Abstract

A laser synthetic wavelength interferometer that is capable of achieving large displacement measurement with nanometer accuracy is developed. The principle and the signal processing method of the interferometer are introduced. The displacement measurement experiments and the comparisons with a commercial interferometer both in small and large ranges are performed in order to verify the performance of the interferometer. Experimental results show that the average errors and standard deviations of the interferometer are in accordance with those obtained from the commercial interferometer. The resolution and the nonlinearity of the interferometer are also discussed in detail. These results show that the development of the interferometer is reasonable and feasible.

©2010 Optical Society of America

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References

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  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]
  2. C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
    [Crossref] [PubMed]
  3. C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quantum Gravity 22(10), S269–S277 (2005).
    [Crossref]
  4. M. S. Kim and S. W. Kim, “Two-way frequency-conversion phase measurement for high-speed and high-resolution heterodyne interferometry,” Meas. Sci. Technol. 15(11), 2341–2348 (2004).
    [Crossref]
  5. B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
    [Crossref] [PubMed]
  6. G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
    [Crossref]
  7. G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
    [Crossref]
  8. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [Crossref]
  9. C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
    [Crossref]
  10. J. Ahn, J. A. Kim, C. S. Kang, J. W. Kim, and S. Kim, “A passive method to compensate nonlinearity in a homodyne interferometer,” Opt. Express 17(25), 23299–23308 (2009).
    [Crossref]
  11. B. Y. Chen, X. Cheng, and D. C. Li, “Dual-wavelength interferometric technique with subnanometric resolution,” Appl. Opt. 41(28), 5933–5937 (2002).
    [Crossref] [PubMed]
  12. L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
    [Crossref]
  13. K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
    [Crossref]
  14. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6(1), 51–59 (1967).
    [Crossref] [PubMed]
  15. R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
    [Crossref]

2010 (1)

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

2009 (2)

J. Ahn, J. A. Kim, C. S. Kang, J. W. Kim, and S. Kim, “A passive method to compensate nonlinearity in a homodyne interferometer,” Opt. Express 17(25), 23299–23308 (2009).
[Crossref]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

2007 (1)

C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

2005 (2)

C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quantum Gravity 22(10), S269–S277 (2005).
[Crossref]

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)

M. S. Kim and S. W. Kim, “Two-way frequency-conversion phase measurement for high-speed and high-resolution heterodyne interferometry,” Meas. Sci. Technol. 15(11), 2341–2348 (2004).
[Crossref]

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

2002 (1)

2000 (1)

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

1996 (1)

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

1994 (1)

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

1985 (1)

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

1967 (1)

Ahn, J.

Aston, S. M.

C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quantum Gravity 22(10), S269–S277 (2005).
[Crossref]

Basile, G.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Becker, P.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Bergamin, A.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Birch, K. P.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[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]

Castell, R.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Cavagnero, G.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Chen, B. Y.

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

B. Y. Chen, X. Cheng, and D. C. Li, “Dual-wavelength interferometric technique with subnanometric resolution,” Appl. Opt. 41(28), 5933–5937 (2002).
[Crossref] [PubMed]

Cheng, X.

Dai, G. L.

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Danzebrink, H. U.

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Demtröder, W.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Downs, M. J.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

Feng, Q. B.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Fischer, A.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Franks, A.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Hasche, K.

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Hong, E.

C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Jackson, K.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Kang, C. S.

Kim, J. A.

Kim, J. W.

Kim, M. S.

M. S. Kim and S. W. Kim, “Two-way frequency-conversion phase measurement for high-speed and high-resolution heterodyne interferometry,” Meas. Sci. Technol. 15(11), 2341–2348 (2004).
[Crossref]

Kim, S.

Kim, S. W.

M. S. Kim and S. W. Kim, “Two-way frequency-conversion phase measurement for high-speed and high-resolution heterodyne interferometry,” Meas. Sci. Technol. 15(11), 2341–2348 (2004).
[Crossref]

Kuang, C. F.

C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Kuetgens, U.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Kullmer, R.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Li, C. R.

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Li, D. C.

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

B. Y. Chen, X. Cheng, and D. C. Li, “Dual-wavelength interferometric technique with subnanometric resolution,” Appl. Opt. 41(28), 5933–5937 (2002).
[Crossref] [PubMed]

Mana, G.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Ni, J.

C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Owens, J. C.

Palmer, E. W.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Pohlenz, F.

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Robbie, C. J.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Speake, C. C.

C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quantum Gravity 22(10), S269–S277 (2005).
[Crossref]

Stedman, M.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Stümpel, J.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Su, C. S.

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

Tang, W. H.

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Weickenmeier, H.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Wickert, K.

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[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]

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Wu, C. M.

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

Xu, M.

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

Yacoot, A.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Yan, L. P.

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Zhang, E. Z.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Zosi, G.

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Appl. Opt. (2)

Appl. Phys., B Photophys. Laser Chem. (1)

R. Castell, W. Demtröder, A. Fischer, R. Kullmer, H. Weickenmeier, and K. Wickert, “The accuracy of laser wavelength meters,” Appl. Phys., B Photophys. Laser Chem. 38(1), 1–10 (1985).
[Crossref]

Class. Quantum Gravity (1)

C. C. Speake and S. M. Aston, “An interferometric sensor for satellite drag-free control,” Class. Quantum Gravity 22(10), S269–S277 (2005).
[Crossref]

Meas. Sci. Technol. (5)

M. S. Kim and S. W. Kim, “Two-way frequency-conversion phase measurement for high-speed and high-resolution heterodyne interferometry,” Meas. Sci. Technol. 15(11), 2341–2348 (2004).
[Crossref]

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]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

L. P. Yan, B. Y. Chen, D. C. Li, C. R. Li, and W. H. Tang, “Signal processing method of a laser synthetic wavelength interferometer,” Meas. Sci. Technol. 21(1), 015106 (2010).
[Crossref]

Metrologia (1)

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31(4), 315–316 (1994).
[Crossref]

Opt. Express (1)

Proc. R. Soc. Lond. A (1)

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, “Combined optical and X-ray interferometry for high-precision dimensional metrology,” Proc. R. Soc. Lond. A 456(1995), 701–729 (2000).
[Crossref]

Rev. Sci. Instrum. (3)

C. F. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

G. L. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75(4), 962–969 (2004).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic diagram of the laser synthetic wavelength interferometer system.
Fig. 2
Fig. 2 A diagram illustrating how to realize interference signals processing.
Fig. 3
Fig. 3 A schematic diagram of the signal processing of LSWI.
Fig. 4
Fig. 4 Photo of the experimental setup.
Fig. 5
Fig. 5 Comparison of displacement measurements in millimeter range.
Fig. 6
Fig. 6 Comparison of displacement measurements in micrometer range.
Fig. 7
Fig. 7 Displacement measurements result in nanometer range.
Fig. 8
Fig. 8 Schematic of nonlinearity analysis.
Fig. 9
Fig. 9 Simulation of the nonlinearity analysis.

Tables (2)

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Table 1 Displacement measurement results in millimeter range

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Table 2 Displacement measurement results in micrometer range

Equations (18)

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Δ l = λ 2 λ s Δ L
Δ l = λ 2 2 N + λ 2 λ s Δ L
Δ l = λ 20 2 n ( λ 2 ) N + λ 20 λ s 0 n ( λ s ) n ( λ 2 ) Δ L
( n 1 ) S = ( 8342.54 + 240617.4 λ 2 130 λ 2 1 + 15998 λ 2 38.9 λ 2 1 ) × 10 8
( n 1 ) t p = P ( n 1 ) S 96095.43 × [ 1 + 10 8 × ( 0.601 0.00972 T ) P ] 1 + 0.003661 T
n t p f n t p = f × ( 3.7345 0.0401 λ 2 ) × 10 10
δ Δ l = ( Δ L λ s δ λ 2 ) 2 + ( λ 2 Δ L λ s 2 δ λ s ) 2 + ( λ 2 λ s δ Δ L ) 2 + ( Δ l δ r r ) 2
λ 2 = c / f 2 = 299792458 m / s 473611744 M H z 0.632998 μ m
λ s = c / Δ f = 299792458 m / s 1085 M H z 276.3064 m m
δ λ 2 = c f 2 2 δ f 2 299792458 ( 473611744 × 10 6 ) 2 × 473611744 × 0.05 3.165 × 10 8 μ m
δ λ s = c ( Δ f ) 2 δ Δ f 299792458 ( 1085 × 10 6 ) 2 × 1085 × 0.05 1.382 × 10 5 m m
δ Δ L = λ 2 × 1 f c l k × ( 1 f V ( λ 1 ) 1 f V ( λ 2 ) ) = λ 2 × 1 f c l k × ( λ 1 / 2 ν λ 2 / 2 ν ) λ 2 × 1 f c l k × λ 2 λ s 1 2 ν = λ s λ ν f c l k
| δ r r | | a ( λ S ) a ( λ 2 ) | δ D S + | b ( λ S ) b ( λ 2 ) | δ D w
b ( λ ) = ( 6487.31 + 58.058 λ 2 0.7115 λ 4 + 0.08851 λ 6 ) × 10 8 .
| δ r r | ( 1.11 δ D S + 1.31 δ D w ) × 10 6 .
{ E 1 = E 1 x + E 1 y = E cos α exp [ i ( 2 π f 1 t + φ 01 x ) ] + E sin α exp [ i ( 2 π f 1 t + φ 01 y ) ] E 2 = E 2 x + E 2 y = E sin β exp [ i ( 2 π f 2 t + φ 02 x ) ] + E cos β exp [ i ( 2 π f 2 t + φ 02 y ) ]
I D 1 = I x ( E 1 x + E 2 x ) ( E 1 x + E 2 x ) = ( E cos α ) 2 cos ( 4 π λ 1 L ) + ( E sin β ) 2 cos ( 4 π λ 2 L ) = E 2 cos ( 4 π λ 1 L ) ( E sin α ) 2 cos ( 4 π λ 1 L ) + ( E sin β ) 2 cos ( 4 π λ 2 L )
I D 2 = 1 2 I y 1 2 ( E 1 y + E 2 y ) ( E 1 y + E 2 y ) * = 1 2 ( E cos β ) 2 cos [ 4 π λ 2 ( L + L 2 ) ] + 1 2 ( E sin α ) 2 cos [ 4 π λ 1 ( L + L 2 ) ] = 1 2 E 2 cos [ 4 π λ 2 ( L + L 2 ) ] 1 2 ( E sin β ) 2 cos [ 4 π λ 2 ( L + L 2 ) ] + 1 2 ( E sin α ) 2 cos [ 4 π λ 1 ( L + L 2 ) ]

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