Abstract

The absolute group refractive index of air at 1563 nm is measured by dispersive interferometry, and a combined uncertainty of 1.2 × 10−8 is achieved. The group refractive index of air is calculated from the dispersive interferograms of the two beams passing through the inner and outer regions of a vacuum cell by fast-Fourier-transform. Experimental results show that the discrepancies between our method and modified Edlén equation are less than 3.43 × 10−8 and 4.4 × 10−8 for short-term and long-term experiments, respectively. The interferogram update rate is 15 ms, which makes it suitable for application of real-time monitoring. Furthermore, it is promising to improve the measurement uncertainty to 3.0 × 10−9 by changing the material of the vacuum cell and measuring its length more accurately through optical interferometry.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Frequency comb calibrated frequency-sweeping interferometry for absolute group refractive index measurement of air

Lijun Yang, Xuejian Wu, Haoyun Wei, and Yan Li
Appl. Opt. 56(11) 3109-3115 (2017)

Absolute distance measurement with correction of air refractive index by using two-color dispersive interferometry

Hanzhong Wu, Fumin Zhang, Tingyang Liu, Jianshuang Li, and Xinghua Qu
Opt. Express 24(21) 24361-24376 (2016)

Air refractive index measurement using low-coherence interferometry

Tomáš Pikálek and Zdeněk Buchta
Appl. Opt. 54(16) 5024-5030 (2015)

References

  • View by:
  • |
  • |
  • |

  1. M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. M. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
    [Crossref] [PubMed]
  2. P. Balling, P. Kren, P. Masika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
    [Crossref] [PubMed]
  3. S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
    [Crossref] [PubMed]
  4. H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014).
    [Crossref] [PubMed]
  5. B. Edlén, “The refractive index of air,” Metrologia 2(2), 71–80 (1966).
    [Crossref]
  6. K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive-index of air,” Metrologia 30(3), 155–162 (1993).
    [Crossref]
  7. 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]
  8. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35(9), 1566–1573 (1996).
    [Crossref] [PubMed]
  9. T. Hieta, M. Merimaa, M. Vainio, J. Seppä, and A. Lassila, “High-precision diode-laser-based temperature measurement for air refractive index compensation,” Appl. Opt. 50(31), 5990–5998 (2011).
    [Crossref] [PubMed]
  10. K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8(4), 647–651 (1991).
    [Crossref]
  11. Q. Chen, H. Luo, S. Wang, and F. Wang, “Measurement of air refractive index based on surface plasmon resonance and phase detection,” Opt. Lett. 37(14), 2916–2918 (2012).
    [Crossref] [PubMed]
  12. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of air with frequency combs,” Opt. Lett. 30(24), 3314–3316 (2005).
    [Crossref] [PubMed]
  13. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb,” Appl. Opt. 47(17), 3143–3151 (2008).
    [Crossref] [PubMed]
  14. G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35(2), 133–139 (1998).
    [Crossref]
  15. L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
    [Crossref]
  16. J. Zhang, P. Huang, Y. Li, and H. Wei, “Design and performance of an absolute gas refractometer based on a synthetic pseudo-wavelength method,” Appl. Opt. 52(16), 3671–3679 (2013).
    [Crossref] [PubMed]
  17. P. Huang, J. Zhang, Y. Li, and H. Wei, “Note: Real-time absolute air refractometer,” Rev. Sci. Instrum. 85(5), 056107 (2014).
    [Crossref] [PubMed]
  18. T. Pikálek and Z. Buchta, “Air refractive index measurement using low-coherence interferometry,” Appl. Opt. 54(16), 5024–5030 (2015).
    [Crossref] [PubMed]
  19. N. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
    [Crossref]
  20. S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
    [Crossref]
  21. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006).
    [Crossref] [PubMed]
  22. K. N. Joo, Y. Kim, and S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799–19806 (2008).
    [Crossref] [PubMed]
  23. M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. M. Braat, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011).
    [Crossref] [PubMed]
  24. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [Crossref]
  25. “Evaluation of measurement data—guide to the expression of uncertainty in measurement,” (2008), http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315ehtml/C045315e.html?csnumberCsnumber=50461 .
  26. K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
    [Crossref]
  27. P. Egan and J. A. Stone, “Absolute refractometry of dry gas to 3 parts in 10⁹,” Appl. Opt. 50(19), 3076–3086 (2011).
    [Crossref] [PubMed]
  28. H. Yu, C. Aleksoff, and J. Ni, “Accuracy of a multiple height-transfer interferometric technique for absolute distance metrology,” Appl. Opt. 51(21), 5283–5294 (2012).
    [Crossref] [PubMed]
  29. X. Wu, L. Yang, H. Zhang, H. Yang, H. Wei, and Y. Li, “Hybrid mode-locked Er-fiber oscillator with wide repetition rate stabilization range,” Appl. Opt. 54(7), 1681–1687 (2015).
    [Crossref]

2015 (2)

2014 (2)

2013 (1)

2012 (3)

2011 (4)

2009 (3)

2008 (2)

2006 (1)

2005 (1)

2002 (1)

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

1998 (1)

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

1996 (1)

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)

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

1991 (1)

1988 (1)

K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
[Crossref]

1982 (1)

1966 (1)

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

Aleksoff, C.

Balling, P.

Bhattacharya, N.

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]

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

K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8(4), 647–651 (1991).
[Crossref]

K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
[Crossref]

Bönsch, G.

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

Braat, J. J. M.

Buchta, Z.

Chen, Q.

Ciddor, P. E.

Cui, M.

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]

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

K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
[Crossref]

Edlén, B.

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

Egan, P.

Ferris, D. H.

K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
[Crossref]

Fujima, I.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Hieta, T.

Hirai, A.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Huang, P.

Ina, H.

Iwasaki, S.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Joo, K. N.

Joo, K.-N.

Kim, S. W.

Kim, S.-W.

Kim, Y.

Kobayashi, S.

Kok, G. J.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Kren, P.

Lassila, A.

Li, Y.

Lu, Z. H.

Luo, H.

Masika, P.

Matsumoto, H.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Merimaa, M.

Newbury, N.

N. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

Ni, J.

Persijn, S. T.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Pikálek, T.

Potulski, E.

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

Seppä, J.

Stone, J. A.

Takeda, M.

Urbach, H. P.

Vainio, M.

van den Berg, S. A.

Wang, F.

Wang, L. J.

Wang, S.

Wei, H.

Wu, X.

Yang, H.

Yang, L.

Yu, H.

Zeitouny, M. G.

Zeng, L. J.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Zhang, H.

Zhang, J.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. E Sci. Instrum. (1)

K. P. Birch, M. J. Downs, and D. H. Ferris, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E Sci. Instrum. 21(7), 690–692 (1988).
[Crossref]

Metrologia (4)

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

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

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]

Nat. Photonics (2)

N. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

Opt. Commun. (1)

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203(3-6), 243–247 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

P. Huang, J. Zhang, Y. Li, and H. Wei, “Note: Real-time absolute air refractometer,” Rev. Sci. Instrum. 85(5), 056107 (2014).
[Crossref] [PubMed]

Other (1)

“Evaluation of measurement data—guide to the expression of uncertainty in measurement,” (2008), http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315ehtml/C045315e.html?csnumberCsnumber=50461 .

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Optical setup of the air refractometer. Iso, isolator; M1, M2, mirror; BSP, beam splitter plate; OSA, optical spectrum analyzer. The red line corresponds to the light that propagates in the free space (the dashed line denotes the light going through the inner region of the vacuum cell) and the yellow line corresponds to the light that propagates in the single mode fiber. The photograph of the vacuum cell is also shown.
Fig. 2
Fig. 2 Data processing procedure for measurement of group refractive index of air. (a) Dispersed interference intensity monitored by the OSA. (b) Fourier transform of the spectral interferogram. (c) Wrapped phase of the filtered peak. (d) The unwrapped phase (red line denotes the fitted straight line).
Fig. 3
Fig. 3 Experimental results of the refractive index of ambient air in short term. (a) Comparison of experimental and reference data of ambient air. Dashed circle with arrow indicates the corresponding y axis of the data curve.(b) Pressure and temperature data in experiment. (c) Humidity data in experiment.
Fig. 4
Fig. 4 Long-term measurement of the refractive index of ambient gas at 1563 nm for about 10 h. (a) Experimental and reference data of ambient air. (b) Difference between experimental and reference data. (c) Pressure and temperature data in experiment. (d) Humidity data in experiment.
Fig. 5
Fig. 5 Parallelism error caused by two ends of the vacuum cell. (a) The two ends of the vacuum cell are inclined in the direction parallel to the incident plane. l1, geometrical path of the upper light; l2, geometrical path of the lower light;l, center length of the vacuum cell. (b) The two transmission surfaces of vacuum cell’s one end are not parallel.

Equations (10)

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

g(v)=a(v)+b(v)cosΦ(v),
Φ(v)=2πvα,
α=2(n(v)1)L/c,
g(v)=a(v)+1/2b(v)exp(j2πvα)+1/2b(v)exp(j2πvα),
G(t)=FT{g(v)}=A(t)+B(t)π[δ(t+α)+δ(tα)],
g ' (v)=F T 1 {B(t)πδ(tα)}=πb(v)exp(jΦ(v)).
Φ(v)=arctan( Im{ g ' (v)} Re{ g ' (v)} ).
dΦ(v) dv = 4π(N-1)L c .
(N1)=( c 4πL ) dΦ(v) dv .
u(N1) N1 = [ ( u(Φ(v)) Φ(v) ) 2 + ( u(L) L ) 2 + ( u(v) v ) 2 ] 1/2 ,

Metrics