Abstract

A two-wavelength interferometer (TWI) based on a sinusoidal-phase-modulation method with an acetylene stabilized laser and a second harmonic generation (SHG) was developed. The periodic non-linearity error for the TWI was estimated to be ± 0.1 µm at a dead path of 0.32 m. A long-term measurement showed that the TWI stability was ± 3 × 10−7 at a dead path of 1.00 m for 12 hours with an ambient pressure variation of 3 hPa under controlled conditions of ambient temperature and humidity. Finally, we confirmed that the TWI has substantially better stability than a single-wavelength interferometer by comparing both interferometers with large temporal and spatial temperature variations.

© 2015 Optical Society of America

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References

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  1. P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
    [Crossref]
  2. H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
    [Crossref]
  3. H. Matsumoto, Y. Zhu, S. Iwasaki, and T. O’ishi, “Measurement of the changes in air refractive index and distance by means of a two-color interferometer,” Appl. Opt. 31(22), 4522–4526 (1992).
    [Crossref] [PubMed]
  4. K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
    [Crossref] [PubMed]
  5. G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
    [Crossref]
  6. G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
    [PubMed]
  7. K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).
  8. S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
    [Crossref]
  9. K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
    [Crossref]
  10. O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137–3140 (1986).
    [Crossref] [PubMed]
  11. O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
    [Crossref]
  12. M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
    [Crossref]
  13. V. G. Badami, S. R. Patterson, and C. A. Zanoni, “Interferometry system having reduced cyclic errors,” US Patent, 6,181,420 B1.
  14. C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
    [Crossref]
  15. V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
    [Crossref]
  16. M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).
  17. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35(9), 1566–1573 (1996).
    [Crossref] [PubMed]

2014 (2)

S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
[Crossref]

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

2013 (2)

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

2011 (2)

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

2009 (1)

V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
[Crossref]

2008 (1)

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

2007 (1)

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

2005 (1)

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

1996 (1)

1992 (2)

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

H. Matsumoto, Y. Zhu, S. Iwasaki, and T. O’ishi, “Measurement of the changes in air refractive index and distance by means of a two-color interferometer,” Appl. Opt. 31(22), 4522–4526 (1992).
[Crossref] [PubMed]

1990 (1)

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

1986 (1)

1965 (1)

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Abou-Zeid, A.

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

Ahtee, V.

V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
[Crossref]

Aketagawa, M.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Arai, K.

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

Araya, A.

S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
[Crossref]

Barwood, G. P.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Bender, P. L.

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Ciddor, P. E.

Edwards, C. S.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Gill, P.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Honda, T.

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

Hongo, J.

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

Inaba, H.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

Iwasaki, S.

Kasai, K.

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

Kumagai, T.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Lea, S. N.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Madden, M.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Maeda, Y.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Margolis, H. S.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Masuda, H.

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

Matsumoto, H.

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

H. Matsumoto, Y. Zhu, S. Iwasaki, and T. O’ishi, “Measurement of the changes in air refractive index and distance by means of a two-color interferometer,” Appl. Opt. 31(22), 4522–4526 (1992).
[Crossref] [PubMed]

Meiners-Hagen, K.

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

Merimaa, M.

V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
[Crossref]

Minoshima, K.

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

Miyata, K.

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

Nakagawa, H.

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

Nakazawa, M.

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

Nyholm, K.

V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
[Crossref]

O’ishi, T.

Okazaki, H.

Okuyama, E.

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Oozeki, H.

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

Owens, J. C.

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Rowley, W. R. C.

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

Sakai, H.

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

Sasaki, O.

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137–3140 (1986).
[Crossref] [PubMed]

Suzuki, T.

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

Takahashi, K.

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

Takahashi, M.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

Takamori, A.

S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
[Crossref]

Telada, S.

S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
[Crossref]

Wu, G.

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

Yoshida, M.

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

Zhu, Y.

Appl. Opt. (3)

Appl. Phys. B (1)

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, “High-accuracy atlas of 13C2H2 in 1.5 µm region,” Appl. Phys. B 80(8), 977–983 (2005).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

V. Ahtee, M. Merimaa, and K. Nyholm, “Fiber-based acetylene-stabilized laser,” IEEE Trans. Instrum. Meas. 58(4), 1211–1216 (2009).
[Crossref]

Int. J. Automot. Techn. (1)

K. Miyata, H. Oozeki, H. Nakagawa, H. Masuda, and H. Sakai, “Two-wavelength laser interferometer system which reduces the uncertainty caused by the fluctuation of the refractive index of air,” Int. J. Automot. Techn. 5(2), 126–131 (2011).

J. Geophys. Res. (1)

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Meas. Sci. Technol. (4)

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

M. Madden, M. Aketagawa, T. Kumagai, Y. Maeda, and E. Okuyama, “Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometer,” Meas. Sci. Technol. 25(9), 094005 (2014).
[Crossref]

Opt. Eng. (1)

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

Opt. Express (1)

Proc. SPIE (1)

M. Yoshida, K. Kasai, J. Hongo, and M. Nakazawa, “A C2H2 frequency-stabilize erbium-doped fiber laser and its application to coherent communication,” Proc. SPIE 6453, 645311 (2007).

Sci. Rep. (1)

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

Technologies (1)

S. Telada, A. Araya, and A. Takamori, “Crustal strain observation using a two-color interferometer with accurate correction of refractive index of air,” Technologies 2(3), 115–128 (2014).
[Crossref]

Other (1)

V. G. Badami, S. R. Patterson, and C. A. Zanoni, “Interferometry system having reduced cyclic errors,” US Patent, 6,181,420 B1.

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Figures (8)

Fig. 1
Fig. 1 Schematic image of an SPM laser interferometer. LD: laser diode, BS: beam splitter, PD: photodetector, dr: geometrical distance between the BS and the reference reflector, dp: geometrical distance between the BS and the probe reflector. Dm is the difference between dp and dr.
Fig. 2
Fig. 2 Configuration of the TWI. Coup.: coupler, OF: optical fiber, WDM: WDM coupler, PM: parabolic mirror, BS: beam splitter, DM: dichroic mirror, L: lens, PD: photodetector, M: mirror.
Fig. 3
Fig. 3 Configuration of the acetylene stabilized laser. The interior of the dotted frame indicates the acetylene stabilized laser. Coup.: optical coupler, OF: optical fiber, WDM: WDM coupler, AD converter: digital to analog converter, AD converter: analog to digital converter.
Fig. 4
Fig. 4 Measurement results for 4 µm probe reflector displacements on the piezo stage with a velocity of 50 nm/s. (a) Displacement measurements for the SHGI (green line) and the FWI (black line) without an environmental correction, and TWI (red line) are plotted as a function of time. To make the plots visible, the red line is shifted by − 0.5 µm from the actual values. (b) Displacement differences between the SHGI and FWII as a function of time. (C) Displacement differences between the TWI and SHGI as a function of time.
Fig. 5
Fig. 5 Displacement differences between the TWI and SHGI as a function of the SHGI displacement.
Fig. 6
Fig. 6 Stability measurement results for (a) Ambient pressure. (b) Ambient temperature. (c) SHGI displacement measurements with no environmental corrections (green line), with environmental corrections (blue line), with only an ambient pressure correction (gray line), and TWI displacement measurements (red line). (d) Displacement differences between the TWI and SHGI with only a pressure correction.
Fig. 7
Fig. 7 Experimental setup for the optical path temperature variation. The 1.00 m probe optical path was covered with a 0.70 m long pipe and wound with a rubber heater to vary the temperature of part of the path. The interferometers were fixed on a ceramic board with a low thermal expansion coefficient.
Fig. 8
Fig. 8 Measurement results while the optical path temperature was changing. (a) Temperature of the external pipe surface center. (b) Ambient temperature close to the pipe. (c) Ceramic surface temperature. (d) Measured SHGI displacements without environmental corrections (green line), SHGI with barometer, hydrometer and thermometer 1 corrections (blue line), SHGI with barometer, hydrometer and thermometer 2 corrections (gray line), and the TWI (the red line) as a function of time.

Equations (11)

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 D= D 2 A( D 2 D 1 )= n 2 DA( n 2 n 1 )D
 A= ( n 2 1 )/( n 2 n 1 )
 f( t )= f o +γcos( ω m t )
 I= I o +Bcos[ ( 2πn/ c o )( 2 D m ){ f o +γcos( ω m t ) } ]
 = I o +Bcos[ m f cos( ω m t )+ϕ ]
 ϕ=( 2πn/ c o )( 2 D m ) f o =2πn( 2 D m )/ λ o
  m f =( 2πn/ c o )( 2 D m )γ
I= I o +Bcos( ϕ ){ J o ( m f ) + 2 J 2 ( m f )cos( 2 ω m t ) + 2 J 4 ( m f )cos( 4 ω m t ) + } Bsin( ϕ ){ 2 J 1 ( m f )cos( ω m t ) + 2 J 3 ( m f )cos(3 ω m t) + }. 
2n D m = ϕ o λ/( 2π ) =arctan{ sin( ϕ )/cos( ϕ ) } λ o /( 2π ).
D t = D s A( D s D f )
D t D s =A( D s D f ).

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