Abstract

This paper presents a design procedure for a fiber interferometer, the optical system, and its associated electronic control. Analog and digital circuits were optimized to achieve an inexpensive and compact system. The lock-in amplifier required for phase control was designed using a field programmable gate array that was also configured to carry out the required phase stepping. The interferometer was built into two stages. The first stage used only one wavelength to measure samples with step heights in the hundreds of nanometers, with improvements in accuracy through averaging of data. The next stage included two measurement wavelengths to extend the measurement range to a few hundreds of micrometers. The paper conducts a systematic study of sources of errors. A least squares method that minimizes measurement time but retains accuracy has been used to measure height.

© 2011 Optical Society of America

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  1. D. A. Jackson, A. Dandridge, and S. K. Sheem, “Measurement of small phase shifts using a single-mode optical-fiber interferometer,” Opt. Lett. 5, 139–141 (1980).
    [CrossRef] [PubMed]
  2. K. Raman and K. N. Bimal, “An all single mode fiber Michelson interferometer sensor,” J. Lightwave Technol. 1, 619–624(1983).
    [CrossRef]
  3. K. Fritsch and G. Adamovsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
    [CrossRef]
  4. A. A. Freschi and J. Frejlich, “Adjustable phase control in stabilized interferometery,” Opt. Lett. 20, 635–637 (1995).
    [CrossRef] [PubMed]
  5. D. Lin, F. Xie, W. Zhang, L. Zhang, and I. Bennionet, “High stability multiplexed fiber interferometer and its application on absolute displacement measurement and on line surface metrology,” Opt. Express 12, 5729–5734 (2004).
    [CrossRef] [PubMed]
  6. F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
    [CrossRef]
  7. D. A. Jackson and A. D. Kersey, “Pseudo-heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1082 (1982).
    [CrossRef]
  8. Y. L. Lo and C. H. Chuang, “New synthetic heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
    [CrossRef]
  9. R. Ulrich, “Polarization stabilization on single mode fibers,” Appl. Phys. Lett. 35, 840–842 (1979).
    [CrossRef]
  10. T. Okoshi, “Polarization state control schemes for heterodyne or homodyne optical fiber communication, ”J. Lightwave Technol. 3, 174–176 (1985).
    [CrossRef]
  11. K. Tomohimo, “Phase shifting interferometer based on changing the direction of linear polarization orthogonally,” Appl. Opt. , 47, 3784–3788 (2008).
    [CrossRef]
  12. C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
    [CrossRef]
  13. A. Kulkarni, G. Lakshminarayan, and S. Bhattacharya, “Comparison of phase stepping algorithm used with an all fiber interferometer,” presented at the International Photonics Conference, New Delhi, India, December 2008.
  14. G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.
  15. F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
    [CrossRef]
  16. W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
    [CrossRef]
  17. K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
    [CrossRef]

2009 (2)

C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
[CrossRef]

F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
[CrossRef]

2008 (1)

2007 (2)

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
[CrossRef]

2004 (1)

2001 (2)

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Y. L. Lo and C. H. Chuang, “New synthetic heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

1995 (1)

1985 (1)

T. Okoshi, “Polarization state control schemes for heterodyne or homodyne optical fiber communication, ”J. Lightwave Technol. 3, 174–176 (1985).
[CrossRef]

1983 (1)

K. Raman and K. N. Bimal, “An all single mode fiber Michelson interferometer sensor,” J. Lightwave Technol. 1, 619–624(1983).
[CrossRef]

1982 (1)

D. A. Jackson and A. D. Kersey, “Pseudo-heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1082 (1982).
[CrossRef]

1981 (1)

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

1980 (1)

1979 (1)

R. Ulrich, “Polarization stabilization on single mode fibers,” Appl. Phys. Lett. 35, 840–842 (1979).
[CrossRef]

Adamovsky, G.

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

Bennionet, I.

Bhattacharya, S.

A. Kulkarni, G. Lakshminarayan, and S. Bhattacharya, “Comparison of phase stepping algorithm used with an all fiber interferometer,” presented at the International Photonics Conference, New Delhi, India, December 2008.

G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.

C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
[CrossRef]

Bimal, K. N.

K. Raman and K. N. Bimal, “An all single mode fiber Michelson interferometer sensor,” J. Lightwave Technol. 1, 619–624(1983).
[CrossRef]

Bu, Y.

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Chen, Z.

F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
[CrossRef]

Chuang, C. H.

Y. L. Lo and C. H. Chuang, “New synthetic heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

Dandridge, A.

Frejlich, J.

Freschi, A. A.

Fritsch, K.

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

Jackson, D. A.

D. A. Jackson and A. D. Kersey, “Pseudo-heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1082 (1982).
[CrossRef]

D. A. Jackson, A. Dandridge, and S. K. Sheem, “Measurement of small phase shifts using a single-mode optical-fiber interferometer,” Opt. Lett. 5, 139–141 (1980).
[CrossRef] [PubMed]

Kersey, A. D.

D. A. Jackson and A. D. Kersey, “Pseudo-heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1082 (1982).
[CrossRef]

Khansa, C. A.

G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.

C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
[CrossRef]

Kitagawa, K.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

Kulkarni, A.

A. Kulkarni, G. Lakshminarayan, and S. Bhattacharya, “Comparison of phase stepping algorithm used with an all fiber interferometer,” presented at the International Photonics Conference, New Delhi, India, December 2008.

Lakshminarayan, G.

A. Kulkarni, G. Lakshminarayan, and S. Bhattacharya, “Comparison of phase stepping algorithm used with an all fiber interferometer,” presented at the International Photonics Conference, New Delhi, India, December 2008.

G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.

Lin, D.

Lo, Y. L.

Y. L. Lo and C. H. Chuang, “New synthetic heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

Lu, H.

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Lu, Y.

F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
[CrossRef]

Matsuzaka, T.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

Ogawa, H.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

Okoshi, T.

T. Okoshi, “Polarization state control schemes for heterodyne or homodyne optical fiber communication, ”J. Lightwave Technol. 3, 174–176 (1985).
[CrossRef]

Prabhakar, A.

G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.

C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
[CrossRef]

Qian, F.

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Raman, K.

K. Raman and K. N. Bimal, “An all single mode fiber Michelson interferometer sensor,” J. Lightwave Technol. 1, 619–624(1983).
[CrossRef]

Ren, J.

F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
[CrossRef]

Sheem, S. K.

Sugiyama, M.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

Suzuki, K.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

Tomohimo, K.

Ulrich, R.

R. Ulrich, “Polarization stabilization on single mode fibers,” Appl. Phys. Lett. 35, 840–842 (1979).
[CrossRef]

Xiangzhao, W.

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Xie, F.

F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
[CrossRef]

F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
[CrossRef]

D. Lin, F. Xie, W. Zhang, L. Zhang, and I. Bennionet, “High stability multiplexed fiber interferometer and its application on absolute displacement measurement and on line surface metrology,” Opt. Express 12, 5729–5734 (2004).
[CrossRef] [PubMed]

Xuefeng, W.

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Zhang, L.

F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
[CrossRef]

D. Lin, F. Xie, W. Zhang, L. Zhang, and I. Bennionet, “High stability multiplexed fiber interferometer and its application on absolute displacement measurement and on line surface metrology,” Opt. Express 12, 5729–5734 (2004).
[CrossRef] [PubMed]

Zhang, W.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Ulrich, “Polarization stabilization on single mode fibers,” Appl. Phys. Lett. 35, 840–842 (1979).
[CrossRef]

Electron. Lett. (1)

D. A. Jackson and A. D. Kersey, “Pseudo-heterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1082 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. L. Lo and C. H. Chuang, “New synthetic heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

J. Lightwave Technol. (2)

K. Raman and K. N. Bimal, “An all single mode fiber Michelson interferometer sensor,” J. Lightwave Technol. 1, 619–624(1983).
[CrossRef]

T. Okoshi, “Polarization state control schemes for heterodyne or homodyne optical fiber communication, ”J. Lightwave Technol. 3, 174–176 (1985).
[CrossRef]

J. Opt. Commun. (1)

C. A. Khansa, S. Bhattacharya, and A. Prabhakar, “Multiwavelength erbium doped fiber ring laser,” J. Opt. Commun. 282, 2380–2387 (2009).
[CrossRef]

Measurement (1)

F. Xie, Z. Chen, and J. Ren, “Stabilization of an optical fiber Michelson interferometer measurement system using a simple feedback circuit,” Measurement 42, 1335–1340 (2009).
[CrossRef]

Opt. Eng. (1)

F. Xie, Y. Lu, and L. Zhang, “Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement,” Opt. Eng. 46, 051011(2007).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

W. Xuefeng, W. Xiangzhao, H. Lu, F. Qian, and Y. Bu, “Laser diode interferometer used for measuring displacements in large range with a nanometer accuracy,” Opt. Laser Technol. 33, 219–223 (2001).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

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

Other (3)

A. Kulkarni, G. Lakshminarayan, and S. Bhattacharya, “Comparison of phase stepping algorithm used with an all fiber interferometer,” presented at the International Photonics Conference, New Delhi, India, December 2008.

G. Lakshminarayan, C. A. Khansa, A. Prabhakar, and S. Bhattacharya, “Development of a fully automated fiber interferometer,” presented at the IMEKO TC2 Conference, Prague, Czech Republic, 25–26 August 2008.

K. Kitagawa, M. Sugiyama, T. Matsuzaka, H. Ogawa, and K. Suzuki, “Two wavelength single shot interferometry,” in SICE Annual Conference (SICE, 2007), pp. 724–728.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Enlarged view of a section sample arrangement shown in Fig. 2.

Fig. 2
Fig. 2

Block schematic of the all-fiber Michelson interferometer.

Fig. 3
Fig. 3

Electronics to stabilize the interferometer.

Fig. 4
Fig. 4

Circuit to reset the PZT.

Fig. 5
Fig. 5

Correction signal to the PZT (a) before and (b) after introduction of the switch.

Fig. 6
Fig. 6

Multiwavelength source in (a) DPBS and (b) ring configurations.

Fig. 7
Fig. 7

Output spectrum from the DPBS and ring lasers.

Fig. 8
Fig. 8

Inputs to the adder demonstrating a phase difference of π / 2 .

Fig. 9
Fig. 9

Least squares fit (Eq. (1)) to data collected as we varied α.

Fig. 10
Fig. 10

Reduction in error by averaging the intensity, at each value of ϕ.

Tables (3)

Tables Icon

Table 1 Effect of Errors on the AFI

Tables Icon

Table 2 Measurements Taken Using the AFI

Tables Icon

Table 3 Extending the Measurement Range of the Interferometer

Equations (11)

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

I = I 0 [ 1 + V cos ( α + ϕ ) ] .
ϕ 1 = atan ( I 1 + I 3 - 2 I 2 I 1 - I 3 ) .
h = λ ( ϕ 2 - ϕ 1 ) 4 π .
h = λ 1 λ 2 2 ( λ 1 - λ 2 ) .
I = I 0 [ 1 + V cos ( α + β m sin Ω t ) ] ,
cos ( β m sin Ω t ) = J 0 ( β m ) + 2 n = 1 J 2 n ( β m ) cos ( 2 n Ω t ) ,
sin ( β m sin Ω t ) = 2 n = 1 J 2 n - 1 ( β m ) sin ( ( 2 n - 1 ) Ω t )
δ f = f ( x , y ) - f ( x 0 , y 0 ) f x | x 0 δ x + f y | y 0 .
δ h = 2 × { δ λ 4 π ϕ 1 + λ 4 π [ ϕ 1 I δ I + ϕ 1 λ δ λ + ϕ 1 V δ V + ϕ 1 α δ α ] + ϕ T } ,
tan ϕ 1 = tan ϕ 1 [ 1 + δ I I 0 ( 2 + 2 V sin ϕ 1 sin ϕ 1 + 1 + V cos ϕ 1 cos ϕ 1 ) ] .
I I 0 = 1 + V cos α [ J 0 ( β m ) - 2 J 2 ( β m ) cos ( 2 Ω t ) ] - 2 V sin α J 1 ( β m ) sin ( Ω t ) .

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