Abstract

In static tests, low-power (<5mW) white light extrinsic Fabry–Perot interferometric position sensors offer high-accuracy (μm) absolute measurements of a target’s position over large (cm) axial-position ranges, and since position is demodulated directly from phase in the interferogram, these sensors are robust to fluctuations in measured power levels. However, target surface dynamics distort the interferogram via Doppler shifting, introducing a bias in the demodulation process. With typical commercial off-the-shelf hardware, a broadband source centered near 1550 nm, and an otherwise typical setup, the bias may be as large as 50–100 μm for target surface velocities as low as 0.1mm/s. In this paper, the authors derive a model for this Doppler-induced position bias, relating its magnitude to three swept-filter tuning parameters. Target velocity (magnitude and direction) is calculated using this relationship in conjunction with a phase-diversity approach, and knowledge of the target’s velocity is then used to compensate exactly for the position bias. The phase-diversity approach exploits side-by-side measurement signals, transmitted through separate swept filters with distinct tuning parameters, and permits simultaneous measurement of target velocity and target position, thereby mitigating the most fundamental performance limitation that exists on dynamic white light interferometric position sensors.

© 2012 Optical Society of America

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References

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    [CrossRef]
  3. Y. Jiang, “Fourier transform white-light interferometry for the measurement of fiber-optic extrinsic Fabry–Perót interferometric displacement sensors,” IEEE Photon. Technol. Lett. 20, 75–77 (2008).
    [CrossRef]
  4. M. Han, “Theoretical and experimental study of low-finesse extrinsic Fabry–Perót interferometric fiber optic sensors,” Ph.D. dissertation (Virginia Polytechnic Institute and State University, 2006.
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    [CrossRef]
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  12. O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
    [CrossRef]
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    [CrossRef]

2012 (1)

2011 (2)

2009 (1)

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

2008 (1)

Y. Jiang, “Fourier transform white-light interferometry for the measurement of fiber-optic extrinsic Fabry–Perót interferometric displacement sensors,” IEEE Photon. Technol. Lett. 20, 75–77 (2008).
[CrossRef]

2007 (1)

A. M. Abdi and S. E. Watkins, “Demodulation of fiber-optic sensors for frequency response measurement,” IEEE Sens. J. 7, 667–676 (2007).
[CrossRef]

2006 (1)

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

2005 (1)

2001 (1)

1999 (2)

1979 (1)

Abdi, A. M.

A. M. Abdi and S. E. Watkins, “Demodulation of fiber-optic sensors for frequency response measurement,” IEEE Sens. J. 7, 667–676 (2007).
[CrossRef]

Byer, R. L.

Cook, R. O.

Ding, W.

Y. Jiang, and W. Ding, “Recent developments in fiber optic spectral white-light interferometry,” Phot. Sens. 1, 62–71 (2011).
[CrossRef]

Goosman, D. R.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Gustafson, E. K.

Hamm, C. W.

Han, M.

M. Han, “Theoretical and experimental study of low-finesse extrinsic Fabry–Perót interferometric fiber optic sensors,” Ph.D. dissertation (Virginia Polytechnic Institute and State University, 2006.

Howard, L. P.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Husman, M. E.

Jiang, Y.

Y. Jiang, and W. Ding, “Recent developments in fiber optic spectral white-light interferometry,” Phot. Sens. 1, 62–71 (2011).
[CrossRef]

Y. Jiang, “Fourier transform white-light interferometry for the measurement of fiber-optic extrinsic Fabry–Perót interferometric displacement sensors,” IEEE Photon. Technol. Lett. 20, 75–77 (2008).
[CrossRef]

Kuhlow, W. W.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Lawrence, M. J.

Martinez, C.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Moro, E. A.

Pratt, J. R.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Puckett, A. D.

Rakhmanov, M.

Shen, F.

Shimamoto, A.

Smith, D. T.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Strand, O. T.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Suganuma, F.

Tanaka, K.

Todd, M. D.

Wang, A.

Watkins, S. E.

A. M. Abdi and S. E. Watkins, “Demodulation of fiber-optic sensors for frequency response measurement,” IEEE Sens. J. 7, 667–676 (2007).
[CrossRef]

Whitworth, T. L.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Willke, B.

Appl. Opt. (6)

IEEE Photon. Technol. Lett. (1)

Y. Jiang, “Fourier transform white-light interferometry for the measurement of fiber-optic extrinsic Fabry–Perót interferometric displacement sensors,” IEEE Photon. Technol. Lett. 20, 75–77 (2008).
[CrossRef]

IEEE Sens. J. (1)

A. M. Abdi and S. E. Watkins, “Demodulation of fiber-optic sensors for frequency response measurement,” IEEE Sens. J. 7, 667–676 (2007).
[CrossRef]

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

Phot. Sens. (1)

Y. Jiang, and W. Ding, “Recent developments in fiber optic spectral white-light interferometry,” Phot. Sens. 1, 62–71 (2011).
[CrossRef]

Rev. Sci. Instrum. (2)

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Other (1)

M. Han, “Theoretical and experimental study of low-finesse extrinsic Fabry–Perót interferometric fiber optic sensors,” Ph.D. dissertation (Virginia Polytechnic Institute and State University, 2006.

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Figures (9)

Fig. 1.
Fig. 1.

Diagram of a typical swept-filter, white light EFPI position sensor is shown here. This configuration, with components that operate in the 1510–1590 nm range, is representative of the one researched in this paper.

Fig. 2.
Fig. 2.

Relationship between DUT velocity, Doppler-shifting, and the resultant beat frequency is illustrated here.

Fig. 3.
Fig. 3.

DUT position data are shown here, where horizontal regions indicate a DUT at rest and sloping regions indicate DUT motion. Note that the actual motion was smooth, although Doppler shifting makes it appear jumpy when motion starts or stops. A DUT velocity of ±0.1mm/s resulted in a bias of approximately 65 μm.

Fig. 4.
Fig. 4.

The proposed phase-diversity approach takes advantage of two tunable filters, each with its own distinct set of tuning parameters.

Fig. 5.
Fig. 5.

Upper and lower velocity limits are calculated using Eq. (22) and plotted here as functions of DUT position. For a given Δf0, these limits are set by fsweep and fDAQ.

Fig. 6.
Fig. 6.

As shown in Eq. (20), there is an inverse relationship between Δf (given here in wavelength units) and Lres. Increasing (or decreasing) Δf0 results in spreading out (or condensing) the PSD estimate, ultimately affecting both Lres and Lmax.

Fig. 7.
Fig. 7.

Raw (biased) DUT position data measured from both filters are shown (a) along with the difference between these measurements (b).

Fig. 8.
Fig. 8.

DUT velocity is estimated using Eq. (16) along with two sets of filter parameters. As expected, the measured velocity follows the prescribed values of 0mm/s, ±0.1mm/s, or ±0.5mm/s.

Fig. 9.
Fig. 9.

Using an estimate of the DUT velocity (Fig. 8), it is possible to remove the Doppler-induced position bias from the raw results shown in Fig. 7. (a) provides the global perspective of a test, while detailed views are shown in (b), (c), and (d).

Tables (1)

Tables Icon

Table 1. Properties of the Tones Present in the Measurement Signal are Summarized Herea

Equations (22)

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B0.65v,
IreflIinc=Fsin2(2πf0Ln/c)1+Fsin2(2πf0Ln/c),
F=4r1r2(1r1r2)2.
f0=Nc2nL
R=c2nL.
L=c2nR.
fR=1RΔf0Δt.
L=c2nfRΔtΔf0.
fb=f0fd=2(vc)f0,
Lb=v(f0ΔtΔf0).
E˜=E˜0+E˜d=E0exp(j2πf0t)+Edexp(j2πfd(tτ))
τ=2Lnc.
I=12cε0E˜E˜*=I0+Id+2I0Idcos(2πfbt+4πfdLnc).
I(t)=I0+IdFsin2(2πfd(t)L(t)n/c)1+Fsin2(2πfd(t)L(t)n/c)+2I0IdFsin2(2πfd(t)L(t)n/c)1+Fsin2(2πfd(t)L(t)n/c)cos(2πfbt+4πfdLnc).
I(t)=I0+IdF2IdF2cos(4πfdLnc)+I0IdF[cos(4πfdLnc+2πfbt)12cos(8πfdLnc+2πfbt)12cos(2πfbt)].
(L+Lb1)(L+Lb2)=v(f0,1Δt1Δf0,1)(v(f0,2Δt2Δf0,2))=v(f0,2Δt2Δf0,2f0,1Δt1Δf0,1),
L=cK2nNFFT|f1f2|,
NFFT=fDAQfsweep,
|f1f2|=Δf0NFFT=frangefsweepfDAQ.
Lres=c2nNFFT(fDAQfsweepΔf0)=c2n(1Δf0).
Lmax=c4n(fDAQfsweepΔf0).
0<(Lf0ΔtΔfv)c4n(fDAQfsweepΔf).

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