Abstract

We present a concept of suppression of the influence of variations of the refractive index of air in displacement measuring interferometry. The principle is based on referencing of wavelength of the coherent laser source in atmospheric conditions instead of traditional stabilization of the optical frequency and indirect evaluation of the refractive index of air. The key advantage is in identical beam paths of the position measuring interferometers and the interferometer used for the wavelength stabilization. Design of the optical arrangement presented here to verify the concept is suitable for real interferometric position sensing in technical practice especially where a high resolution measurement within some limited range in atmospheric conditions is needed, e.g. in nanometrology.

© 2012 OSA

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  1. G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
    [CrossRef]
  2. T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40(2), 103–133 (2003).
    [CrossRef]
  3. B. Edlén, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
    [CrossRef]
  4. B. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
    [CrossRef]
  5. K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive-index of air,” Metrologia 30(3), 155–162 (1993).
    [CrossRef]
  6. P. E. Ciddor, “Refractive index of air: New equations for the visible and near infrared,” Appl. Opt. 35(9), 1566–1573 (1996).
    [CrossRef] [PubMed]
  7. K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive-index of air,” Metrologia 31(4), 315–316 (1994).
    [CrossRef]
  8. M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
    [CrossRef]
  9. J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).
  10. B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
    [CrossRef]
  11. T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
    [CrossRef]
  12. S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).
  13. H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).
  14. J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
    [CrossRef] [PubMed]
  15. J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).
  16. J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
    [CrossRef]
  17. J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
    [CrossRef]
  18. J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
    [CrossRef]
  19. O. Číp and F. Petrů, “A scale-linearization method for precise laser interferometry,” Meas. Sci. Technol. 11(2), 133–141 (2000).
    [CrossRef]
  20. K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
    [CrossRef]
  21. R. W. Fox, B. R. Washburn, N. R. Newbury, and L. Hollberg, “Wavelength references for interferometry in air,” Appl. Opt. 44(36), 7793–7801 (2005).
    [CrossRef] [PubMed]

2012 (1)

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

2011 (4)

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

2010 (1)

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

2009 (2)

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

2005 (1)

2004 (1)

J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).

2003 (3)

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40(2), 103–133 (2003).
[CrossRef]

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

2002 (1)

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

2000 (1)

O. Číp and F. Petrů, “A scale-linearization method for precise laser interferometry,” Meas. Sci. Technol. 11(2), 133–141 (2000).
[CrossRef]

1998 (1)

B. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[CrossRef]

1996 (1)

1994 (1)

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

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive-index of air,” Metrologia 30(3), 155–162 (1993).
[CrossRef]

1990 (1)

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

1966 (1)

B. Edlén, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Acef, O.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Aketagawa, M.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

Alayli, Y.

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

Birch, K. P.

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

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive-index of air,” Metrologia 30(3), 155–162 (1993).
[CrossRef]

Bönsch, B.

B. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[CrossRef]

Buchta, Z.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

Ciddor, P. E.

Cíp, O.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

O. Číp and F. Petrů, “A scale-linearization method for precise laser interferometry,” Meas. Sci. Technol. 11(2), 133–141 (2000).
[CrossRef]

Cížek, M.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

Downs, M. J.

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

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive-index of air,” Metrologia 30(3), 155–162 (1993).
[CrossRef]

Ducos, F.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Ellis, J. D.

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

Fejfar, A.

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

Fox, R. W.

Höfler, H.

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

Holá, M.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

Hollberg, L.

Hoshino, Y.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

Hrabina, J.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

Ishige, M.

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

Jedlicka, P.

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

Joo, K.-N.

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

Juncar, P.

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

Knight, J. C.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Kulmus, K.

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

Lazar, J.

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

Mikel, B.

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

Molnar, J.

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

Newbury, N. R.

Ohkubo, Y.

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

Oulehla, J.

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

Petru, F.

O. Číp and F. Petrů, “A scale-linearization method for precise laser interferometry,” Meas. Sci. Technol. 11(2), 133–141 (2000).
[CrossRef]

Pokorný, P.

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

Potulski, E.

B. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[CrossRef]

Quinn, T. J.

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40(2), 103–133 (2003).
[CrossRef]

Quoc, T. B.

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

Rovera, G. D.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Russell, P. S.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Ružicka, B.

J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

Schmidt, R. H. M.

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

Schröder, C.

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

Spronck, J. W.

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

Stuchlík, J.

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

Topcu, S.

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

Wallerand, J. P.

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Washburn, B. R.

Zondy, J. J.

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

Appl. Opt. (2)

Eur. Phys. J.: Appl. Phys. (1)

S. Topcu, Y. Alayli, J. P. Wallerand, and P. Juncar, “Heterodyne refractometer and air wavelength reference at 633 nm,” Eur. Phys. J.: Appl. Phys. 24, 85–90 (2003).

Meas. Sci. Technol. (5)

T. B. Quoc, M. Ishige, Y. Ohkubo, and M. Aketagawa, “Measurement of air-refractive-index fluctuation from laser frequency shift with uncertainty of order 10(−9),” Meas. Sci. Technol. 20(12), 125302 (2009).
[CrossRef]

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20(8), 084019 (2009).
[CrossRef]

J. Lazar, O. Číp, and B. Růžička, “The design of a compact and tunable extended-cavity semiconductor laser,” Meas. Sci. Technol. 15(6–N), 9 (2004).

G. D. Rovera, F. Ducos, J. J. Zondy, O. Acef, J. P. Wallerand, J. C. Knight, and P. S. Russell, “Absolute frequency measurement of an I-2 stabilized Nd:YAG optical frequency standard,” Meas. Sci. Technol. 13(6), 918–922 (2002).
[CrossRef]

O. Číp and F. Petrů, “A scale-linearization method for precise laser interferometry,” Meas. Sci. Technol. 11(2), 133–141 (2000).
[CrossRef]

Metrologia (5)

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40(2), 103–133 (2003).
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[CrossRef]

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

Precis. Eng. (1)

K.-N. Joo, J. D. Ellis, J. W. Spronck, and R. H. M. Schmidt, “Real-time wavelength corrected heterodyne laser interferometry,” Precis. Eng. 35(1), 38–43 (2011).
[CrossRef]

Proc. SPIE (3)

B. Mikel, B. Růžička, O. Číp, J. Lazar, and P. Jedlička, “Highly coherent tunable semiconductor lasers in metrology of length,” Proc. SPIE 5036, 8–13 (2003).
[CrossRef]

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Interferometry with direct compensation of fluctuations of refractive index of air,” Proc. SPIE 7746(77460E), 1–6 (2010).

J. Lazar, O. Číp, J. Oulehla, P. Pokorný, A. Fejfar, and J. Stuchlík, “Position measurement in standing wave interferometer for metrology of length,” Proc. SPIE 8306, 830607, 830607-7 (2011).
[CrossRef]

Sensors (Basel Switzerland) (1)

J. Lazar, M. Holá, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Refractive index compensation in over-determined interferometric systems,” Sensors (Basel Switzerland) 12(10), 14084–14094 (2012).
[CrossRef]

Sensors (Basel) (1)

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Suppression of air Refractive index variations in high-resolution interferometry,” Sensors (Basel) 11(8), 7644–7655 (2011).
[CrossRef] [PubMed]

Tech. Mess (2)

H. Höfler, J. Molnar, C. Schröder, and K. Kulmus, “Interferometrische Wegmessung mit automatischer Brechzahlkompensation,” Tech. Mess 57, 346–350 (1990).

J. Lazar, O. Číp, M. Čížek, J. Hrabina, and Z. Buchta, “Standing wave interferometer with stabilization of wavelength on air,” Tech. Mess 78(11), 484–488 (2011).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Configuration with corner-cube reflectors measuring directly the overall length and two particluar displacements. CC: corner-cube reflector, PBS: polarizing beamsplitter, NP: non-polarizing plane, λ/2: half-wave plate, F: fiber-optic light delivery, OA, OB, OC outputs, Lc. La, Lb: particular lengths determining the position of the moving carriage.

Fig. 2
Fig. 2

Recording of the variations of the interferometers A (red line), B (yellow line), and overall length measuring C (blue line) together with the sum of A and B (green line) over time in a closed thermal box (left) and opened (right).

Fig. 3
Fig. 3

Recording of a slow refractive index drift evaluated from measurement of air temperature, pressure, humidity and CO2 content.

Fig. 4
Fig. 4

Recording of the optical frequency tuning of the laser following stabilized wavelength over the measuring range.

Equations (4)

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

λ a = 1 n a c ν stab
n a  =f(υ, p, RH,  p CO2 )
ν= 1 n a c λ a
λ a = L C N

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