Abstract

A robust white-light interferometric sensing system for fast displacement measurement is presented. In order to increase the speed of the sensing system in comparison with the standard realization based on the postprocessing of the captured interferometric signal, a real-time algorithm based on the modified centroid algorithm has been implemented. The modified centroid algorithm generates the error signal that is proportional to the interferometer optical path difference (OPD) during every scan of the used white-light source coherence zone. In order to keep zero OPD, an amplified version of the error signal has been brought to the input of the piezo bimorph actuator (PBA) that on the other side serves for the fast coherence zone scan. In this way the PBA tracks the position of the object whose displacement is to be measured. Therefore, the voltage signal at the PBA input is proportional to the measured displacement. The realized sensing system has an overall bandwidth of almost 10 Hz, where the sensor full scale range of 200 μm has been measured with a resolution of 3 nm.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (1)

2012 (2)

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

2010 (2)

D. F. Murphy and D. A. Flavin, “Statically scanned single and tandem low-coherence interferometers,” Meas. Sci. Technol. 21, 094031 (2010).
[CrossRef]

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Lasers Eng. 48, 486–490 (2010).
[CrossRef]

2008 (2)

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

M. C. Tomic and Z. V. Djinovic, “Inline liquid concentration measurement in nanoliter volume using fiber-optic low-coherence interferometry,” IEEE Sens. J. 8, 587–592 (2008).
[CrossRef]

2006 (1)

1998 (1)

R.-J. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

1996 (1)

Y.-J. Rao and D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

1994 (1)

1992 (2)

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef]

Bajic, J. S.

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

Chen, S.

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

de Groot, P.

Deck, L.

Djinovic, Z. V.

M. C. Tomic and Z. V. Djinovic, “Inline liquid concentration measurement in nanoliter volume using fiber-optic low-coherence interferometry,” IEEE Sens. J. 8, 587–592 (2008).
[CrossRef]

Flavin, D. A.

D. F. Murphy and D. A. Flavin, “Statically scanned single and tandem low-coherence interferometers,” Meas. Sci. Technol. 21, 094031 (2010).
[CrossRef]

Grattan, K. T. V.

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef]

Jackson, D. A.

Y.-J. Rao and D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

Jiang, Z.

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

Li, X.

Liu, B.

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

Ma, C.

Manojlovic, L. M.

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Lasers Eng. 48, 486–490 (2010).
[CrossRef]

Meggitt, B. T.

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

Murphy, D. F.

D. F. Murphy and D. A. Flavin, “Statically scanned single and tandem low-coherence interferometers,” Meas. Sci. Technol. 21, 094031 (2010).
[CrossRef]

Notni, G.

R.-J. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Palmer, A. W.

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef]

Park, J.

Rao, Y.-J.

Y.-J. Rao and D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

Recknagel, R.-J.

R.-J. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Slankamenac, M. P.

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

Stupar, D. Z.

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

Tian, A.

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

Tomic, M. C.

M. C. Tomic and Z. V. Djinovic, “Inline liquid concentration measurement in nanoliter volume using fiber-optic low-coherence interferometry,” IEEE Sens. J. 8, 587–592 (2008).
[CrossRef]

Wang, A.

Wang, C.

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

Wang, H.

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

Živanov, M. B.

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, J. S. Bajić, and D. Z. Stupar, “High-speed and high-sensitivity displacement measurement with phase-locked low-coherence interferometry,” Appl. Opt. 51, 4333–4342 (2012).
[CrossRef]

Appl. Opt. (4)

Electron. Lett. (1)

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Fringe order identification in optical fibre white-light interferometry using centroid algorithm method,” Electron. Lett. 28, 553–554 (1992).
[CrossRef]

IEEE Sens. J. (1)

M. C. Tomic and Z. V. Djinovic, “Inline liquid concentration measurement in nanoliter volume using fiber-optic low-coherence interferometry,” IEEE Sens. J. 8, 587–592 (2008).
[CrossRef]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (2)

D. F. Murphy and D. A. Flavin, “Statically scanned single and tandem low-coherence interferometers,” Meas. Sci. Technol. 21, 094031 (2010).
[CrossRef]

Y.-J. Rao and D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

Opt. Commun. (1)

R.-J. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Opt. Lasers Eng. (1)

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Lasers Eng. 48, 486–490 (2010).
[CrossRef]

Phys. Scripta (1)

L. M. Manojlović, M. B. Živanov, M. P. Slankamenac, D. Z. Stupar, and J. S. Bajić, “A simple low-coherence interferometric sensor for absolute position measurement based on central fringe maximum identification,” Phys. Scripta T149, 014023 (2012).
[CrossRef]

Proc. SPIE (1)

A. Tian, C. Wang, Z. Jiang, H. Wang, and B. Liu, “Study on key algorithm for scanning white-light interferometry,” Proc. SPIE 7155, 71552N (2008).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Block schematic of the displacement measurement setup.

Fig. 2.
Fig. 2.

(a) Signal at the HPF output (channel 1) and (b) signal at the integrator input (channel 1) when the servo loop is switched off.

Fig. 3.
Fig. 3.

(a) Signal at the HPF output (channel 1) and (b) signal at the integrator input (channel 1) when the servo loop is switched on.

Fig. 4.
Fig. 4.

Measured output voltage signal versus the actual displacement of the SM. The measured data are represented by the gray line (1) and the linear fit of the measured data is represented by the black line (2).

Fig. 5.
Fig. 5.

Step response of the sensing system where the gray line (1) denotes the input voltage signal of the high-voltage amplifier and the black line and (2) denotes the output voltage signal of the sensing system.

Fig. 6.
Fig. 6.

Displacement measurement error captured during 10 s (top diagram) together with its PDF (bottom diagram).

Fig. 7.
Fig. 7.

PSD of the captured output signal when the SM position was fixed.

Equations (9)

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sHPF(t)=exp{[L(t)LC]2}cos[2πL(t)λ],
sAGC(t)=exp{8[Dsin(ωt)x(t)LC]2}{1+cos{8πλ[Dsin(ωt)x(t)]}}.
e(t)=exp{8[Dsin(ωt)x(t)LC]2}{1+cos{8πλ[Dsin(ωt)x(t)]}}sin(ωt),
eT(t)=1TT/2T/2e(t)dt=12πππexp{8[psinθr(t)]2}{1+cos{8πq[psinθr(t)]}}sinθdθ,
eT(t)12πππexp{8[psinθr(t)]2}sinθdθ.
eT(t)12πππexp(8p2sin2θ)[1+16pr(t)sinθ]sinθdθ.
eT(t)[32πp0π/2exp(8p2sin2θ)sin2θdθ]r(t)=S(p)r(t),
S(p)=8pexp(4p2)[J0(j4p2)jJ1(j4p2)],
eT(t)S(p)r(t)=S(p)LCx(t)xS(t)xR(t),

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