. Helmers, “Active phase stabilisation in electronic speckle pattern interferometry without additional components,” Opt. Commun. 173, 95–100 (2000).
[CrossRef]

1998 (1)

1995 (1)

1991 (1)

1990 (1)

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

1987 (1)

1985 (1)

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

1982 (5)

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

A. Dandridge, A. B. Tveten, “Phase compensation in interferometric fiber-optic sensors,” Opt. Lett. 7, 279–281 (1982).
[CrossRef] [PubMed]

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]

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilisation scheme for fibre interferometers using (3 × 3) fibre directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[CrossRef]

1981 (2)

D. A. Jackson, “A prototype digital phase tracker for the fibre interferometer,” J. Phys. E 14, 1274–1278 (1981).
[CrossRef]

K. Fritsch, G. Adamovsky, “Simple circuit feedback stabilisation of a single-mode optical fibre interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

1980 (1)

1968 (1)

1967 (1)

1954 (1)

Adamovsky, G.

K. Fritsch, G. Adamovsky, “Simple circuit feedback stabilisation of a single-mode optical fibre interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Barton, J. S.

J. D. C. Jones, J. S. Barton, “Fibre-optic sensors for condition monitoring and engineering diagnostics,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1997), Vol. 4, Chap. 12, pp. 207–259.

Beheim, G.

Brozeit, A.

A. Brozeit, J. Burke, H. Helmers, “Active phase stabilisation in electronic speckle pattern interferometry without additional components,” Opt. Commun. 173, 95–100 (2000).
[CrossRef]

Burke, J.

A. Brozeit, J. Burke, H. Helmers, “Active phase stabilisation in electronic speckle pattern interferometry without additional components,” Opt. Commun. 173, 95–100 (2000).
[CrossRef]

Corke, M.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Creath, K.

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

Dandridge, A.

A. Dandridge, A. B. Tveten, “Phase compensation in interferometric fiber-optic sensors,” Opt. Lett. 7, 279–281 (1982).
[CrossRef] [PubMed]

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilisation scheme for fibre interferometers using (3 × 3) fibre directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

D. A. Jackson, R. Priest, A. Dandridge, A. B. Tveten, “Elimination of drift in a single-mode optical fiber interferometer using a piezoelectrically stretched coiled fiber,” Appl. Opt. 19, 2926–2929 (1980).
[CrossRef] [PubMed]

A. Dandridge, “Fibre optic sensors based on the Mach–Zehnder and Michelson interferometers,” in Fibre Optic Sensors: An Introduction for Engineers and Scientists, E. Udd, ed. (Wiley, New York, 1991), Chap. 10, pp. 271–323.

Dorf, R. C.

R. C. Dorf, Modern Control Systems, 6th ed. (Addison-Wesley, New York, 1992).

Frejlich, J.

Fresci, A. A.

Fritsch, K.

K. Fritsch, G. Adamovsky, “Simple circuit feedback stabilisation of a single-mode optical fibre interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Giallorenzi, T. G.

Helmers, H.

A. Brozeit, J. Burke, H. Helmers, “Active phase stabilisation in electronic speckle pattern interferometry without additional components,” Opt. Commun. 173, 95–100 (2000).
[CrossRef]

Huntoon, R. D.

Jackson, D. A.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[CrossRef]

D. A. Jackson, “A prototype digital phase tracker for the fibre interferometer,” J. Phys. E 14, 1274–1278 (1981).
[CrossRef]

D. A. Jackson, R. Priest, A. Dandridge, A. B. Tveten, “Elimination of drift in a single-mode optical fiber interferometer using a piezoelectrically stretched coiled fiber,” Appl. Opt. 19, 2926–2929 (1980).
[CrossRef] [PubMed]

D. A. Jackson, J. D. C. Jones, “Interferometers,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1990), Vol. 2, Chap. 10, pp. 329–380.

Jones, J. D. C.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

D. A. Jackson, J. D. C. Jones, “Interferometers,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1990), Vol. 2, Chap. 10, pp. 329–380.

J. D. C. Jones, J. S. Barton, “Fibre-optic sensors for condition monitoring and engineering diagnostics,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1997), Vol. 4, Chap. 12, pp. 207–259.

Kersey, A. D.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[CrossRef]

Koo, K.

Koo, K. P.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilisation scheme for fibre interferometers using (3 × 3) fibre directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Lee, B. S.

Mercer, C. R.

Mnatzakanian, S.

Nara, M.

Neumann, D. B.

Priest, R.

Pruett, H. D.

Rose, H. W.

Sasaki, O.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Sheem, S. K.

Smith, W.

Strand, T. C.

Suzuki, T.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Takahashi, K.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Tveten, A. B.

Weiss, A.

Yamaguchi, H.

Yoshino, T.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilisation scheme for fibre interferometers using (3 × 3) fibre directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Electron. Lett. (2)

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudo heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E (2)

D. A. Jackson, “A prototype digital phase tracker for the fibre interferometer,” J. Phys. E 14, 1274–1278 (1981).
[CrossRef]

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All single-mode fibre optic holographic system with active fringe stabilisation,” J. Phys. E 18, 185–186 (1985).
[CrossRef]

Opt. Commun. (1)

A. Brozeit, J. Burke, H. Helmers, “Active phase stabilisation in electronic speckle pattern interferometry without additional components,” Opt. Commun. 173, 95–100 (2000).
[CrossRef]

Opt. Eng. (1)

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

K. Fritsch, G. Adamovsky, “Simple circuit feedback stabilisation of a single-mode optical fibre interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Other (5)

J. D. C. Jones, J. S. Barton, “Fibre-optic sensors for condition monitoring and engineering diagnostics,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1997), Vol. 4, Chap. 12, pp. 207–259.

R. C. Dorf, Modern Control Systems, 6th ed. (Addison-Wesley, New York, 1992).

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

D. A. Jackson, J. D. C. Jones, “Interferometers,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Boston, Mass., 1990), Vol. 2, Chap. 10, pp. 329–380.

A. Dandridge, “Fibre optic sensors based on the Mach–Zehnder and Michelson interferometers,” in Fibre Optic Sensors: An Introduction for Engineers and Scientists, E. Udd, ed. (Wiley, New York, 1991), Chap. 10, pp. 271–323.

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of the fiber-optic fringe projector. DL, diode laser; FI, Faraday isolator; DC, directional coupler; PC, polarization controller; PZ, phase controller; CCD, charge-coupled device digital camera; PD, photodiode.

Fig. 2
Fig. 2

(a) One of four phase-stepped projected interference fringes for a plane test surface and (b) a calculated wrapped phase map.

Fig. 3
Fig. 3

Block diagram of the feedback control system.

Fig. 4
Fig. 4

Evaluation of K F and K D . Top trace is the triangular-wave modulation applied to PZ2. The lower trace is the voltage recorded by photodiode PD2 corresponding to the interference irradiance after subtraction of the dc term. K F = Nπ/V c = 2π/4.8 = 1.3 rad/V and K D = 0.8 V/rad.

Fig. 5
Fig. 5

Electrical spectrum analyzer trace for the voltage from photodiode PD1. (a) The small-amplitude harmonic signal used to calibrate the dc pedestal removal can be seen at 5 kHz. (b) At quadrature, the second harmonic of this signal is zero. (c) When the servo is not operating, the noise level increases below the -3-dB cutoff frequency of 1.7 kHz. (d) The calculated attenuation of the feedback loop, based on the parameters K D , K F , and K 1(jω).

Fig. 6
Fig. 6

Signal sequence for stabilized phase stepping.

Equations (9)

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

ϕ=tan-1I4-I2I1-I3.
ϕ=-2πλr-ri|r-ri| · Δri,
IA=kI01+V cos 2ϕo-ϕr,
VA=KAI01-V2ϕe,
Ve=VB-VA=KAI0V2ϕe=KD2ϕe,
ϕeϕd=11+GjωHjω,
ω-3dB=2KDKFK1.
IA=kI01+V cos 2ϕd+ϕs sin ωst.
IA=kI0+kI0V cos2ϕdJ02ϕs+2J22ϕscos2ωst+2J42ϕscos4ωst+-kI0V sin2ϕd2J12ϕssinωst+2J32ϕssin3ωst+,

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