Abstract

We report high-precision absolute distance and vibration measurements performed with frequency scanned interferometry using a pair of single-mode optical fibers. Absolute distance was determined by counting the interference fringes produced while scanning the laser frequency. A high-finesse Fabry–Perot interferometer was used to determine frequency changes during scanning. Two multiple-distance-measurement analysis techniques were developed to improve distance precision and to extract the amplitude and frequency of vibrations. Under laboratory conditions, measurement precision of ∼50 nm was achieved for absolute distances ranging from 0.1 to 0.7 m by use of the first multiple-distance-measurement technique. The second analysis technique has the capability to measure vibration frequencies ranging from 0.1 to 100 Hz with an amplitude as small as a few nanometers without a priori knowledge.

© 2005 Optical Society of America

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References

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  1. A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
    [CrossRef]
  2. American Linear Collider Working Group, “Linear Collider Physics, Resource Book for Snowmass 2001,” hep-ex/0106058, SLAC-R-570 299-423 (Stanford Linear Collider Center, Stanford University, 2001), pp. 299–423.
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    [CrossRef]
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    [CrossRef]
  5. G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
    [CrossRef]
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    [CrossRef]
  7. J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2002 (1)

1999 (1)

1998 (3)

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

K. H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

1996 (2)

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
[CrossRef] [PubMed]

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

1995 (1)

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

1986 (1)

1972 (1)

Abe, K.

Barwood, G. P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Bechstein, K. H.

K. H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Ciddor, P. E.

Coe, P. A.

P. A. Coe, “An investigation of frequency scanning interferometry for the alignment of the ATLAS semiconductor tracker,” Ph.D. dissertation (St. Peter’s College, University of Oxford, Oxford, UK, 2001).

Fox-Murphy, A. F.

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

Fuchs, W.

K. H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Gill, P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Haetmann, M.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Howard, L.

Howell, D. F.

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

Katuo, S.

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Kikuta, H.

Ko, J. Y.

Lim, T. S.

Nagata, R.

Nickerson, R. B.

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

Otsuka, K.

Peck, E. R.

Pfeifer, T.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Reeder, K.

Rowley, W. R. C.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Stejskal, A.

Stone, J. A.

Thiel, J.

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Weidberg, A. R.

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

Xiaoli, D.

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Appl. Opt. (3)

J. Opt. (1)

K. H. Bechstein, W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (2)

D. Xiaoli, S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Measurement (1)

J. Thiel, T. Pfeifer, M. Haetmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Nucl. Instrum. Methods A (1)

A. F. Fox-Murphy, D. F. Howell, R. B. Nickerson, A. R. Weidberg, “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry,” Nucl. Instrum. Methods A 383, 229–237 (1996).
[CrossRef]

Opt. Lett. (1)

Other (3)

American Linear Collider Working Group, “Linear Collider Physics, Resource Book for Snowmass 2001,” hep-ex/0106058, SLAC-R-570 299-423 (Stanford Linear Collider Center, Stanford University, 2001), pp. 299–423.

P. A. Coe, “An investigation of frequency scanning interferometry for the alignment of the ATLAS semiconductor tracker,” Ph.D. dissertation (St. Peter’s College, University of Oxford, Oxford, UK, 2001).

SCHOTT’96 for Windows Catalog Optical Glass (Schott Glaswerke Mainz, Germany, 1996), http://us.schott.com/sgt/english/products/catalogs.html .

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Figures (7)

Fig. 1
Fig. 1

Schematic of an optical fiber FSI system. BS, beam splitter.

Fig. 2
Fig. 2

Schematic of two multiple-distance-measurement techniques. The interference fringes from the femtowatt photoreceiver and the scanning frequency peaks from the F–P interferometer for the optical fiber FSI system recorded simultaneously by a data-acquisition card are shown as waves and sharp peaks, respectively. The free spectral range of two adjacent F–P peaks (1.5 GHz) provides a calibration of the scanned frequency range.

Fig. 3
Fig. 3

Distance measurement residual spreads versus number of distance measurement Nmeas (a) for one typical scan, (b) for ten sequential scans, (c) the standard deviation of distance measurements for ten sequential scans versus Nmeas.

Fig. 4
Fig. 4

Distance measurement residual spreads versus Nmeas in one scan: (a) for the open box with a scanning rate of 2 nm/s, (b) for the closed box with a scanning rate of 2 nm/s, (c) for the open box with a scanning rate of 0.5 nm/s, (d) for the closed box with a scanning rate of 0.5 nm/s.

Fig. 5
Fig. 5

Frequency and amplitude of the controlled vibration source are 1 Hz and 140 nm. (a) Magnification factor versus number of distance measurements, (b) distance measurement residual versus number of distance measurements, (c) corrected measurement residual versus number of distance measurements.

Fig. 6
Fig. 6

Frequency and amplitude of the controlled vibration source are 1 Hz and 9.5 nm. (a) Magnification factor versus number of distance measurements, (b) distance measurement residual versus number of distance measurements, (c) corrected measurement residual versus number of distance measurements.

Fig. 7
Fig. 7

Residuals of 2000 distance measurements for one typical scan; the corner cube prism is used as retroreflector.

Tables (1)

Tables Icon

Table 1 Distance Measurement Precisions for Various Setups with the Multiple-Distance-Measurement Technique

Equations (6)

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I = I 1 + I 2 + 2 I 1 I 2 cos ( ϕ 1 ϕ 2 ) ,
Δ N = | L 1 L 2 | ( Δ ν / c ) = L Δ ν / c ,
Δ N = L Δ ν / c + 2 [ x vib ( t ) ν ( t ) x vib ( t 0 ) ν ( t 0 ) ] / c .
L meas = L true 4 a vib Ω sin [ π f vib ( t t 0 ) ] × sin [ π f vib ( t + t 0 ) + ϕ vib ] ,
L meas = | L ( t ) / λ ( t ) = L ( t 0 ) / λ ( t 0 ) | c / Δ ν , L ( t ) = 2 { D 1 n air + D 2 n [ λ ( t ) ] corner cube } ,
n 2 ( λ ) = 1 + B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 + B 3 λ 2 λ 2 C 3 ,

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