Abstract

A novel signal processing method based on phase shift of reference signal is proposed for heterodyne interferometer. The integer fringe counting method based on overflow judgment and compensation can realize longtime and correct integer number measurement. In order to eliminate the influence of jitter in measurement signals on combination of integer and fraction fringe counting, the reference signal with phase shift of 180° is used to obtain integer compensating number to compensate the unstable integer number in unstable phase zone, which guarantees the correct combination of integer and fraction fringe counting. The principle of the proposed signal processing was described in detail. The static and dynamic resolution of the proposed method were discussed. A signal processing board based on FPGA was developed, and three tests were performed to verify the feasibility of the proposed method. A displacement measurement experimental setup was constructed, and two experiments verified the effectiveness of proposed method in application of an interferometer to realize precision displacement and testing of a stage.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  3. M. Kajima and H. Matsumoto, “Super-heterodyne laser interferometer using femtosecond frequency comb for linear encoder calibration system,” Proc. SPIE 6616, 66160G (2007).
    [Crossref]
  4. P. Yang, G. Xing, and L. He, “Calibration of high-frequency hydrophone up to 40 MHz by heterodyne interferometer,” Ultrasonics 54(1), 402–407 (2014).
    [Crossref] [PubMed]
  5. H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
    [Crossref]
  6. B. Shirinzadeh, “Laser interferometry based tracking for dynamic measurements,” Ind. Rob. 25(1), 35–41 (1998).
    [Crossref]
  7. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  15. G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
    [Crossref]
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    [Crossref]
  17. P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
    [Crossref]
  18. T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
    [Crossref]
  19. E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
    [Crossref] [PubMed]
  20. B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 84112 (2015).
[Crossref]

2014 (3)

P. Yang, G. Xing, and L. He, “Calibration of high-frequency hydrophone up to 40 MHz by heterodyne interferometer,” Ultrasonics 54(1), 402–407 (2014).
[Crossref] [PubMed]

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

G. Wang, S. H. Yan, W. H. Zhou, and C. H. Gu, “Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer,” Opt. Eng. 51(8), 81512 (2012).
[Crossref]

Y. R. Liang, H. Z. Duan, H. C. Yeh, and J. Luo, “Fundamental limits on the digital phase measurement method based on cross-correlation analysis,” Rev. Sci. Instrum. 83(9), 095110 (2012).
[Crossref] [PubMed]

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

2010 (1)

2008 (1)

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

2007 (1)

M. Kajima and H. Matsumoto, “Super-heterodyne laser interferometer using femtosecond frequency comb for linear encoder calibration system,” Proc. SPIE 6616, 66160G (2007).
[Crossref]

2005 (1)

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

2004 (2)

P. F. Luo, S. P. Pan, and T. C. Chu, “Application of computer vision and laser interferometer to the inspection of line scale,” Opt. Lasers Eng. 42(5), 563–584 (2004).
[Crossref]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

2000 (2)

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[Crossref]

N. B. Yim, C. Eom, and S. W. Kim, “Dual mode phase measurement for optical heterodyne interferometry,” Meas. Sci. Technol. 11(8), 1131–1137 (2000).
[Crossref]

1998 (2)

B. Shirinzadeh, “Laser interferometry based tracking for dynamic measurements,” Ind. Rob. 25(1), 35–41 (1998).
[Crossref]

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

Bosse, H.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

Braxmaier, C.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Chassagne, L.

Chen, B.

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[Crossref] [PubMed]

Chen, B. Y.

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

Chen, L.

Chu, T. C.

P. F. Luo, S. P. Pan, and T. C. Chu, “Application of computer vision and laser interferometer to the inspection of line scale,” Opt. Lasers Eng. 42(5), 563–584 (2004).
[Crossref]

Danzmann, K.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

Diao, X.

Dong, W.

Duan, H. Z.

Y. R. Liang, H. Z. Duan, H. C. Yeh, and J. Luo, “Fundamental limits on the digital phase measurement method based on cross-correlation analysis,” Rev. Sci. Instrum. 83(9), 095110 (2012).
[Crossref] [PubMed]

Eom, C.

N. B. Yim, C. Eom, and S. W. Kim, “Dual mode phase measurement for optical heterodyne interferometry,” Meas. Sci. Technol. 11(8), 1131–1137 (2000).
[Crossref]

Eom, T. B.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

Flügge, J.

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

García, A.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Gray, M. B.

Gu, C. H.

G. Wang, S. H. Yan, W. H. Zhou, and C. H. Gu, “Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer,” Opt. Eng. 51(8), 81512 (2012).
[Crossref]

Hao, Q.

He, L.

P. Yang, G. Xing, and L. He, “Calibration of high-frequency hydrophone up to 40 MHz by heterodyne interferometer,” Ultrasonics 54(1), 402–407 (2014).
[Crossref] [PubMed]

Heinzel, G.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Herrmann, J.

Hoyland, D.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Hsu, M. T.

Hu, P.

Jennrich, O.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Johann, U.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Kajima, M.

M. Kajima and H. Matsumoto, “Super-heterodyne laser interferometer using femtosecond frequency comb for linear encoder calibration system,” Proc. SPIE 6616, 66160G (2007).
[Crossref]

Kang, C. S.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

Kang, Y.

Kessler, E.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[Crossref]

Kim, J. A.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

Kim, J. W.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

Kim, S. W.

N. B. Yim, C. Eom, and S. W. Kim, “Dual mode phase measurement for optical heterodyne interferometry,” Meas. Sci. Technol. 11(8), 1131–1137 (2000).
[Crossref]

Köchert, P.

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

Köning, R.

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

Lawall, J.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[Crossref]

Li, C.

Li, Y.

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 84112 (2015).
[Crossref]

Liang, Y. R.

Y. R. Liang, H. Z. Duan, H. C. Yeh, and J. Luo, “Fundamental limits on the digital phase measurement method based on cross-correlation analysis,” Rev. Sci. Instrum. 83(9), 095110 (2012).
[Crossref] [PubMed]

Littler, I. C.

Liu, Y.

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

Liu, Y. N.

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

Luo, J.

Y. R. Liang, H. Z. Duan, H. C. Yeh, and J. Luo, “Fundamental limits on the digital phase measurement method based on cross-correlation analysis,” Rev. Sci. Instrum. 83(9), 095110 (2012).
[Crossref] [PubMed]

Luo, P. F.

P. F. Luo, S. P. Pan, and T. C. Chu, “Application of computer vision and laser interferometer to the inspection of line scale,” Opt. Lasers Eng. 42(5), 563–584 (2004).
[Crossref]

Manske, E.

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

Matsumoto, H.

M. Kajima and H. Matsumoto, “Super-heterodyne laser interferometer using femtosecond frequency comb for linear encoder calibration system,” Proc. SPIE 6616, 66160G (2007).
[Crossref]

Middleton, K.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Pan, S. P.

P. F. Luo, S. P. Pan, and T. C. Chu, “Application of computer vision and laser interferometer to the inspection of line scale,” Opt. Lasers Eng. 42(5), 563–584 (2004).
[Crossref]

Park, B. C.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 75302 (2008).
[Crossref]

Robertson, D.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Rüdiger, A.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Schilling, R.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Shaddock, D. A.

Shirinzadeh, B.

B. Shirinzadeh, “Laser interferometry based tracking for dynamic measurements,” Ind. Rob. 25(1), 35–41 (1998).
[Crossref]

Sun, J.

Tian, Q. H.

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

Topcu, S.

Wand, V.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Gravity 21(5), S581–S587 (2004).
[Crossref]

Wang, G.

G. Wang, S. H. Yan, W. H. Zhou, and C. H. Gu, “Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer,” Opt. Eng. 51(8), 81512 (2012).
[Crossref]

Warrington, R. B.

Wei, H. Y.

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 84112 (2015).
[Crossref]

Weichert, C.

P. Köchert, J. Flügge, C. Weichert, R. Köning, and E. Manske, “Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 74005 (2012).
[Crossref]

Wilkening, G.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

Xing, G.

P. Yang, G. Xing, and L. He, “Calibration of high-frequency hydrophone up to 40 MHz by heterodyne interferometer,” Ultrasonics 54(1), 402–407 (2014).
[Crossref] [PubMed]

Xu, S. A.

Xue, Z.

Yan, L.

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[Crossref] [PubMed]

Yan, L. P.

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

Yan, S. H.

G. Wang, S. H. Yan, W. H. Zhou, and C. H. Gu, “Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer,” Opt. Eng. 51(8), 81512 (2012).
[Crossref]

Yan, T. H.

Yang, P.

P. Yang, G. Xing, and L. He, “Calibration of high-frequency hydrophone up to 40 MHz by heterodyne interferometer,” Ultrasonics 54(1), 402–407 (2014).
[Crossref] [PubMed]

Yang, T.

T. Yang, L. P. Yan, B. Y. Chen, Y. N. Liu, and Q. H. Tian, “Signal processing method of phase correction for laser heterodyne interferometry,” Opt. Lasers Eng. 57, 93–100 (2014).
[Crossref]

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[Crossref] [PubMed]

Yeh, H. C.

Y. R. Liang, H. Z. Duan, H. C. Yeh, and J. Luo, “Fundamental limits on the digital phase measurement method based on cross-correlation analysis,” Rev. Sci. Instrum. 83(9), 095110 (2012).
[Crossref] [PubMed]

Yim, N. B.

N. B. Yim, C. Eom, and S. W. Kim, “Dual mode phase measurement for optical heterodyne interferometry,” Meas. Sci. Technol. 11(8), 1131–1137 (2000).
[Crossref]

Zhang, E.

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[Crossref] [PubMed]

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Figures (15)

Fig. 1
Fig. 1 System configuration of a heterodyne interferometer for testing the proposed signal processing method.
Fig. 2
Fig. 2 The block diagram of the proposed signal processing method.
Fig. 3
Fig. 3 Integer fringe counting based on overflow judgment and compensation.
Fig. 4
Fig. 4 Fraction fringe counting method based on filling-pulse.
Fig. 5
Fig. 5 Influence of jitter on combination of integer and fraction fringe counting.
Fig. 6
Fig. 6 Combination of integer and fraction fringe counting based on phase shift of reference signal. (a) status of signals. (b) schematic of combination principle.
Fig. 7
Fig. 7 Simulation result of static displacement resolution.
Fig. 8
Fig. 8 Simulation result of dynamic resolution.
Fig. 9
Fig. 9 Experimental results of integer fringe counting test.
Fig. 10
Fig. 10 Experimental results of combination of integer and fraction fringe counting. (a) combination without compensation. (b) combination by using the proposed method.
Fig. 11
Fig. 11 Experimental result of stability test.
Fig. 12
Fig. 12 Experimental results of precision test. (a) static precision test of simulating equivalent position. (b) dynamic resolution and precision test.
Fig. 13
Fig. 13 Experimental setup for displacement measurement comparison.
Fig. 14
Fig. 14 Experimental results of displacement comparison. (a) millimeter comparison with a step increment of 1mm in range of 300 mm. (b) nanometer comparison with a step increment of 50 nm in range of 15 μm. To make the plots visible, the red dot line presenting displacement measured by Renishaw interferometer are shifted 20 mm and 2 μm from actual values in the millimeter and nanometer comparison, respectively.
Fig. 15
Fig. 15 Experimental results of bi-directional displacement measurement. The black dot line presenting displacement provided by the XML350 stage is shifted 0.2 mm from actual values.

Tables (1)

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Table 1 Experimental result of stability test of combination number measurement

Equations (9)

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L = N Re al λ 4 n
N Int0 = { C Mea +2 n +1 C Re f0 , C Mea C Ref 0 < C L C Mea C Re f0 , C L C Mea C Re f0 C L C Mea 2 n 1 C Re f0 , C Mea C Re f0 > C L
N Frac = n PD n P
N Re al = { Δ N + N Int 180 + 0.5 + N Frac , 0 N Frac N FracR Δ N + N Int 180 0.5 + N Frac , N FracL N Frac < 1 N Int 0 + N Frac , N FracR < N Frac < N FracL
Δ N = { N Int0 0 N Int180 0 0.5 , 0 N Frac 0 < 0.5 N Int0 0 N Int180 0 + 0.5 , 0.5 N Frac 0 < 1
Δ S static = λ 4 / f clk Δ f 0
Δ S d y n a m i c = λ 4 n p
v = λ ( f clk n p Δ f 0 ) 4
Δ S d y n a m i c = λ 4 f clk ( 4 v λ + Δ f 0 )

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