Numerical study on uncertainty of two-color method

D. Wei; M. Xiao; M. Aketagawa

doi:10.2971/jeos.2015.15051

Journal of the European Optical Society - Rapid publications, Vol 10 (2015)

Numerical study on uncertainty of two-color method

D. Wei, M. Xiao, M. Aketagawa

Abstract

The two-color method is one of the commonly used approaches for converting a length measured in air to a length in vacuum to eliminate the influence of the refractive index of air. However, the error of the technique is not well known. We investigate this uncertainty based on a generalized expression of the two-color method proposed in this paper and using numerical simulations. Numerical calculations reveal the change of the error with temperature, air pressure, and wavelengths. These characteristics can be used to optimize the two-color method.

Full Text: PDF

Citation Details

Cite this article

References

P. L. Bender, and J. C. Owens, ”Correction of Optical Distance Measurements for the Fluctuating Atmospheric Index of Refraction,” J. Geophys. Res. 70, 2461-2462 (1965).

E. Bengt, ”The Refractive Index of Air,” Metrologia 2, 71 (1966).

K. P. Birch, and M. J. Downs, ”An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30, 155 (1993).

P. E. Ciddor, ”Refractive index of air: new equations for the visible and near infrared,” Appl. Optics 35, 1566–1573 (1996).

J. A. Stone, and J. H. Zimmerman, ”Refractive index of air calculator,” http://emtoolbox.nist.gov/Wavelength/Edlen.asp.

B. Querzola, ”High accuracy distance measurement by twowavelength pulsed laser sources,” Appl. Optics 18, 3035–3047 (1979).

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, 1084 (1992).

K. Minoshima, and H. Matsumoto, ”High-Accuracy Measurement of 240-m Distance in an Optical Tunnel by use of a Compact Femtosecond Laser,” Appl. Optics 39, 5512–5517 (2000).

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, 26095–26105 (2011).

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

D. Wei, M. Aketagawa, K. Takamasu, and H. Matsumoto, ”Twocolor absolute length measuring method based on pulse repetition interval lengths,” Opt. Eng. 53, 122413 (2014).

D. Wei, and M. Aketagawa, ”Comparison of two-color methods based on wavelength and adjacent pulse repetition interval length,” J. Eur. Opt. Soc.-Rapid 9, 14031 (2014).

J. Ye, and S. T. Cundiff, Femtosecond optical frequency comb: principle, operation, and applications (Springer, New York, 2005).

D. Wei, and M. Aketagawa, ”Uncertainty in length conversion due to change of sensitivity coefficients of refractive index,” Opt. Commun. 345, 67–70 (2015).

H. W. Coleman, and W. G. Steele, Experimentation and Uncertainty Analysis for Engineers (Wiley, Haboken, 1999).

B. Walter, G. C. Maurice, and M. H. Peter, ”Evolution of the ’Guide to the Expression of Uncertainty in Measurement’,” Metrologia 43, S161 (2006).

A. Ishida, ”Two-Wavelength Displacement-Measuring Interferometer Using Second-Harmonic Light to Eliminate Air-TurbulenceInduced Errors,” Jpn. J. Appl. Phys. 28, L473 (1989).

H. Matsumoto, Y. Zhu, S. Iwasaki, and T. Oishi, ”Measurement of the changes in air refractive index and distance by means of a two-color interferometer,” Appl. Optics 31, 4522–4526 (1992).

A. N. Golubev, and A. M. Chekhovsky, ”Three-color optical range finding,” Appl. Optics 33, 7511–7517 (1994).

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

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